FRN: Fractal-Based Recursive Spectral Reconstruction Network
Authors: Ge Meng
Zhongnan Cai
Ruizhe Chen
Jingyan Tu
Yingying Wang
Yue Huang
Xinghao Ding
Venue: NeurIPS 2025 poster ()
Keywords: Hyperspectral Image
Spectral Reconstruction
Fractal
State Space Model
Primary area: deep_learning

Abstract: Generating hyperspectral images (HSIs) from RGB images through spectral reconstruction can significantly reduce the cost of HSI acquisition. In this paper, we propose a Fractal-Based Recursive Spectral Reconstruction Network (FRN), which differs from existing paradigms that attempt to directly integrate the full-spectrum information from the R, G, and B channels in a one-shot manner. Instead, it treats spectral reconstruction as a progressive process, predicting from broad to narrow bands or employing a coarse-to-fine approach for predicting the next wavelength. Inspired by fractals in mathematics, FRN establishes a novel spectral reconstruction paradigm by recursively invoking an atomic reconstruction module. In each invocation, only the spectral information from neighboring bands is used to provide clues for the generation of the image at the next wavelength, which follows the low-rank property of spectral data. Moreover, we design a band-aware state space model that employs a pixel-differentiated scanning strategy at different stages of the generation process, further suppressing interference from low-correlation regions caused by reflectance differences. Through extensive experimentation across different datasets, FRN achieves superior reconstruction performance compared to state-of-the-art methods. Code is available at https://github.com/mongko007/frn.

FRN: Fractal-Based Recursive Spectral Reconstruction Network
Ge Meng', Zhongnan Cai', Ruizhe Chen', Jingyan Tu', Yingying Wang', Yue Huang', Xinghao Ding
Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University, Xiamen, Fujian, China mengge0001 @gmall.mm......... itgmail.com com
Abstract
Generating hyperspectral images (HSIs) from RGB images through spectral re- construction can significantly reduce the cost of HSI acquisition. In this paper, we propose Fractal-Based Recursive Spectral Reconstruction Network (FRN), which differs from existing paradigms that attempt directly integrate the full-spectrum information from the R, G, and B channels in a one-shot manner. Instead, it treats progressive process, predicting from broad narrow
spectral reconstruction bands or employing a coarse-to-fine approach for predicting the next wavelength. Inspired by fractals in mathematics, FRN establishes novel spectral reconstruc- tion paradigm by recursively invoking an atomic reconstruction module. In each invocation, only the spectral information from neighboring bands is used to provide clues for the generation of the image at the next wavelength, which follows the low-rank property spectral data. Moreover, we design band-aware state space model that employs pixel-differentiated scanning strategy at different stages of the generation process, further suppressing interference from low-correlation re- gions caused by reflectance differences. Through extensive experimentation across different datasets, FRN achieves superior reconstruction performance compared state-of-the-an art methods. Code is available at https//github..ommmonggoooo
Introduction
Hyperspectral images (HSIs) contain more spectral bands (channels) than RGB images, enabling them to capture richer emission information that more accurately reflects the properties of objects. As a
41
FRN (surs)
LTTRN
result, HSIs commonly used in applications such
BSNK (8B)
39
MST++
as medical imaging [33 35 3, remote sensing [55
AHSRRcct
38
46
34 19]. material classification
[25] 26 and
object tracking
48 31. etc.
37
Conventional hyperspectral imaging systems typi- cally employ a single ID or 2D sensor to sean the scene along the spatial or spectral dimension, cap- turing hyperspectral information through prolonged, repeated exposures. However, this approach is not well-suited for dynamic scenes. The coded aperture snapshot spectral imaging (CASSI) system takes advantage of the sparsity of spectral data, acquiring
38
2.0 Number of parameters (M)
Figure 1: PSNR-Parameters comparisons of FRN and SOTA methods. FRN achieves out- standing HSI reconstruction performance with only a minimal number of parameters.
"Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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HEAT
646 fnm
594. 594.3mm
543 &nm
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(b) The recursive invocation process of the atomic reconstruction module in FRN.
progressive spectral reconstruction framework.
