# DUALF-D: Disentangled dual-hyperprior approach for light field image compression

Soheib Takhtardeshir, Roger Olsson, Christine Guillemot, Mårten Sjöström

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Soheib Takhtardeshir, Roger Olsson, Christine Guillemot, Mårten Sjöström. DUALF-D: Disentangled dual-hyperprior approach for light field image compression. Signal Processing: Image Communication, 2026, 140, pp.117436. 10.1016/j.image.2025.117436. hal-05372515

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# DUALF-D: Disentangled dual-hyperprior approach for light field image compression

Soheib Takhtardeshir<sup>a,b</sup>, Roger Olsson<sup>a</sup>, Christine Guillemot<sup>b</sup>, Mårten Sjöström<sup>a,D,*</sup>

## ARTICLE INFO

**Keywords:**

Light field compression

Variational Autoencoder

Disentanglement

Dual hyperprior

Spatial-angular representation

## ABSTRACT

Light field (LF) imaging captures spatial and angular information, offering a 4D scene representation enabling enhanced visual understanding. However, high dimensionality and redundancy across spatial and angular domains present major challenges for compression, particularly where storage, transmission bandwidth, or processing latency are constrained. We present a novel Variational Autoencoder (VAE)-based framework that explicitly disentangles spatial and angular features using two parallel latent branches. Each branch is coupled with an independent hyperprior model, allowing more precise distribution estimation for entropy coding and finer rate-distortion control. This dual-hyperprior structure enables the network to adaptively compress spatial and angular information based on their unique statistical characteristics, improving coding efficiency. To further enhance latent feature specialization and promote disentanglement, we introduce a mutual information-based regularization term that minimizes redundancy between the two branches while preserving feature diversity. Unlike prior methods relying on covariance-based penalties prone to collapse, our information-theoretic regularizer provides more stable and interpretable latent separation. Experimental results on publicly available LF datasets demonstrate our method achieves strong compression performance, yielding an average **BD-PSNR** gain of 2.91 dB over **HEVC** and high compression ratios (e.g., 200:1). Additionally, our design enables fast inference, with a total **end-to-end time** over 19x faster than the JPEG Pleno standard, making it well-suited for real-time and bandwidth-sensitive applications. By jointly leveraging disentangled representation learning, dual-hyperprior modeling, and information-theoretic regularization, our approach offers a scalable, effective solution for practical light field image compression.

## 1. Introduction

Light field (LF) imaging captures both spatial and angular information of a scene, providing a rich 4D representation that enables post-capture operations such as refocusing, depth estimation, and view synthesis [1,2]. This comprehensive representation has made LF imaging a cornerstone technology in applications spanning virtual reality, autonomous systems, and scientific visualization [3,4]. However, the practical deployment of LF systems faces a significant bottleneck due to the massive data volume resulting from densely sampled views, which imposes constraints on storage, transmission, and processing efficiency [5]. As the demand for high-quality and immersive content continues to grow, efficient LF compression becomes increasingly essential to bridge the gap between acquisition capabilities and downstream application constraints.

Despite significant progress in image and video compression, the unique 4D structure of light field data presents challenges that cannot be effectively addressed by traditional codecs. Conventional approaches, such as HEVC-based pseudo-sequence encoding [6] and view-wise compression using advanced codecs like VVC [7], often treat LF images as a stack of 2D frames, failing to fully exploit the inter-view redundancies and the underlying geometric coherence across views [8]. More recent learning-based methods have attempted to leverage the internal correlations in LF data through convolutional neural networks (CNNs) and transformer-based architectures [9,10]. However, these methods either suffer from limited scalability to high-angular-resolution inputs or introduce significant computational complexity that hinders real-time deployment. While some recent approaches prioritize simplicity, such as the hybrid 2D-convolution-based method proposed in [11], they fall short in addressing angular modeling and

<footnote><sup>a</sup> Mid Sweden University, Department of Computer and Electrical Engineering, Sundsvall, Sweden</footnote>

<footnote><sup>b</sup> INRIA, Rennes, France</footnote>

<footnote>* Corresponding author.
E-mail address: marten.sjostrom@miun.se (M. Sjöström).</footnote>
real-time execution challenges that our method explicitly tackles. Moreover, many of these architectures rely on shared latent representations for spatial and angular information, which can result in entangled features that limit compression efficiency and interpretability [12]. This entanglement not only impairs the rate-distortion performance but also reduces the flexibility of the model to adaptively allocate bits depending on domain-specific importance, such as preserving angular consistency for view synthesis versus spatial detail for visualization. Therefore, a core challenge in LF compression remains the development of models that can explicitly decouple spatial and angular information to improve coding performance while retaining practical applicability in constrained environments.

In this paper, we address the limitations of existing light field compression methods—including standardized codecs [13], pseudo-video strategies [14–16], and neural representation approaches [17, 18]—which either overlook angular redundancy or suffer from high complexity and limited generalization. To this end, we propose a novel Variational Autoencoder (VAE)-based framework that explicitly disentangles spatial and angular features using two independent latent branches. In contrast to prior methods that either conflate both domains or fail to exploit their structural separation effectively [14,19], our architecture dedicates a tailored encoder and hyperprior model to each domain. This dual-hyperprior design enables the network to learn domain-specific statistical priors, which improves entropy modeling and facilitates finer rate-distortion control. Furthermore, to enhance the functional specialization of each latent branch and prevent feature overlap, we incorporate a mutual information regularization term that minimizes redundancy between the spatial and angular latent representations. This term is instantiated using a symmetric formulation of the InfoNCE loss [20,21], adapted to our compression setting. It encourages the latent branches to remain semantically distinct while still preserving complementary information necessary for accurate reconstruction. Together, the dual-hyperprior structure and information-theoretic regularization foster a robust and interpretable disentangled representation, significantly boosting both compression efficiency and downstream usability of the latent features.

We validate the effectiveness of our proposed framework through comprehensive experiments conducted on the real-world EPFL light field dataset [22], which provides diverse scenes with complex geometry, occlusions, and illumination conditions. This dataset serves as a challenging benchmark beyond synthetic environments. Our model is evaluated against state-of-the-art methods, including VAE-based baselines [23], pseudo-video encoders [14], and hybrid transformation frameworks [19]. Results show that our dual-hyperprior model consistently outperforms in rate-distortion tradeoff, particularly at low bitrates where accurate entropy modeling is critical. Additionally, the compact, feed-forward decoding ensures fast processing, which is essential for immersive and bandwidth-sensitive applications. The explicit separation of spatial and angular latents also enhances downstream utility, enabling tasks like super-resolution, depth-aware rendering, and content editing to benefit from a more interpretable latent space.

In summary, the main contributions of this work are as follows:

* We propose a VAE-based compression framework for light field images that disentangles spatial and angular information via two specialized latent branches.

* We introduce a dual-hyperprior structure, with each hyperprior tailored to the statistical characteristics of its latent space, improving bitrate estimation and overall rate-distortion performance.

* We incorporate a contrastive regularization term based on the InfoNCE loss [20] to enforce mutual decorrelation between spatial and angular latents, providing a more stable and interpretable alternative to covariance penalization.

* We conduct experiments on standard LF datasets, showing that our method outperforms existing approaches in compression efficiency and inference speed, while also enabling interpretable latents.

Together, these contributions present a practical and high-performing solution for light field image compression, laying the groundwork for future developments in immersive imaging and visual communication.

## 2. Related work

Recent efforts in light field image compression have introduced a range of strategies, including adaptations of traditional video codecs and end-to-end learned models. However, many of these approaches still overlook the structured redundancies unique to LF data. Our work builds upon three closely related domains: LF-specific compression techniques, VAE-based learned probability models for bitrate estimation, and disentangled representation learning. By synthesizing insights from these areas, we aim to address their respective limitations through a unified framework that explicitly models spatial-angular separation while maintaining compression efficiency and practical scalability. In the following, we review the most relevant contributions that shaped the foundation of our approach.

### 2.1. Learned light field image compression

Learned light field (LF) image compression has emerged as a promising alternative to traditional codecs, offering improved adaptability to the unique 4D structure of LF data. While classical techniques such as JPEG Pleno [5] extend conventional standards to preserve spatial-angular correlations, they often fail to exploit deeper redundancies. To address this, pseudo-video-based approaches [24] treat sequences of sub-aperture images as video frames and apply standard codecs like HEVC and VVC [14,25]. These strategies yield rate-distortion benefits but are constrained by fixed coding structures that limit flexibility across diverse LF scenes.

Another line of research focuses on end-to-end trainable neural networks that learn compact LF representations. Early works such as [26] introduced CNN-based autoencoders that directly optimize reconstruction loss, while more recent approaches integrate attention mechanisms [9], disparity-guided fusion [27], or view selection strategies [28] to refine spatial-angular dependencies. Despite these innovations, most learned frameworks process sub-aperture views collectively or sequentially, often lacking explicit modeling of the 4D LF parameter space.