Figure 2: Overview of the Fractal-Based Progressive Spectral Reconstruction Paradigm: (a) illustrates how FRN reconstructs images at specific wavelengths in coarse-to-fine manner, transitioning from wide spectral bands to narrow ones across multiple levels. (b) demonstrates the structural self- similarity of the modules within each level.
compressed 2D measurements by modulating spectral signals different wavelengths. The original HSIs are then reconstructed from these measurements using reconstruction algorithms 9 23 24
[6] Despite its effectiveness, the high cost of CASSI devices has led researchers explore more affordable alternatives. Given the widespread availability of RGB cameras, spectral reconstruction (SR) algorithms have been developed to recover HSIs from RGB input [10
52 15].
The SR task is inherently ill-posed [5 52). Due to the variability in camera response functions. sin- gle RGB image may correspond to multiple HSIs, complicating the accurate retrieval hyperspectral information from limited RGB data. Traditional methods rely on statistical principles or hand-crafted sparse priors
However, the scarcity of paired RGB-HSI data limits the ability fully capture and explore these prior assumptions. Convolutional neural networks (CNNs) have demonstrated strong performance in addressing various ill ill-posed problems, with some studies exploring their 29 20 Nevertheless, CNNs struggle to capture non-local spatial dependencies and model correlations between spectral bands. In contrast, transformers, owing to their multi-head self-attention mechanism, are better suited for handling long-range spatial dependencies and inter-band relationships, and have thus been widely applied to SR task [10 52
application to the SR task [15] 45
27]. However, such methods typically integrate spectral information from RGB images in brute-force manner, leading to significant computational overhead and increased training complexity for neural networks.
Fractals are common patterns observed neural networks 33) Numerous studies have demonstrated the effectiveness of fractal or scale-invariant world network structures in the brain and its functional networks 4 6 This inspires the idea that larger network can be recursively constructed from smaller atomic modules. In addition to neural networks, fractal or near-fractal patterns are also commonly observed in natural data [30]. HSI data consists of sub-images from different bands, where sub-bands with slow variations in object emission characteristics can be treated as atomic cubes. Therefore, the SR task can be decomposed into the reconstruction these sub-bands.
Based on the above analysis, we attempt introduce the concept of fractals into the SR task. Fig. [ shows the superior performance of our method. By employing the recursive principle, our method achieves superior HSI reconstruction performance while requiring only minimal number of parameters. Fig. (a) illustrates the progressive spectral reconstruction from wide to narrow bands. During the generation of a specific wavelength image, only spectral information from neighboring channels is used as cues for reconstruction, which aligns with the low-rank properties of HSL. Unlike integrating all hyperspectral information from an RGB image in single step, this recursive generation approach mitigates the ill- ill-posed problem by increasing the input and reducing the output each

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level. Fig. (b) depicts our recursive generation framework, which exhibits self- self-similarity across levels by recursively invoking atomic reconstruction modules within atomic reconstruction modules.
major challenge of recursively invoking the model the substantial increase the number of parameters and FL.OPs. Visual Mamba (VMamba) models sequential dependencies by dividing image into sequential blocks. A key advantage of VMamba is its linear computational complexity [57] 13 42 41 43), which is particularly critical for handling high-dimensional hyperspectral features. Therefore, we design a state space model (SSM) with an adaptive band-aware mask (BAMamba) that filters out pixels with low spatial correlation before pross-scanning. This approach reduces computational cost while enabling the network to learn spatial sparsity effectively. In summary, our contributions are listed as follow:
1) We propose "ractal-based recursive spectral reconstruction network (FRN), to the best of our knowledge, it the first attempt to introduce fractals to the SR task. FRN decomposes SR task into the reconstruction of sub-band images, establishing new paradigm for spectral reconstruction.
2) FRN effectively leverages the low-rank characteristics of HSI while reducing the complexity of solving the ill-posed problem. Moreover, it exhibits self-similarity between atomic reconstruction modules across different levels.
3) We design a SSM with an adaptive band-aware mask (BAMamba), which reduces the computational cost by filtering out pixels with lower spatial correlation and forces the network to learn more compact pixel-wise inductive biases.
4) Through experiments conducted on different datasets, FRN demonstrates outstanding per- formance in both qualitative and quantitative metrics.
2 Related Work
2.1 Hyperspectral Image Reconstruction
Conventional hyperspectral imaging systems typically use spectrometers to scan scenes along the spa- tial or spectral dimensions. These scanners- suche as pushbroom and whiskbroom types have been widely applied in remote sensing, medical imaging, and environmental monitoring [5] 40 However, they require long exposure times during scanning, rendering them unsuitable for dynamic scenes, and the imaging devices are too large to be easily portable.
overcome these limitations, snapshot These systems compress 3D HSI data into 2D measurements. The original HSIs are then reconstructed from these measure- ments using reconstruction algorithms. A representative example is the CASSI system. Despite their advantages, SCI systems are costly. As a more accessible alternative, many researchers have explored spectral reconstruction algorithms that aim to recover hyperspectral data from conventional RGB images [6 53 52 10 leveraging the widespread availability of RGB cameras.
compressive imaging (SCI) systems have been developed [12] [8] 32 49)
2.2 Model-Based Methods
Model-based SR methods generally introduce prior knowledge to help the model reduce the difficulty of the ill-posed problem. Given the intrinsic low-rank nature of HSIs, sparse representation has become one of the most typically techniques for incorporating prior knowledge [38] 2
Some methods assume that the camera response function is known and learn mapping from RGB images
hyperspectral reflectance (37 27 53 However, this assumption is overly restrictive in practice. In addition, mathematical techniques such as singular value decomposition (SVD) [21] and Gaussian [ are also employed to reconstruct HSIs. These methods place excessive reliance on priors, which constrains the model's ' representational ability and generalization capability.
processes
2.3 Deep-Lear -aased Methods
Thanks to the powerful nonlinear fitting capabilities of CNNs, many researchers have applied them on SR. Convolutional blocks are used for spectral upsampling [53 or stacked layer by layer to enable the network model more complex functions [45). Considering the significant emission differences of objects across different spectral bands, efficient spatial-spectral attention mechanisms have been
3

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Band-awared State Space Model (BSSM)
Band-aware Mask
LEvErN
Generation
BSSM
Conv
BSSM
Sir
Jownsample
pesumpll
Conv Item
0.6 vap 48
BSSM
Comy item
BSSM
direction 2:
b. Ale dr,
cb. Dz.
①
Downsample
U Unsumple
direction 4:
BSSM
(a) Overview of BAMamba.
(b) Illustration of BSSM.
The details of BAMamba. BAMamba is a U-Net style network built with state space models equipped with band-aware masks (BSSM). BSSM introduces band-aware spatial mask that adaptively perceives the reflectance of objects at specific wavelengths, suppressing interference from pixels with lower correlation.
Figure 3:
designed to achieve more realistic reconstruction results [22 28 39]. To address the limitations of CNNs in capturing long-range spatial dependencies, a variety of Transformer-based SR methods have since emerged [10 II 52 These methods learn inter-channel relationships by designing effective spectral-wist self-attention mechanisms. However, the above methods follow one-shot reconstruction paradigm for HSI, overlooking the potential of recursive generation strategy to reduce the complexity of SR.
Method
3.1 Problem Formulation
The sensor an RGB camera transfers the incident light to the R, G, and channels through filters. This process be regarded interaction between the camera response function (CRF) and the hyperspectral image
Amaz
X (h, A)
@ (Ar) Y (h, w. dA,
(1)
Ammin
where X E Hx represents the RGB image and Y E RHx is the corresponding HSI. Y (h, w. A;) denotes the spectral reflectance in the location(h, w) at the wavelength of A; & (A,) represents the spectral response of the sensors at the wavelength of A; and [Amin, Amaz] the band
range of X (h, w, A). The spectral information within the specified band range is integrated and stored channels of the RGB image. Eq. [ can be rewritten in a discrete form
K
X (h, w. c)
Σ ò (X.) Y (h, w. A4),
where c E RR, G. B] and is the number channels within the corresponding band. Furthermore, Eq. can be simplified matrix form
X = Y
(3)
where E HWW x3 denotes the vectorial representation of RGB image, and E HWWL the corresponding HSI with L channels, &b BL represents the CRF.