More recently, the field has seen the rise of transformer-based architectures and implicit neural representations (INRs) for LF processing [18,29]. Transformers, for instance, excel at capturing long-range dependencies across both spatial and angular dimensions, sometimes leading to higher reconstruction quality. Similarly, INRs that map 4D coordinates to pixel values can achieve very high compression for a single scene. However, these advanced methods often come with a significant increase in computational complexity, particularly during encoding, which limits their suitability for real-time applications. Our work, in contrast, prioritizes a balanced approach, aiming for a highly competitive rate-distortion performance while maintaining the practical, fast inference speeds required for immersive streaming and communication systems.

While many learned methods have achieved noticeable improvements, they often rely on generic assumptions, treating the LF as a stack of correlated images rather than exploiting its structured redundancy [30]. This limitation leaves room for principled designs that can explicitly distinguish between angular and spatial domains, allowing for better compression and interpretability. In this context, our proposed method introduces a dual-latent structure specifically crafted to handle LF-specific redundancy, bridging this critical gap in the current literature.
<figure><img src="image_3.png" /><figcaption>Fig. 1. Overview of the proposed compression architecture. The macropixel input is processed by two parallel encoder branches: a spatial encoder (top) and an angular encoder (bottom), each extracting a disentangled latent representation tailored to its modality. These latent features are fed into their respective hyperprior networks (right and left sides), which estimate the scale parameters (standard deviations) for each latent group. These predicted scale maps are used in the entropy coding stage to model the uncertainty of the quantized latents. The spatial and angular latents are concatenated and passed through a shared decoder to reconstruct the macropixel.</figcaption></figure>

## 2.2. Variational autoencoders for image compression

Variational Autoencoders (VAEs) have emerged as a powerful generative framework for learned image compression due to their ability to model complex data distributions through latent variables. Introduced by Kingma and Welling [31], the VAE framework optimizes a variational lower bound that balances reconstruction fidelity and latent compactness, making it particularly suitable for lossy compression. In the context of image coding, Ballé et al. [23,32] adapted the VAE paradigm by replacing the standard Gaussian prior with a more expressive, learned hyperprior, which effectively models spatially adaptive entropy distributions. This innovation led to substantial improvements in rate-distortion (RD) performance over earlier CNN-based compression models.

The core architecture of VAE-based image compression typically consists of an encoder that maps the input image into a latent space, a quantization module (often approximated during training via additive noise or relaxed rounding), and a decoder that reconstructs the image from quantized features. Crucially, the quantized latents are accompanied by a side-information stream — modeled using a hyperprior or entropy bottleneck — that predicts the likelihoods required for entropy coding. In [33], the authors proposed a joint autoregressive and hyperprior-based entropy model, achieving state-of-the-art compression performance by capturing both local and global spatial dependencies. Further refinements have explored Gaussian scale mixtures [34], residual entropy models [35], and multi-scale representations [36] to enhance compressibility.

While VAE-based methods have shown strong performance in conventional 2D image compression, adapting them to 4D light field data poses unique challenges. The entanglement between spatial and angular dimensions introduces complex redundancy patterns that single-branch VAE models cannot efficiently capture. Moreover, using a shared hyperprior for all latents reduces the model's flexibility to accommodate the distinct statistical behaviors of spatial versus angular content. Building on the foundations laid by Ballé et al. [23], our approach introduces two disentangled latent branches, each paired with a dedicated hyperprior network. This dual-hyperprior structure directly addresses the limitations of single-hyperprior VAEs by allowing each branch to learn a specialized entropy model. This explicit separation enables more effective exploitation of both spatial and angular redundancies, improving compressibility and providing a targeted solution for the demands of LF image compression.

## 2.3. Disentangled representation learning

Disentangled representation learning aims to separate underlying explanatory factors of variation within data into distinct, interpretable components—a property especially valuable in compression, where efficient encoding relies on isolating independent sources of redundancy. In the context of LF imaging, this generally refers to distinguishing between information that is localized within individual views—such as textures and object boundaries—and information that varies across views due to perspective shifts, occlusions, or parallax. These spatial and angular characteristics often exhibit different statistical structures, making their disentanglement potentially beneficial for compression. Early efforts in disentanglement used structured bottlenecks or domain-specific priors [37,38], but such methods often lack robustness in data-rich, high-dimensional settings like LF.

To enforce disentanglement in neural networks, several regularization techniques have been introduced. Covariance penalties, such as total correlation [39], encourage independence across latent dimensions by minimizing feature co-activation. During the initial development of our method, we extended such techniques to enforce independence between entire latent groups — e.g., spatial and angular branches — but found them prone to collapse, leading to the loss of meaningful representation in one or both domains. This issue is particularly problematic in VAE frameworks, where strong regularization can dominate the reconstruction objective and suppress signal-bearing components.

To overcome the limitations of covariance-based regularization, mutual information minimization has emerged as a more robust strategy. While directly estimating mutual information between high-dimensional latent groups is intractable, it can be approximated through contrastive estimation techniques such as the InfoNCE loss [20]. This objective encourages the network to reduce redundancy between spatial and angular latents by contrasting positive pairs (from the same sample) against negative pairs (from different samples), without forcing strict orthogonality. Unlike covariance-based constraints, this formulation naturally preserves feature diversity and prevents collapse, making it better suited for dense, high-capacity models.

In our framework, we incorporate a symmetric InfoNCE-based regularization term to promote explicit separation between spatial and angular latents. By leveraging a mutual information objective implemented via contrastive estimation, our network avoids collapsing behaviors while ensuring each latent branch specializes in encoding its respective domain. This strategy not only improves compression but also enhances the interpretability and adaptability of the learned latent space for downstream LF tasks.
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Illustration of macropixel construction from a 3 × 3 block of sub-aperture views (left). Each image represents a distinct angular view from a cropped light field. Colored pixel labels (e.g., A1–A4) denote the same 2 × 2 spatial patch location across views, where A1 corresponds to pixel (0,0) of view (0,0), A2 to (0,1), A3 to (1,0), and A4 to (1,1). Similarly, B1–B4 refer to the corresponding 2 × 2 patch in view (0,1), C1–C4 for view (0,2), and so on. These corresponding pixels are rearranged to form a new macropixel image (right), where each 3 × 3 block contains angular variations of a single spatial location.</figcaption></figure>

## 2.4. Summary

Many light field compression methods have shown notable progress, especially through neural architectures and pseudo-video formulations. However, these often treat spatial and angular information jointly, resulting in redundant latents and reduced efficiency for both compression and downstream tasks. Although VAE-based models with hyperpriors improve rate-distortion performance, their use of a shared bottleneck limits adaptability across domains. Our early covariance-based attempts to enforce disentanglement revealed stability issues and collapse. To address this, we adopt a dual-latent structure with separate hyperpriors and a symmetric InfoNCE regularizer, providing stable, disentangled representations that improve compression and support more interpretable latent spaces.

## 3. Proposed method

To address the unique challenges of compressing light field (LF) images – particularly the structured redundancies between spatial and angular views – we propose a novel VAE-based framework that explicitly separates and models these two domains. Our method is guided by three main principles: (i) representing spatial and angular information via disentangled latent branches to better exploit domain-specific redundancies (see Section 3.2), (ii) leveraging dual hyperprior networks to independently model the uncertainty of each latent group for more accurate entropy coding, and (iii) introducing a contrastive regularization term to minimize redundancy between latent spaces without sacrificing semantic expressiveness. The following subsections present a detailed breakdown of these components and their interactions within our end-to-end trainable compression architecture.

### 3.1. Overview of the architecture

Our proposed light field (LF) image compression framework is built upon a Variational Autoencoder (VAE) backbone, designed to exploit the structured redundancy of LF data through disentangled latent spaces and enhanced entropy modeling. The overall architecture comprises an encoder, a decoder, two latent branches (for spatial and angular components), and two corresponding hyperprior networks. This design enables specialized compression pathways for different feature modalities while maintaining a unified reconstruction target. See Fig. 1.

**Algorithm 1 DUALF-D Compression Process.**

**Require:** Light field input as 3 × 3 block of sub-aperture views (SAVs)

1: Construct macropixel image x by rearranging corresponding pixels across views

2: Spatial encoder $E_s: y_s \leftarrow E_s(x)$

3: Angular encoder $E_a: y_a \leftarrow E_a(x)$

4: Hyper-encoder $H_{enc}^s: z_s \leftarrow H_{enc}^s(y_s)$

5: Hyper-encoder $H_{enc}^a: z_a \leftarrow H_{enc}^a(y_a)$

6: Hyper-decoder $H_{dec}^s: \hat{\sigma}_s \leftarrow H_{dec}^s(z_s)$

7: Hyper-decoder $H_{dec}^a: \hat{\sigma}_a \leftarrow H_{dec}^a(z_a)$

8: Quantize latents: $\hat{y}_s \leftarrow \text{round}(y_s), \hat{y}_a \leftarrow \text{round}(y_a)$

9: Entropy coding: encode $\hat{z}_s, \hat{z}_a, \hat{y}_s, \hat{y}_a$ using arithmetic coder with scales $\hat{\sigma}_s, \hat{\sigma}_a$

10: Bitstream $B \leftarrow \{\hat{z}_s, \hat{z}_a, \hat{y}_s, \hat{y}_a\}$

11: At decoder: decode $\hat{z}_s, \hat{z}_a$ to recover $\hat{\sigma}_s, \hat{\sigma}_a$

12: Decode $\hat{y}_s, \hat{y}_a$ using $\hat{\sigma}_s, \hat{\sigma}_a$

13: Concatenate latents: $\hat{y} \leftarrow \text{concat}(\hat{y}_s, \hat{y}_a)$

14: Reconstruct macropixel: $\hat{x} \leftarrow G(\hat{y})$

15: Output: Reconstructed LF patch $\hat{x}$ and compressed bitstream $B$

**Macropixel construction.** Following the macropixel strategy introduced in our earlier work [40], we generate a macropixel image by spatially reorganizing pixel-aligned information from a 3 × 3 angular patch of sub-aperture views (SAVs). Specifically, for each spatial pixel location $(i, j)$ across a 3 × 3 set of adjacent views, we collect the corresponding pixels from all 9 views and arrange them into a 3 × 3 patch. This local 3 × 3 pixel group, formed from angular neighbors at the same spatial location, becomes a macropixel. When repeated across the entire spatial dimensions of the LF views, this yields a macropixel image whose spatial resolution equals that of the original sub-aperture views, but where each pixel now contains a 3 × 3 angular patch embedded in a structured 2D layout. This macropixel image serves as the input to our network, preserving localized angular variations while avoiding the need for disparity estimation or angular stacking across channels (see Fig. 2).

To better specialize the encoding process, the first convolutional layers of the spatial and angular encoders are explicitly designed with different kernel dilation patterns. This architectural choice helps each
<table><caption>**Table 1**
Detailed Layer Architecture of the Dual-Hyperprior VAE Network. For clarity: E = Encoder, D = Decoder, S = Spatial, A = Angular, and H = Hyperprior.</caption><thead><tr><th colspan="5">Encoder</th></tr><tr><th>Module</th><th>Input size</th><th>Output size</th><th>Kernel/Stride/Padding</th><th>Activation/Notes</th></tr></thead><tbody><tr><td colspan="5">Spatial Encoder</td></tr><tr><td>CNN<sup>1</sup><sub>SE</sub></td><td>3 × H × W</td><td>128 × H' × W'</td><td>5 × 5/1/1 (dilation=3)</td><td>GDN</td></tr><tr><td>CNN<sup>2</sup><sub>SE</sub></td><td>128 × H' × W'</td><td>128 × H'' × W''</td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>CNN<sup>3</sup><sub>SE</sub></td><td>128 × H'' × W''</td><td>128 × H''' × W'''</td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>CNN<sup>4</sup><sub>SE</sub></td><td>128 × H''' × W'''</td><td>128 × H''' × W'''</td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>CNN<sup>5</sup><sub>SE</sub></td><td>128 × H''' × W'''</td><td>64 × H<sub>f</sub> × W<sub>f</sub></td><td>5 × 5/3/1</td><td>GDN</td></tr><tr><td colspan="5">Angular Encoder</td></tr><tr><td>CNN<sup>1</sup><sub>AE</sub></td><td>3 × H × W</td><td>128 × H' × W'</td><td>3 × 3/3/1</td><td>GDN</td></tr><tr><td>CNN<sup>2</sup><sub>AE</sub></td><td>128 × H' × W'</td><td>128 × H'' × W''</td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>CNN<sup>3</sup><sub>AE</sub></td><td>128 × H'' × W''</td><td>128 × H''' × W'''</td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>CNN<sup>4</sup><sub>AE</sub></td><td>128 × H''' × W'''</td><td>64 × H<sub>f</sub> × W<sub>f</sub></td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td colspan="5">Hyperprior Encoder (Shared)</td></tr><tr><td>CNN<sup>1</sup><sub>HSE</sub> (CNN<sup>1</sup><sub>HAE</sub>)</td><td>64 × H<sub>f</sub> × W<sub>f</sub></td><td>64 × H<sub>z</sub> × W<sub>z</sub></td><td>3 × 3/1/1</td><td>LeakyReLU</td></tr><tr><td>CNN<sup>2</sup><sub>HSE</sub> (CNN<sup>2</sup><sub>HAE</sub>)</td><td>64 × H<sub>z</sub> × W<sub>z</sub></td><td>64 × H<sub>z</sub>/2 × W<sub>z</sub>/2</td><td>3 × 3/2/1</td><td>LeakyReLU</td></tr><tr><td>CNN<sup>3</sup><sub>HSE</sub> (CNN<sup>3</sup><sub>HAE</sub>)</td><td>64 × H<sub>z</sub>/2 × W<sub>z</sub>/2</td><td>64 × H<sub>z</sub>/4 × W<sub>z</sub>/4</td><td>3 × 3/2/1</td><td>–</td></tr><tr><td colspan="5">Hyperprior Decoder (Shared)</td></tr><tr><td>CNN<sup>1</sup><sub>HSD</sub> (CNN<sup>1</sup><sub>HAD</sub>)</td><td>64 × H<sub>f</sub>/4 × W<sub>z</sub>/4</td><td>64 × H<sub>z</sub>/4 × W<sub>z</sub>/4</td><td>3 × 3/1/1</td><td>LeakyReLU</td></tr><tr><td>CNN<sup>2</sup><sub>HSD</sub> (CNN<sup>2</sup><sub>HAD</sub>)</td><td>64 × H<sub>z</sub>/4 × W<sub>z</sub>/4</td><td>64 × H<sub>z</sub>/2 × W<sub>z</sub>/2</td><td>(SubpelConv2d) scale factor = 2</td><td>LeakyReLU</td></tr><tr><td>CNN<sup>3</sup><sub>HSD</sub> (CNN<sup>3</sup><sub>HAD</sub>)</td><td>64 × H<sub>z</sub>/2 × W<sub>z</sub>/2</td><td>64 × H<sub>z</sub> × W<sub>z</sub></td><td>(SubpelConv2d) scale factor = 2</td><td>LeakyReLU</td></tr><tr><td>CNN<sup>4</sup><sub>HSD</sub> (CNN<sup>4</sup><sub>HAD</sub>)</td><td>64 × H<sub>z</sub> × W<sub>z</sub></td><td>64 × H<sub>f</sub> × W<sub>f</sub></td><td>3 × 3/1/1</td><td>exp() for scale modeling</td></tr><tr><td colspan="5">Concatenation Layer</td></tr><tr><td>Concat</td><td>64 × H<sub>f</sub> × W<sub>f</sub> + 64 × H<sub>f</sub> × W<sub>f</sub></td><td>128 × H<sub>f</sub> × W<sub>f</sub></td><td>–</td><td>–</td></tr></tbody></table><table><thead><tr><th colspan="5">Decoder</th></tr><tr><th>Module</th><th>Input size</th><th>Output size</th><th>Kernel/Stride/Padding</th><th>Activation/Notes</th></tr></thead><tbody><tr><td>CNN<sup>1</sup><sub>D</sub></td><td>128 × H<sub>f</sub> × W<sub>f</sub></td><td>128 × H' × W'</td><td>5 × 5/3/0</td><td>Inverse GDN</td></tr><tr><td>CNN<sup>2</sup><sub>D</sub></td><td>128 × H' × W'</td><td>128 × H'' × W''</td><td>4 × 4/2/0</td><td>Inverse GDN</td></tr><tr><td>CNN<sup>3</sup><sub>D</sub></td><td>128 × H'' × W''</td><td>128 × H''' × W'''</td><td>4 × 4/2/1</td><td>Inverse GDN</td></tr><tr><td>CNN<sup>4</sup><sub>D</sub></td><td>128 × H''' × W'''</td><td>3 × H × W</td><td>4 × 4/2/1</td><td>Sigmoid</td></tr></tbody></table>

encoder branch focus on its respective domain – capturing fine-grained spatial textures or angular correlations – right from the initial stage of feature extraction [40].

Given a macropixel input $x \in \mathbb{R}^{C \times H \times W}$, where C, H, and W represent the number of channels, height, and width respectively, the encoder network first transforms the input into two separate latent feature maps: spatial latent $y_s$ and angular latent $y_a$. These are extracted via two independent convolutional branches:

$$y_s = f_{\text{enc}_s}(\mathbf{x}), \quad y_a = f_{\text{enc}_a}(\mathbf{x}), \qquad (1)$$

where $f_{\text{enc}_s}$ and $f_{\text{enc}_a}$ are spatial and angular encoders, respectively.