3.2
Spectral Reconstruction via Fractal Generator
Due to the self-similarity observed among local bands in HSI, we propose to construct structurally self-similar SR network by following recursive principle. We define fractal generator gi as

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atomic module that generates next-level data 21+1 from the previous-level result 2;; 2i+1 (x;), as illustrated Fig. (b). Since the generator each level can produce multiple outputs from small amount of input, the fractal framework enables exponential growth of generated outputs with only linear number of recursive levels [30], as shown Fig. 2 (a). This property makes particularly suitable for modeling high-dimensional HSI data using only limited number of recursive
levels. Specifically, we design an SSM with an adaptive band-aware mask (BAMamba) as the atomic generator, which will be described in Section 3.3
The neural network learns the recursive principle from inter-band spectral correlations. For SR task, the objective is to learn the joint distribution of images at all wavelengths (y), M/z: .3A ). However, it is difficult model the joint distribution in single step. To address this, we adopt a progressive strategy. which can be viewed as a divide-and-conquer approach, which model the conditional distribution p (y x) at different generation levels. Assume that each atomic generator produces a data sequence of length n, and the number of channels in the HSI is K, let K = n"" where m = log,, K' the number of recursive levels. The atomic generator the first level divides the joint distribution p (31, y2, .KK into subsets, each containing n n1m01 variables. The joint distribution is decomposed
p (y1, 122
-P= (Mi- mm==-)))m=+++""" -iimm-1 y1 3(6 ((1-1)-nm 1)-mm1)).
Each conditional distribution is modeled by the atomic generator at the corresponding level. Fig. 2 illustrates the overall process. Through this typical divide-and-conquer strategy, FRN models the joint distribution over K variables by employing m levels of generators. The self-similarity of HSI along the spectral (channel) dimension, also known as its low-rank property, is effectively captured via the recursive principle, enabling a progressive approximation of the CRF &b in Eq.
3.3 Architecture of BAMamba
Visual Mamba (VMamba) exhibits linear computational complexity, enabling it especially well- suited for processing HSI data, which has dimensionality much higher than that of RGB images. To address the computational burden introduced by recursive calls, we propose VMamba-based sub-band generator that balances efficiency with performance, as shown in Fig. (a).
The SSM employs system of linear ordinary differential equations to connect inputs and outputs via intermediate hidden state representation. For a system with input signal sr()) E R24, hidden state h(t) E C and output response y(t) R², the model can be formulated as
h (t) = Ah(() + Br((), y(f) Ch(() + Dr(t),
(5)
where A E CNNN, B,C E CN and D E C² are weighting parameters. Eq. is typically discretized using zero-order keeper (ZOH)
= (Ap) B (AA) (expl AA) - I)- AB,
(6)
where is a time scale parameter used to transform the continuous parameters A, B into discrete parameters A, B. The discretized Eq. ( can be written as
h Ah4-1 + B
y/ Ch2 + Dry.
Different objects may exhibit substantial differ- ences in emissivity at the same wavelength, which implics that the energy intensity in HSI can un- dergo significant spatial variations. Furthermore, as illustrated in Fig. objects exhibit varying degrees of distinction across different spectral bands.
R-G
R-B
G-B
1.0
0.8
0.4
0.2
In SSMs, hidden states capture long-range de- pendencies by propagating historical information along the sequence. By accumulating and carrying previous data from earlier time steps, they enable
Figure 4: Residual maps across the R, G, and B channels from a CAVE dataset sample.
5

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the model to retain past context and effectively establish global receptive field. However, varia- tions in the spatial distribution of spectral features across different bands can negatively impact the network's $ generalization ability. As shown in Fig. T significant differences may exist between the same (or different) objects across different (or the same) spectral bands. To mitigate the influence of accumulated band-specific information in hidden states, we attempt to suppress the interference from low-correlation regions by generating band-aware masks. According to the Eq. (6). AA controls the impact of the current input sequence the hidden states, with positive correlation. Based on the value of the coefficients AA, a band-aware mask M is generated during each sub-band generation
1, AA2c { O, AA<E
M
(8)
y/ = (C&M)) h4:
where [0, a). and is hyperparameter. According to Eq. and Eq. (9) features in the hidden states associated with coefficient AA that fall below a defined threshold are suppressed. As illustrated in Fig. 3 (b), some pixels with low spatial correlation (shaded areas) are filtered out. The overall working mechanism of the Band-awared SSM block (BSSM) is as follows
featx+1 = CS (LN (feat))) O SILU (LN (feat*)) + featy.