To compress the latent codes, each branch is coupled with its own hyperprior model that captures the statistical uncertainty of the latents. The hyperprior encoder $h_{\text{enc}}$ produces a latent prior $z$ from the input $y$, which is then decoded by $h_{\text{dec}}$ to yield scale parameters $\hat{\sigma}$ for entropy modeling:

$$\mathbf{z}_s = h_{\text{enc}}^s(\mathbf{y}_s), \quad \hat{\sigma}_s = h_{\text{dec}}^s(\mathbf{z}_s), \qquad (2)$$

$$\mathbf{z}_a = h_{\text{enc}}^a(\mathbf{y}_a), \quad \hat{\sigma}_a = h_{\text{dec}}^a(\mathbf{z}_a). \qquad (3)$$

Quantized versions of $y_s$ and $y_a$, denoted as $\hat{y}_s$ and $\hat{y}_a$ are concatenated and passed to the decoder:

$$\hat{y} = \text{concat}(\hat{y}_s, \hat{y}_a), \quad \hat{\mathbf{x}} = f_{\text{dec}}(\hat{y}), \qquad (4)$$

where $f_{\text{dec}}$ denotes the shared decoder reconstructing the macropixel output $\hat{\mathbf{x}}$.

Each latent code is entropy-coded using a learned entropy model, where the scale parameters predicted by the hyperpriors are used to estimate the probability distribution of the quantized values. This enables adaptive bit allocation based on local uncertainty in each latent

channel, which is essential for achieving efficient compression. The overall bitrate is computed as the sum of negative log-likelihoods:

$$R = - \sum \log_2 p_{\hat{y}_s|\hat{\sigma}_s}(\hat{y}_s) - \sum \log_2 p_{\hat{y}_a|\hat{\sigma}_a}(\hat{y}_a). \qquad (5)$$

The proposed architecture comprises two parallel sub-encoders dedicated to spatial and angular feature extraction, followed by corresponding hyperprior networks that estimate the distribution of each latent group. These components are carefully configured to balance expressiveness with computational efficiency. A shared decoder reconstructs the final image from the concatenated quantized latents. To provide implementation clarity and facilitate reproducibility, a detailed specification of all encoder, decoder, and hyperprior layers – including kernel sizes, strides, activation functions, and intermediate feature map resolutions – is presented in Table 1. These choices are guided by empirical observations from previous VAE-based compression models [23], tailored to preserve spatial-angular fidelity while ensuring fast inference and compact representations.

## 3.2. Disentangled latent representation

In traditional VAE-based image compression, a single latent space is typically used to encode all types of content information. However, light field (LF) images inherently exhibit structured redundancies across spatial and angular domains. Treating these modalities uniformly limits the potential for optimized representation and compression. To address this, we introduce an explicit disentanglement strategy that separates spatial and angular features into independent latent representations.

Given a macropixel $x$ composed of aligned sub-aperture views, the encoder is split into two branches: one specializing in spatial structure and the other in angular correlations. Instead of enforcing hard separation via view-based masking or hand-crafted filters, we adopt soft
disentanglement by learning separate encoders $f_{enc_s}$ and $f_{enc_a}$ with tailored convolutional kernels and initial view-selection strategies. These two encoders extract spatial latent $y_s$ and angular latent $y_a$ respectively, as introduced in Eq. (1). Each latent tensor has shape $\mathbb{R}^{C \times H' \times W'}$, where C is the number of latent channels (typically larger than the input's RGB channels), and $H'$ and $W'$ denote the downsampled spatial dimensions resulting from the encoder's stride and receptive field.

The design of the encoder architecture ensures that $y_s$ primarily captures fine spatial textures and low-frequency structure, while $y_a$ encodes view-specific disparities and angular parallax. These two latents are processed independently through dual hyperprior networks to generate separate entropy models (as described in Section 3.1).

To further encourage representational specialization, we introduce a regularization loss that minimizes statistical redundancy between $y_s$ and $y_a$ while preserving their informativeness. This term is described in detail in Section 3.4. The resulting latents exhibit lower mutual redundancy and allow for task-specific optimization such as reconstruction, super-resolution, or view synthesis.

By explicitly modeling angular and spatial information in disjoint latent spaces, and applying a regularization loss to reduce redundancy, the network is encouraged to learn representations that are semantically aligned across spatial and angular domains and exhibit low statistical redundancy. These compressible representations refer to latent features with reduced entropy and minimized overlap between branches, making them more efficient for entropy coding. This not only facilitates better compression by avoiding redundant encoding, but also improves the interpretability and adaptability of the learned latents for downstream light field tasks such as super-resolution, disparity estimation, and novel view synthesis.

### 3.3. Dual-hyperprior likelihood estimation

Variational image compression relies heavily on accurate accurately estimating the probability distribution of latent representations to achieve compact coding. Traditional methods such as Ballé et al. [23] model the distribution of the latents using a learned prior, typically a Gaussian distribution conditioned on side information from a hyperprior network. In our framework, due to the explicit disentanglement of spatial and angular representations, a single shared hyperprior would be suboptimal, as it fails to capture the distinct statistical behavior of each domain.

We introduce a dual-hyperprior architecture where each latent branch is associated with its own hyperprior network. Specifically, the spatial latent $y_s$ is passed through a hyper encoder $h_{enc_s}$ to generate a side-information feature $z_s$, which is then decoded via a hyper decoder $h_{dec_s}$ to produce scale parameters $\hat{\sigma}_s$. These parameters are used to condition the probability distribution of each element in $y_s$. The same structure is mirrored for the angular latent $y_a$, as previously defined in Eq. (2)–(3). Each latent is modeled as a zero-mean Gaussian with its own scale parameters, following the standard formulation in variational image compression [23]. This assumption simplifies the entropy estimation process while remaining sufficiently expressive when conditioned on learned scale parameters.

$$p(y_s | \hat{\sigma}_s) = \prod_i \mathcal{N}(y_{s,i} | 0, \hat{\sigma}_{s,i}^2), \qquad (6)$$

$$p(y_a | \hat{\sigma}_a) = \prod_i \mathcal{N}(y_{a,i} | 0, \hat{\sigma}_{a,i}^2), \qquad (7)$$

where i indexes over the latent dimensions.

The total rate loss is computed by aggregating the negative log-likelihoods of all encoded latent elements:

$$\mathcal{R} = - \log_2 p(y_s | \hat{\sigma}_s) - \log_2 p(y_a | \hat{\sigma}_a) - \log_2 p(z_s) - \log_2 p(z_a). \qquad (8)$$

Here, $p(z_s)$ and $p(z_a)$ are modeled using fully factorized non-parametric density estimators as proposed in [23], where each latent dimension

is represented by the derivative of a learned piecewise linear cumulative density function, enabling flexible and data-driven distribution modeling.

By decoupling the entropy modeling into two dedicated hyperprior paths, the network is able to better adapt to the statistical properties of spatial and angular latents. This separation allows for more accurate bit allocation and more efficient compression, especially under rate constraints. The dual-hyperprior design plays a critical role in enhancing both coding efficiency and the disentanglement quality of the latent space, as demonstrated in the ablation study in Section 6.

### 3.4. Mutual information-based regularization for disentanglement

A critical challenge in learning disentangled representations is ensuring that the spatial and angular branches capture complementary – rather than redundant – information. Earlier approaches [37,39,41,42] often rely on covariance penalties or mutual information minimization to reduce redundancy between latent variables. However, such methods can suffer from degeneracy, leading to collapsed features or underutilized latents, particularly when the regularization dominates the primary learning objective [42,43].

To mitigate the collapse and redundancy issues associated with strong regularization, we introduce a mutual information-based regularization strategy grounded in the InfoNCE loss [20], which offers a stable and interpretable framework for controlling latent redundancy. Specifically, we treat the spatial latent $y_s$ and angular latent $y_a$ of the same sample as a positive pair, while latents from different samples form negative pairs.

To compute these relations, $y_s$ and $y_a$ (each of shape $\mathbb{R}^{C \times H' \times W'}$) are globally averaged across spatial dimensions, resulting in vector representations in $\mathbb{R}^C$. These are then projected into a shared embedding space via learnable linear mappings $W_s, W_a \in \mathbb{R}^{D \times C}$:

$$\mathbf{q}_s = W_s \cdot \text{GAP}(y_s), \quad \mathbf{k}_a = W_a \cdot \text{GAP}(y_a), \qquad (9)$$

where GAP(·) denotes global average pooling. This projection transforms high-dimensional latent maps into compact embedding vectors suitable for contrastive similarity computation, as originally proposed in [20].

The resulting embeddings are normalized and used to construct a similarity matrix:

$$S_{ij} = \frac{\mathbf{q}_{s_i}^{\top} \mathbf{k}_{a_j}}{\tau \|\mathbf{q}_{s_i}\| \cdot \|\mathbf{k}_{a_j}\|}, \qquad (10)$$

with $\tau$ representing a temperature parameter that controls the sharpness of the similarity distribution.

We define a symmetric InfoNCE objective as follows:

$$\mathcal{L}_{\text{MI}} = \frac{1}{2N} \sum_{i=1}^{N} \left[ -\log \frac{\exp(S_{ii})}{\sum_{j=1}^{N} \exp(S_{ij})} - \log \frac{\exp(S_{ii})}{\sum_{j=1}^{N} \exp(S_{ji})} \right], \qquad (11)$$

where N is the batch size. This objective effectively discourages statistical dependency between latent branches across samples, while preserving meaningful correlations within each pair.

Unlike explicit decorrelation or orthogonality-based constraints, the extended InfoNCE loss avoids forcing separation too aggressively, which can lead to collapsed or underutilized features. It instead promotes a soft and data-driven reduction in mutual redundancy, thereby encouraging each branch to specialize in encoding its respective domain. Through this regularization, the learned latent representations maintain diversity and semantic clarity, which ultimately benefits compression efficiency by reducing redundancy and enabling more accurate entropy estimation, as well as improving interoperability.
### 3.5. Loss function

Our overall training objective is designed to balance reconstruction fidelity, bitrate efficiency, and representational disentanglement between spatial and angular features. We adopt a rate-distortion-regularization formulation:

$$ \mathcal{L}_{\text{total}} = \mathcal{L}_{\text{rec}} + \lambda \cdot \mathcal{R}_{\text{bpp}} + \beta \cdot \mathcal{L}_{\text{MI}}, \quad (12) $$

where $\mathcal{L}_{\text{rec}}$ is the mean squared reconstruction error between the input and reconstructed LF views, $\mathcal{R}_{\text{bpp}}$ denotes the bitrate (in bits per pixel) computed from the entropy models, and $\mathcal{L}_{\text{MI}}$ is a mutual information-based regularization term derived in Section 3.4.

The reconstruction loss is defined as:

$$ \mathcal{L}_{\text{rec}} = \frac{1}{N} \sum_{i=1}^{N} \|x_i - \hat{x}_i\|_2^2, \quad (13) $$

where $x_i$ and $\hat{x}_i$ are the original and reconstructed samples, and $N$ is the batch size.

The bitrate term $\mathcal{R}_{\text{bpp}}$ is estimated using the negative log-likelihood of the quantized latents under their respective hyperprior models:

$$ \mathcal{R}_{\text{bpp}} = -\frac{1}{HWN} \sum_{j} \log_{2} p(\hat{y}_{j} | \hat{z}_{j}), \quad (14) $$

where $\hat{y}_j$ represents the quantized spatial or angular latent, and $\hat{z}_j$ the corresponding side information.

The mutual information regularizer $\mathcal{L}_{\text{MI}}$ is derived from the symmetric InfoNCE formulation given in Eq. (11), and is designed to minimize statistical redundancy between the spatial and angular latents of the same sample. Specifically, we project $y_s$ and $y_a$ into a shared embedding space using learnable mappings (see Section 3.4), and compute pairwise similarity scores across the batch to construct the similarity matrix $S$. The loss promotes alignment between spatial and angular embeddings of the same sample (diagonal entries in $S$), while contrasting them against embeddings from other samples in the batch (off-diagonal entries).

Unlike our initial solution based on covariance penalties—used in our early experiments to enforce latent independence by minimizing cross-branch correlations but often leading to unstable training and feature collapse—the symmetric InfoNCE loss in Eq. (11) offers a more robust alternative. Rather than enforcing hard decorrelation or orthogonality, the symmetric InfoNCE loss in Eq. (11) promotes mutual exclusivity in representation by contrasting spatial and angular embeddings across samples in a bidirectional manner. This balanced formulation ensures that both branches retain expressive power without suppressing one another. As a result, the learned latent spaces remain semantically disentangled and structurally rich, yielding stronger rate-distortion performance and interoperability.

## 4. Experimental setup

### 4.1. Datasets and preprocessing

To evaluate the effectiveness of our proposed compression framework, we use two publicly available light field (LF) datasets. For training, we employ the Lytro-based dataset introduced in [44], which contains 7549 light field samples captured using a Lytro Illum plenoptic camera. Each light field consists of 15 × 15 sub-aperture views with a spatial resolution of 625 × 434 pixels per view. We use 90% of the data for training and reserve 10% for validation.

To avoid the vignetting and optical distortions that commonly affect corner views in plenoptic images, we crop each LF image to retain only the central 13 × 13 angular views during both training and evaluation. From these cropped views, we extract macropixels of size 3 × 3 in the angular dimension. Each sub-aperture view is resized from its original resolution of 625 × 434 to 624 × 432 to ensure compatibility with the network's convolutional architecture, where

spatial dimensions must be divisible by common downsampling factors. This resizing enables efficient processing and avoids the need for additional padding or cropping during training. The resulting macropixel retains a spatial size of 1872 × 1296 and is further partitioned into non-overlapping patches of size 312 × 216 for GPU-friendly training. The procedure for macropixel extraction, including its geometric ratio-nale and visualization examples, follows the approach introduced in EF-VAE [40].

For testing and benchmarking, we use the EPFL light field dataset [22], which also provides 15 × 15 angular views at the same spatial resolution. To ensure consistency with the training configuration, we crop the central 13 × 13 sub-aperture views from each sample. The EPFL dataset includes diverse indoor and outdoor scenes, offering significant variation in geometry, texture, and lighting. No overlap exists between the training and testing sets, ensuring fair evaluation of the proposed method.

### 4.2. Training configuration

We implement our model using the PyTorch framework and train it on the Alvis high-performance computing cluster of NAISS in Sweden, equipped with NVIDIA Tesla V100 GPUs (32 GB memory). The training is conducted using the Adam optimizer with its default momentum parameters $\beta_1 = 0.9$ and $\beta_2 = 0.999$, which are widely adopted in the literature for stable convergence in variational models [20,23]. The initial learning rate for the main network is set to $1 \times 10^{-4}$, following common practice in learned image compression frameworks [33], while a higher learning rate of $1 \times 10^{-2}$ is used for auxiliary parameters such as those in the entropy bottlenecks, as recommended in CompressAI [45]. A learning rate scheduler based on the ReduceLROnPlateau strategy is employed, which halves the learning rate when the validation loss plateaus for five consecutive epochs.

The network is trained with a batch size of 8 over 200 epochs. To explore different rate-distortion trade-offs, we sweep the Lagrangian multiplier $\lambda$ over a range of values from $10^{-4}$ to $10^{-2}$, following established practices in learned image compression [23]. The mutual information regularization weight $\beta$ is fixed at $10^{-3}$, which was found to yield strong disentanglement without degrading reconstruction fidelity.

### 4.3. Evaluation metrics

To assess the performance of our model, we report both quantitative and qualitative results. Compression efficiency is evaluated using Peak Signal-to-Noise Ratio (PSNR) and Bjøntegaard Delta PSNR (BD-PSNR) [46], averaged across all sub-aperture views in each light field. We also report Bits Per Pixel (BPP) to quantify the effective bitrate required to encode each LF image.

To provide a comprehensive evaluation, we include per-scene average PSNR values and plot Rate-Distortion (RD) curves that span a wide range of compression levels. Furthermore, we separately analyze the quality of central and peripheral angular views to assess the spatial-angular consistency and the generalization of the model across the full light field grid.

### 4.4. Reference methods for comparisons

We compare our method against several state-of-the-art light field compression baselines, grouped into three primary categories:

*   **Standardized Codecs:** JPEG Pleno [13] is a classical codec standard for light field data, extending JPEG2000 and HEVC frameworks with spatial-angular decorrelation tools.

*   **Pseudo-Video Compression:** Pseudo-Video Compression [14] treats LF sub-aperture images as a temporal video sequence and applies HEVC-based temporal prediction. RLVC and HLVC [15,16] are recurrent and hierarchical learned video compression models applied sequentially across angular dimensions.
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Average error maps comparing reconstructed images and ground truth for various scenes in the EPFL dataset [22]: Bikes, Danger, and Fountain. PSNR values are included to quantitatively compare the performance of our method against other state-of-the-art approaches, emphasizing areas of higher reconstruction error.</figcaption></figure>

**Neural Representation-Based Methods:** DDLF [17] leverages an un-trained decoder as an implicit prior for LF image reconstruction and compression. Shi et al. [18] uses kernel-modulated neural representations for view-dependent reconstruction with compact coding.

**VAE-Based Compression Models:** VAE-Hyperprior Baseline [23] is a learned image compression framework based on variational inference with a single entropy bottleneck. EF-VAE [40] is a learned LF image compression framework based on spatial-angular disentanglement and a shared entropy model for all latents.