(10)
where feat denotes the backbone features and CS (-) represents the band-awared scanning operation which employs the following operation sequence: OWCon + SiLU - SSM + LN.
3.4 Loss Function
In this paper, we use C1 loss to optimize the reconstructed HSI at the pixel level
Cree
1
-Y)
(11)
H
where C is the number of channels in the reconstructed HSI, Ý (1) represents the predicted value for pixel and Y (i) is its corresponding ground truth.
Empirical Results
4.1 Experimental Settings
Dataset. To validate the effectiveness of the proposed network, we conducted experiments on two datasets. The first dataset is the CAVE dataset (54] provided by Columbia University, which contains 32 HSIs. Each HSI consists of 31 spectral bands with a spectral interval of 10 nm, covering the spectral range from 400 nm to 700 nm. We randomly selected 20 HSIs for training, 6 HSIs for validation, and HSIs for testing. The second dataset the Harvard dataset (14] provided by Harvard University. It contains 50 HSIs covering both indoor and outdoor scenes. Each HSI consists of 31 spectral bands with 10 nm interval, covering the spectral range from 420 nm to 720 nm. We randomly selected 30 HSIs for training, 10 HSIs for validation, and 10 HSIs for testing.
Implementation Details. We implemented GPU and built in the PyTorch framework. In the training phase, the Adam optimizer [17 was used to optimize the model parameters. The initial learning rate set to 4 10 4 and the learning rate was decayed using a cosine annealing schedule with minimum value of x 10 The batch size was set to 32. We cropped 64 64 patches from 3D cubes and input them into the network. We the number of recursive levels to 5, where each atomic generation module reconstructs a two-channel image. The threshold parameter in Eq. (8) empirically set 0.5.
network the PC with single NVIDIA RTX 4090
4.2 Baseline Methods
We compared our FRN with seven SOTA spectral reconstruction methods: HSACS 29], SSRNet [6 HSRNet (20), AWAN (28), MST++ [10), LTRN [15), and MSFN [52).

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4.3 Metrics
To evaluate the reconstruction quality of HSIs, we adopt four widely used IQA metries: peak signal- to-noise ratio (PSNR), structural similarity index (SSIM) [5I]. root mean square error (RMSE), and universal image quality index (UIQI) [5). PSNR quantifies reconstruction quality by computing the ratio of signal variance to noise, providing a measure sensitive to pixel-level errors. SSIM assesses the perceptual similarity between the reconstructed image and the ground truth by jointly considering luminance, contrast, and structural information. UIQI evaluates the consistency of pixel distributions by comparing the means and variances of the reconstruction and ground truth. Moreover, we compared the number of parameters of FRN with those methods.
Table 1: Performance comparison of different methods on CAVE and Harvard datasets. The best values are bolded. The up or down arrow indicates higher or lower metric, corresponding to better performance.
CAVE
Harvard
Method
Pa
PSNRT
RMSEL
UIQIT
SSIM
PSNRT
RMSE,
UIQIf
SSIM
HSACS
19.74
37.9112
5.4099
0.8389
0.9765
42.1360
3.3203
0.8586
0.9762
SSRNet
0.39
38.6807
4.9824
0.8573
0.9794
42.1070
3.5370
0.8608
0.9760
HSRNet
0.77
38.4459
4.6511
0.8527
0.9801
41.6952
3.5459
0.8571
0.9747
MST++
1.62
38.5511
4.6304
0.8731
0.9832
42.4756
3,2552
0.8623
0.9773
AWAN
21.36
39.4262
4.8245
0.8597
0.9798
42.2312
3.5034
0.8616
0.9769
LTRN
0.67
39.7349
4,3095
0.8702
0.9832
42.4953
3.3112
0.8632
0.9770
MSEN
2.48
39.8430
4.0372
0.8877
0.9860
42.6455
2.9916
0.8715
0.9771
Ours
0,30
41.0522
3.6243
0.9010
0.9900
42.8762
2.8933
0.8791
0.9774
1
HSACS
SSRNet
HISRNN
AWAN
LTRN
MISEN
0
0.01
0.08
0.12
0.16
0.2
Figure 5: Comparison the reconstruction results different methods on one scene from the CAVE dataset, including seven SOTA methods and our FRN. We select three bands (20, 25, and 31) for visualization.