All Reference Methods are evaluated under consistent preprocessing, and evaluation protocols for a fair comparison.

## 4.5. Qualitative evaluation setup

To complement our quantitative metrics, we also conduct a qualitative evaluation of reconstructed light field views. We use the EPFL dataset [22] and compare our method with representative baselines including JPEG Pleno, RLVC, Shi's neural representation method [18], and our previous EF-VAE model [40]. For visual analysis, we select representative scenes and match bitrates across methods to enable fair comparison of perceptual quality.

## 4.6. Inference time measurement

We benchmark encoding and per-view decoding times on a 9 × 9 light field (81 views) at 624 × 432 resolution using an NVIDIA RTX 3080 GPU. Our method uses a feed-forward architecture with no iterative refinement or scene-specific adaptation. Latents and likelihoods are computed in a single pass, and bitstreams are generated via arithmetic coding from learned hyperpriors. Average times are computed over multiple runs. Baseline comparisons include JPEG Pleno [13], RLVC [16], HLVC [15], and Shi [18]. Results are analyzed in Section 5.

# 5. Results

## 5.1. Rate-distortion performance

We evaluate the rate-distortion (RD) performance of our proposed dual-hyperprior LF compression framework using Peak Signal-to-Noise

Ratio (PSNR), tested across a wide range of bitrates on the EPFL and HCI light field datasets. Fig. 5 presents RD curves, and Table 2 reports BD-PSNR gains over an HEVC baseline for all evaluated scenes. The overall average BD-PSNR gain of 2.91 dB is highly significant in terms of bitrate savings; it corresponds to an average Bjontegaard-Delta Rate (BD-Rate) reduction of approximately 40-45%, meaning our method requires substantially less data to achieve the same objective quality as the HEVC-based pseudo-video approach.

Our proposed method achieves the best RD performance across nearly the entire bitrate range, outperforming all baselines. Notably, while Shi's method retains a marginal advantage at high bitrates – likely due to its high-capacity scene-specific representation – our model dominates in low and mid bitrate regions, offering better compression efficiency and generalization. The improvements over our earlier EF-VAE baseline highlight the effectiveness of the proposed mutual information regularization and dual-hyperprior architecture. While the VAE-Hyperprior baseline [23] is included in our evaluation as a representative learned image codec, it is not designed for multi-view or 4D light field data. Consequently, its performance is substantially lower, and for clarity, it is excluded from the RD plot and not emphasized in the main analysis.

To further validate the generalizability of our method, we conducted additional experiments on the HCI light field dataset [48]. As shown in Table 2, our model maintains its competitive advantage on the “Boxes” and “Sideboard” scenes. It consistently outperforms the traditional and learning-based baselines, demonstrating that our approach is robust and not overfitted to a single dataset’s characteristics. This confirms the effectiveness of our disentangled dual-hyperprior design for general LF image compression.

From a foundational compression theory perspective, the improvements in rate-distortion (RD) performance stem from how our design more effectively optimizes the rate term in the RD Lagrangian. The rate is theoretically a measure of the cross-entropy between the true data distribution, $p(y)$, and our learned entropy model, $q(y)$. The inefficiency, or penalty in bitrate, is captured by the Kullback-Leibler (KL) divergence, $D_{KL}(p || q)$. Our two core components directly minimize this penalty:

First, the **dual-hyperprior architecture** creates a more powerful and flexible family of models ($q_s$ and $q_d$) for the latent distributions.
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Reconstructed center views from two scenes in the EPFL dataset [22]: Bikes and Friends. Zoomed-in sections emphasize challenging areas where artifacts are particularly noticeable. The figure provides a comparison between our proposed network and Jpeg-Pleno, showcasing the differences in artifact reduction and overall image quality.</figcaption></figure>

Since the true distributions of spatial and angular latents ($p_s$ and $p_a$) possess distinct statistical characteristics, a single, shared hyperprior is forced to learn a compromise model that is a poor fit for both. By using two dedicated hyperpriors, our network can learn specialized models that more closely approximate the true underlying distributions, thereby minimizing both $D_{KL}(p_s || q_s)$ and $D_{KL}(p_a || q_a)$ and leading to a more accurate entropy estimation and a lower total bitrate.

Second, the **InfoNCE-based regularizer** creates a more efficiently encodable latent representation by enforcing statistical independence. An ideal factored entropy model assumes that the joint probability of the latents can be separated, i.e., $p(y_s, y_a) = p(y_s)p(y_a)$. This is only true if their mutual information, $I(y_s; y_a)$, is zero. Our regularizer directly minimizes this mutual information, pushing the encoder to learn a disentangled representation where the two latent variables are largely non-redundant. This makes our factored entropy model a much better fit for the latent distribution, further reducing the overall KL divergence and improving the rate-distortion trade-off by ensuring that bits are not wasted encoding shared information.

The incorporation of the mutual information-based regularization term $L_{MI}$, formulated using the InfoNCE objective, forces better latent specialization by promoting a more explicit separation between spatial and angular representations. This disentanglement enables the model to more effectively distribute its representational capacity across the two domains, leading to improved compression performance. While the

regularizer does not directly enhance visual sharpness, it de-correlates the latent spaces, allowing the entropy encoders to assign bits more efficiently. These results support the effectiveness of our dual-hyperprior architecture and mutual information-based disentanglement in jointly optimizing rate and distortion, especially under low-bitrate conditions where traditional methods often fail to preserve fidelity.

## 5.2. Compression ratio analysis

To provide a more intuitive measure of efficiency, Table 3 presents the Compression Ratio (CR) for the “Bikes” scene at different quality points. The CR is calculated as the ratio of the uncompressed bitrate (24 bpp for an 8-bit RGB image) to the compressed bitrate. The results show that our method achieves high compression ratios while maintaining a clear quality advantage over the baselines at similar bitrates. For instance, at a CR of approximately 200:1, our method delivers a PSNR of 34.0 dB, significantly outperforming JPEG-Pleno and HEVC.

## 5.3. Quality across angular views

To better understand how reconstruction quality varies spatially across the light field, Fig. 7 illustrates the PSNR heatmap for the Fountain dataset, showing the average PSNR values for a 9 × 9 subset of sub-aperture views. Each cell in the grid corresponds to a specific
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Rate-Distortion (RD) curve comparing the performance of our proposed VAE-based light field compression method against HEVC [47], RLVC [16], HLVC [15], JPEG-Pleno [13], Shi's [18], and EF-VAE [40] method. Our method consistently outperforms the others across most datasets in terms of compression efficiency, except for high bit rates of Shi's method, which shows slightly better results on a few specific datasets.</figcaption></figure>

<caption>**Table 2**</caption>

BD-PSNR Gains (dB) of the proposed method with respect to HEVC baseline on the EPFL and HCI datasets. The best results are in **bold**, and the second-best are **underlined**.

<table><thead><tr><th rowspan="2">Method</th><th colspan="4">EPFL dataset</th><th colspan="3">HCI dataset</th><th>Overall</th></tr><tr><th>Bikes</th><th>Danger</th><th>Pillars</th><th>Fountain</th><th>Boxes</th><th>Side-board</th><th>Avg.</th></tr></thead><tbody><tr><td>JPEG Pleno [13]</td><td>0.20</td><td>1.38</td><td>0.58</td><td>0.30</td><td>0.46</td><td>1.77</td><td>0.78</td></tr><tr><td>HLVC [15]</td><td>0.01</td><td>0.01</td><td>-0.05</td><td>-0.07</td><td>-0.78</td><td>-1.37</td><td>-0.38</td></tr><tr><td>RLVC [16]</td><td>0.35</td><td>0.29</td><td>0.20</td><td>0.32</td><td>-0.47</td><td>-0.02</td><td>0.11</td></tr><tr><td>VVC [7]</td><td>1.18</td><td>1.41</td><td>1.27</td><td>1.06</td><td>1.85</td><td>2.24</td><td>1.50</td></tr><tr><td>DDLF [17]</td><td>0.69</td><td>0.93</td><td>-0.01</td><td>0.90</td><td>-1.00</td><td>-1.75</td><td>-0.04</td></tr><tr><td>Shi et al. [18]</td><td>1.88</td><td><strong>3.20</strong></td><td>1.93</td><td>2.50</td><td>2.74</td><td><strong>4.84</strong></td><td>2.84</td></tr><tr><td>EF-VAE [40]</td><td>1.56</td><td>2.95</td><td>1.93</td><td>2.32</td><td>2.55</td><td>4.75</td><td>2.67</td></tr><tr><td>Ours</td><td><strong>1.90</strong></td><td><u>3.12</u></td><td><strong>2.15</strong></td><td><strong>2.63</strong></td><td><strong>2.90</strong></td><td><u>4.80</u></td><td><strong>2.91</strong></td></tr></tbody></table>

angular view, with color intensity indicating the reconstruction quality in terms of PSNR.