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4.4 Performance Evaluation
Numerical Results. The quantitative results of different methods on the CAVE and Harvard datasets are presented in Tab. [ Our method consistently achieves superior performance across all evaluation metrics. On the CAVE dataset, the average PSNR and SSIM our method reach 41.08 41.05 dB and 0.99, respectively, outperforming the second-best results by 1.2 dB and 0.004. On the Harvard dataset, our method achieves a PSNR 42.87 dB, surpassing the second-best results by 0.23 dB. Additionally, can be observed that, compared to other methods, FRN achieves higher reconstruction quality while requiring the fewest model parameters.
HSACS
SSRNet
HSKNet
AWAN
MST++
LTRN
MSFN
Ours
Figure 6: Comparison of the reconstruction results of different methods on one scene from the Harvard dataset, including seven SOTA methods and our FRN. We select three bands (10, 20, and 31) for visualization.
Spedral Density Curves
Spectral Densit Curves
GT, 10000
07, 10000ommt1 0000
Our,,
03
0.3
LTRN, coemo sona
LTRN commt 9632
MSFNL comm5
MSFK, camo 5673
HSPtod, comoo U077
Höitree con-o 2945
AWAN
canvo
Densty
02
HSACS cormo 596a
Denaky
0.2
HSACS coemo 9630
0.15
0.15
0.06
0.05
400
450
500
580
800
650
700
400
450
500
600
650
700
Wavalength
Wavelangth (nm)
Figure 7: Comparison of the spectral curves among different methods on CAVE (left) and Harvard (right) datasets.
Visual Results. Fig. and Fig. show the reconstruction results of different methods on the CAVE and Harvard datasets, respectively. We select three channels from each scene for qualitative comparison. To provide more intuitive comparison, we also present the residual maps between the predicted results and the ground truth. By zooming into local regions, it can be observed that our method reconstructs results that are closer to the ground truth in terms of spatial details and contrast.
The corresponding spectral curve in Fig. 7 indicates FRN achieves higher spectral accuracy.

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Table 2: Ablation studies of suppression threshold a on CAVE dataset. 'w/o' refers the setting where the band-aware mask not used (only with vanilla VMamba).
Config
PSNR1
RMSEL
UIQ
SSIM
w/o
39.7482
4.2998
0.8758
0.9840
a 0.2
39,9022
4.1562
0.8820
0.9852
a 0.3
40.3285
3,8683
0.8911
0.9866
a 0.5
41.0522
3.6243
0.9010
0.9900
a 0.7
40.1822
4.1022
0.8854
0,9860
a 0.8
37,4822
5.8448
0.7822
0.9573
Table 3: Ablation studies of the number of recursive levels on CAVE dataset. "w/o' means reconstruct the HSI from the RGB image in one step.
Table 4: Ablation studies the number of reference spectral on CAVE dataset. "w/o RGB' refers to exclud- ing the RGB image from each reconstruction level.
Config
PSNRT
RMSEJ
UIQIT
SSIM
Config
PSNR1
RMSEL
UIQIT
SSIM
w/o
39.8644
3,8683
0.8898
0.9883
w/ RGB
38.6244
5.1320
0.8448
0.9773
M-2
40.2210
3.7996
0,9001
0.9884
S=2
40.3981
3.8862
0.8962
0.9884
M=3
40.6382
3.7057
0,9004
0.9886
S=3
40.8286
3.7900
0.8989
0.9886
M=5
41.0522
3.6243
0.9010
0.9900
S=4
41.0522
3.6243
0,9010
0.9900
S=5
40.8744
3.7458
0.8993
0.9888
4.5 Ablation Study
Band-awared Mask. We investigated the impact of the suppression threshold Tab. 2 shows that setting a either too high or too low negatively affects the network performance. When the threshold too low, the suppression effect is weakened, and low-correlation regions introduce redundant interference to feature learning. Conversely, an excessively high a causes the SSM to suppress informative features, resulting in information loss.