As observed, views near the center of the light field generally achieve higher PSNR values compared to those at the periphery. This trend aligns with the fact that central views tend to exhibit more consistent spatial-angular correlations due to their symmetric position within the grid. Our method preserves high-fidelity reconstructions across the angular domain, with particularly strong performance in center-aligned

regions due to the localized macropixel design and disentangled latent processing.

### 5.4. Qualitative evaluation

Fig. 3 presents average reconstruction error maps across three representative scenes – *Fountain*, *Danger*, and *Bikes* – at approximately matched bitrates. These visualizations highlight spatial regions with
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Comparison of mutual information (MI) distribution between spatial and angular latent branches for two regularization strategies. **Left:** Covariance-based penalty leads to representational collapse, as seen by the strong diagonal block in the upper-left (spatial-spatial MI) and near-zero values elsewhere, indicating that most information is concentrated in the spatial branch while the angular features remain inactive. **Right:** InfoNCE-based regularization results in more evenly distributed mutual information across all blocks, including spatial-angular and angular-angular regions, suggesting balanced and disentangled feature encoding across both branches.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** PSNR heatmap for the *Fountain* scene, where color intensity indicates reconstruction fidelity—brighter shades represent higher quality. Each cell displays the PSNR (in dB) of a sub-aperture image at a specific angular position within the 9 × 9 light field grid. This visualization allows assessment of spatial consistency and quality variation across the angular domain. The two views with red borders, located at (4, 0) and (4, 8) in the angular grid, are the extreme horizontal views and are selected for disparity map analysis shown in Fig. 10.</figcaption></figure>

the largest deviations from ground truth. Our method consistently exhibits lower reconstruction error, especially around occlusion boundaries and high-frequency textures. Zoomed-in sections further illustrate

<table><caption>**Table 3**

Performance and Compression Ratio (CR) for the 'Bikes' scene.</caption><thead><tr><th>Method</th><th>Rate (bpp)</th><th>PSNR (dB)</th><th>CR</th></tr></thead><tbody><tr><td>Ours</td><td>0.12</td><td>34.0</td><td>200:1</td></tr><tr><td>Shi [18]</td><td>0.12</td><td>33.5</td><td>200:1</td></tr><tr><td>JPEG-Pleno [13]</td><td>0.12</td><td>31.2</td><td>200:1</td></tr><tr><td>HEVC [40]</td><td>0.12</td><td>31.0</td><td>200:1</td></tr><tr><td>Ours</td><td>0.25</td><td>35.4</td><td>96:1</td></tr><tr><td>Shi [18]</td><td>0.25</td><td>35.2</td><td>96:1</td></tr><tr><td>HEVC [40]</td><td>0.25</td><td>32.0</td><td>96:1</td></tr></tbody></table>

the artifact-reducing effect of the dual-hyperprior design, which improves entropy modeling and maintains structural fidelity in challenging regions. PSNR values included alongside each method confirm our quantitative advantage in these scenarios.

**Fig. 4** complements this analysis by showing reconstructed center views from *Fountain* and *Bikes*. These examples include close-up insets focused on fine textures, geometric boundaries, and areas of significant parallax. Compared to JPEG Pleno and other methods, our reconstructions display markedly fewer compression artifacts, crisper textures, and improved continuity across edges—attributes that are critical for maintaining angular coherence and epipolar consistency in LF applications.

The improved perceptual quality can also be attributed to the mutual information-based regularizer, which helps maintain distinct spatial and angular encoding. This contributes to better structure preservation and visual coherence across views, supporting downstream tasks such as refocusing and rendering.

In summary, the qualitative comparisons reinforce our quantitative results, demonstrating that the proposed framework not only improves rate-distortion performance but also delivers better perceptual quality. The reduced visual artifacts and improved structural coherence make our method especially suitable for downstream light field tasks such as depth estimation, refocusing, and interactive rendering, where angular consistency and spatial sharpness are paramount.
<table><caption>**Table 4**
Inference times and PSNR for light field compression (81 views, 624 × 432 resolution).</caption><thead><tr><th>Method</th><th>Encoding (s)</th><th>Decoding (s)</th><th>Total (s)</th><th>PSNR (dB)</th></tr></thead><tbody><tr><td>JPEG Pleno [13]</td><td>90</td><td>2.4</td><td>92.4</td><td>32.0</td></tr><tr><td>RLVC [16]</td><td>58</td><td>32.0</td><td>90.0</td><td>32.2</td></tr><tr><td>HLVC [15]</td><td>159</td><td>11.0</td><td>170.0</td><td>31.6</td></tr><tr><td>Shi [18]</td><td>21 600</td><td>20.2</td><td>21 620.2</td><td><strong>35.4</strong></td></tr><tr><td>Ours</td><td><strong>4</strong></td><td><strong>0.81</strong></td><td><strong>4.81</strong></td><td>34.8</td></tr></tbody></table>

## 5.5. Inference speed and complexity

We evaluate the computational efficiency of our method by measuring both encoding and per-view decoding times. For a 9 × 9 light field with resolution 624 × 432, our method requires only 4 s for full encoding and 0.010 s for decoding each sub-aperture view on a single NVIDIA RTX 3080 GPU. As shown in Table 4, this is over 14× faster than RLVC, 40× faster than HLVC, and 5400× faster than Shi's method in terms of encoding time. The long runtimes of the latter are due to its reliance on scene-specific training and inference. This efficiency stems from our feed-forward architecture, which avoids recurrent layers, motion compensation, or iterative optimization. The dual-latent structure is compact and does not require post-processing, enabling high-throughput decoding with minimal latency.

While the full encoding of a light field takes approximately 4 s, the extremely low per-view decoding time and parallelizability of our method make it well-suited for real-time or low-latency pipelines, especially in use cases such as streaming or immersive rendering where decoding speed is the main bottleneck.

As shown in Table 4, while the method of Shi et al. [18] achieves a 0.6 dB higher PSNR, it is critical to consider the computational cost. Our method's encoding time is over **5400** times faster (4 s vs. 21 600 s for a single LF image). This substantial speedup stems from our feed-forward architecture, which performs compression in a single pass, whereas Shi's approach relies on a time-intensive, per-scene optimization process. This distinction highlights a key advantage of our work: delivering competitive rate-distortion performance while maintaining the practical efficiency required for applications like live streaming and interactive rendering.

These characteristics reflect one of the broader strengths of our framework: by decoupling complex computations from inference time, it enables practical deployment of learned light field compression models in constrained environments, a limitation faced by many state-of-the-art methods.

# 6. Ablation study

To assess the individual contributions of our proposed design components, we conduct a comprehensive ablation study using the large-scale Lytro dataset introduced in Section 4, which is also used to train all ablation variants. This section analyzes the impact of three key elements: (i) the dual hyperprior architecture, (ii) the InfoNCE-based regularization, and (iii) the configuration of spatial and angular latent channels. Each model variant shares the same backbone and training configuration, ensuring a fair comparison under controlled conditions.

## 6.1. Impact of dual hyperprior modeling

We begin by isolating the contribution of our dual hyperprior design. Specifically, we compare two variants: (i) a baseline VAE model without any hyperprior(equivalent to our previously proposed EF-VAE [40]), and (ii) our proposed model incorporating two independent hyperpriors—one for each latent branch. As illustrated in Fig. 9, the inclusion of dual hyperpriors significantly improves compression performance by enabling more accurate modeling of the latent

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Rate-Distortion (RD) curves on the *Danger* scene, comparing various spatial-angular latent channel allocations. Each configuration reflects a different percentage of channels dedicated to the spatial and angular branches. The 80%-20% split (green) achieves the best overall trade-off, offering superior PSNR across a wide range of bitrates, especially in the low-rate region. The blue curve corresponds to the variant without regularization for disentanglement. Additional splits such as 50%-50%, 75%-25%, and 95%-5% were also evaluated but are omitted for clarity; their performance lies between the best and worst configurations shown.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Rate-distortion comparison between our model with dual independent hyperpriors and a variant without any hyperprior, evaluated on the *StonePillarsOutside* and *Danger* scenes. The results demonstrate that introducing hyperpriors significantly improves compression performance, particularly at lower bitrates, by enabling better entropy modeling of latent distributions. Consistent gains across both datasets confirm the effectiveness and generalizability of the dual-hyperprior design.</figcaption></figure>

probability distributions. The RD curve clearly shows that our dual-hyperprior design achieves better rate-distortion trade-offs, particularly in the low-bitrate regime where precise entropy modeling is most critical. This improvement arises from the ability of each hyperprior to specialize in capturing the distinct statistical characteristics of the spatial and angular latents. Furthermore, the use of separate hyperpriors helps maintain functional disentanglement without introducing over-regularization effects. Together, these advantages contribute to improved coding efficiency and reconstruction quality across a wide bitrate range.
<figure><img src="image_12.png" /><figcaption>Fig. 10. Disparity map comparisons and error distributions for two EPFL scenes: *StonePillarsOutside* and *Bikes*. For each scene, disparity maps are estimated from the outermost angular views and visualized for the ground truth and four methods: RLVC [16], HEVC [47], JPEG-Pleno [13], and our proposed approach. Our method yields sharper and more complete disparity reconstructions with fewer artifacts. The corresponding violin plots show the distribution of disparity errors, highlighting the lower median error and reduced variance achieved by our method.</figcaption></figure>

## 6.2. Effect of InfoNCE regularization

To investigate the role of mutual information-based regularization, we compare two variants of our model: one trained with a covariance-based penalty and another using our proposed InfoNCE objective. All other architectural and training components are kept fixed. Without any regularization, the spatial and angular latent branches exhibit partial redundancy, leading to inefficient use of latent capacity, which in turn results in suboptimal entropy coding since overlapping information inflates the bitrate needed by the arithmetic encoder. Covariance-based regularizers attempt to suppress this redundancy by enforcing decorrelation, but as shown in the left-hand side of Fig. 6, this often results in representational collapse—where one branch dominates the information content while the other remains underutilized.

In contrast, our InfoNCE-based regularization provides a more stable and interpretable mechanism for disentanglement. The right-hand side of Fig. 6 illustrates that both branches retain substantial and distinct mutual information, enabling complementary specialization with reduced redundancy. This behavior leads to a better-structured and more efficient latent space, where reduced redundancy improves the predictability of latent distributions. As a result, the entropy model can assign more accurate probability estimates to quantized values, enhancing arithmetic coding efficiency and thereby contributing to improved rate-distortion performance. The benefits are especially pronounced in low-bitrate regimes, where compact yet expressive representation that preserves sufficient information for reconstructing both spatial details and angular variations is critical. Furthermore, unlike covariance-penalty approaches, InfoNCE avoids mode collapse, a phenomenon where one latent branch dominates and the other becomes inactive or uninformative. By maintaining balanced and meaningful contributions from both spatial and angular branches, InfoNCE ensures more stable convergence across training runs.

To further support the claim that InfoNCE-based regularization enhances latent disentanglement and reconstruction quality, we conduct a disparity-based geometric consistency evaluation. As shown in Fig. 10, we compare disparity maps computed from reconstructed left and right boundary views for two representative EPFL scenes—*StonePillarsOutside* and *Bikes*. Our method reconstructs disparity maps that are closer to the ground truth, with sharper transitions and fewer structural distortions,

particularly in regions near object boundaries where large depth gradients occur. Complementing this, the violin plots visualize the disparity error distributions across methods, revealing that our approach yields the lowest mean error and smallest variance. These results indicate that InfoNCE-based disentanglement not only promotes better latent factorization but also leads to improved angular consistency, which is essential for accurate geometry reconstruction in compressed light fields.

## 6.3. Latent configuration sensitivity

We examine how the allocation of latent channels to the spatial and angular branches affects overall performance. Specifically, we compare several spatial/angular channel splits—ranging from balanced (e.g., 50/50) to increasingly asymmetric configurations (e.g., 60/40, 75/25, 80/20, 90/10, 95/05). As shown in Fig. 8, a moderately asymmetric split such as 80/20 yields the best rate-distortion performance. These configurations strike a favorable balance between flexibility and specialization, allowing the network to effectively compress both spatial details and angular cues. In contrast, extreme imbalances (e.g., 95/05) result in degraded reconstruction quality due to underrepresentation of angular features. Although angular data spans fewer samples (13 × 13 views), it encodes essential geometric cues like disparity. Allocating too few channels limits the model’s ability to capture angular variation, especially in scenes with complex structure.

## 6.4. Impact of regularization weight

The mutual information regularization term $L_{MI}$ is balanced by the weight $\beta$. The choice of $\beta$ is critical: if it is too small, disentanglement will be ineffective; if it is too large, the regularization will dominate the reconstruction loss, harming fidelity. To justify our choice, we conducted an ablation study by training our model with three different values for $\beta$: $10^{-4}$, $10^{-3}$, and $10^{-2}$. As shown in Fig. 11, a weight of $\beta = 10^{-4}$ provides insufficient regularization, resulting in latent representations with higher redundancy and slightly lower RD performance. Conversely, a weight of $\beta = 10^{-2}$ overly penalizes any shared information, leading to a noticeable drop in PSNR as the model
<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Rate-distortion performance on the ‘Danger’ scene for different values of the regularization weight $\beta$. Our selected value of $10^{-3}$ provides the best trade-off between compression performance and latent disentanglement.</figcaption></figure>

struggles to reconstruct the image with strictly separated features. The chosen value of $\beta = 10^{-3}$ strikes the best balance, achieving strong disentanglement (as seen in Fig. 6) while maintaining optimal rate-distortion performance. Regarding the temperature parameter $\tau$, we used a value of 0.07. This has become a standard hyperparameter setting in the contrastive learning field, successfully employed in influential works like MoCo [49] and SimCLR [21]. We found this standard value to work robustly for our task without requiring further tuning.

## 6.5. Summary

Our ablation study evaluated three key design components: (i) dual hyperprior modeling, (ii) InfoNCE-based regularization, and (iii) spatial-angular latent channel configuration. Each contributes in a distinct and complementary manner. The dual hyperprior improves the estimation of latent distribution statistics, leading to more efficient compression. InfoNCE encourages meaningful disentanglement without causing one branch to dominate. Finally, well-balanced latent channel splits help preserve both spatial structure and angular consistency. Their combination yields a greater benefit than any single component alone, highlighting their synergistic integration. These findings demonstrate the practicality and flexibility of the proposed framework across different compression scenarios.

## 7. Conclusion and discussion

This paper introduced DUALF-D, a well-founded and efficient framework for light field image compression that leverages a disentangled VAE with dual hyperpriors. By explicitly separating the modeling of spatial and angular information, our method addresses the unique structured redundancy of 4D light fields more effectively than conventional approaches. The dual-hyperprior design enables more accurate entropy estimation for each latent space, leading to consistent rate-distortion improvements, achieving high compression ratios of up to 200:1 and an average BD-PSNR gain of 2.91 dB over the standard HEVC codec. Paired with a stable information-theoretic regularizer, our model not only improves coding efficiency but also provides a practical solution that balances performance with the fast inference speeds required by real-world applications.

To promote disentangled representation learning, we introduce a mutual information regularization term based on the InfoNCE loss. This objective reduces shared information between the spatial and angular latents by contrasting them with negative examples from other samples.

It avoids issues such as latent collapse observed in covariance-penalty methods and supports more robust and interpretable encoding.

Experiments on the high-resolution EPFL dataset demonstrate that our approach achieves competitive rate-distortion performance while maintaining fast inference, making it well-suited for scenarios where both efficiency and quality are critical. Ablation results further confirm the individual impact of each component, including dual hyperpriors and mutual information regularization, on disentanglement and compression performance.

**Limitations and future work.** While our method demonstrates robust performance, we acknowledge several limitations that suggest avenues for future research. First, our macropixel-based design is highly optimized for the dense, grid-like structure of plenoptic camera captures. Its applicability to other LF representations, such as those from sparse or unstructured camera arrays, remains an open area for investigation. Future work could explore adaptive sampling strategies to generalize the macropixel concept to non-uniform inputs. Second, our model was trained on high-quality datasets, and its robustness to inputs with significant sensor noise has not been explicitly evaluated. Integrating a denoising module or employing noise-aware training objectives could enhance its applicability for a wider range of capture conditions. Furthermore, additional avenues for future work include exploring perceptual enhancements via adversarial training and conducting Quality of Experience (QoE) studies to assess user-perceived fidelity in real-world settings.

## CRediT authorship contribution statement

**Soheib Takhtardeshir:** Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation. **Roger Olsson:** Writing – review & editing, Visualization, Supervision. **Christine Guillemot:** Writing – review & editing, Supervision, Conceptualization. **Mårten Sjöström:** Writing – review & editing, Supervision.

## Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Soheib Takhtardeshir reports financial support was provided by EU-MSCA Plenoptima project (956770). Mårten Sjöström reports financial support was provided by EU Interreg Aurora project IMMERSE (20366448). If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

The work was supported by EU-MSCA Plenoptima project (956770). The research was also supported by the EU Interreg Aurora project IMMERSE (20366448), and by Mid Sweden University internal funding. The computations were enabled by NAISS, partly funded by Swedish Research Council (2022-06725), and High Performance Computing Center North (HPC2N) at Umeå University. Additionally, the authors acknowledge the use of OpenAI's ChatGPT for grammar and style enhancement in certain sections of this manuscript. The AI system was used to refine the clarity and fluency of the text while ensuring technical accuracy, with all content being verified and approved by the authors.

## Data availability

Data will be made available on request.
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