Recursive Levels. We evaluated the impact of the number of recursive levels on the reconstruction performance on CAVE dataset. By default, we set M 5, which means that each BAMamba
generated new spectral channels based on the input from the previous level (23 = 32). In addition, also attempted reconstruct the HSI from the RGB image in one step. Tab. 3 shows that the reconstruction quality improves as the number of recursive levels increases. This is because each atomic generation step deals with fewer unknowns, thereby reducing the difficulty of solving the ill-posed problem.
Spectral Cues. We conducted ablation studies the number of reference channels (wavelengths), denoted as S, fed into each atomic generator. By default, we input RGB images into each atomic generator to provide spectral priors. In Tab. we found that setting S 4 yields relatively optimal performance. smaller value of limits the amount of reference information available to the network, while larger value may introduce noisy features. Another notable finding that excluding the RGB image from each reconstruction level leads to substantial decline in reconstruction quality. This degradation is attributed to the loss of structural and contrast priors inherently embedded in the RGB image, which are essential for accurate spectral learning.
5 Conclusion
In this paper, we propose fractal-based recursive spectral reconstruction network (FRN). FRN estab- lishes new paradigm for spectral reconstruction by recursively invoking an atomic reconstruction module to progressively predict spectra from wide to narrow bands. By introducing the concept of fractals, FRN aligns with the low-rank nature HSI data and exhibits structural self- silf-iiiilarity across different levels of the network. Furthermore, to alleviate the computational burden caused by the recursive design, we develop BAMamba, an atomic generation module based on SSM. Extensive experiments on multiple datasets demonstrate that FRN achieves outstanding performance in HSI reconstruction. Nevertheless, the recursive calling mechanism introduces significant computational overhead, which represents important direction for future optimization.

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6 Acknowledgments
This work was supported in part by the Dreams Foundation of Jianghuai Advance Technology Center project under Grant D002: in part by the National Natural Science Foundation of China under Grant 82172073, and Grant 6227144 1430; and in part by the Open Fund of the National Key Laboratory of Infrared Detection Technologies.
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Reviews:
[{"review_id": "YDZnfVCeab", "reviewer": "Reviewer_XWjn", "summary": "This paper introduces FRN, a novel framework for reconstructing hyperspectral images (HSIs) from RGB inputs. Drawing inspiration from fractal geometry, FRN decomposes the spectral reconstruction task into a recursive hierarchy of atomic sub-band generators. This design progressively models spectral correlations from coarse to fine granularity, aligning with the self-similar and low-rank nature of hyperspectral data. Complementing this, the authors propose BAMamba, a state-space model enhanced with adaptive, band-aware spatial masking, which selectively suppresses spatially uninformative regions. Extensive experiments on CAVE and Harvard datasets demonstrate that FRN significantly outperforms state-of-the-art methods in both accuracy and parameter efficiency.", "questions": "1. In Table 3, deeper recursion levels appear to yield better performance. Is there a trade-off point where performance saturates or degrades due to over-recursion? Reporting trends beyond 5 levels or plotting performance vs. depth could offer insight into this trade-off.\n2. Since the architecture is jointly inspired by fractal generative principles and integrates Mamba-style state-space modeling, it would be insightful to include an ablation that disentangles the contributions from the fractal recursion and from BAMamba. How much gain is attributable to each component? \n3. Given the novelty and competitive performance, open sourcing would benefit the research community and increase the impact of the work.", "limitations": "Yes. The authors have clearly articulated the limitations of their work and have thoughtfully considered potential societal risks.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n1. The use of fractal-based recursion to progressively reconstruct spectral bands introduces a new paradigm in hyperspectral image reconstruction, well-aligned with the hierarchical structure and redundancy in HSI data.\n2. The BAMamba module effectively leverages the spatial sparsity of informative regions, reducing unnecessary information and improving generalization.\n3. The proposed method achieves strong performance on standard datasets, outperforming prior works with notably fewer parameters, showcasing both effectiveness and efficiency.\n\n## Weaknesses\n1. While the model reduces parameter count and theoretical complexity, the recursive nature of inference introduces sequential dependencies that may hinder real-time performance, especially for high-resolution HSI reconstruction. Notably, the paper does not report any runtime or latency metrics, which would be essential for evaluating deployment feasibility.\n2. The ablation studies, though helpful, do not fully disentangle the relative contributions of the fractal recursion and BAMamba (see following Additional Feedback). A dedicated component-wise analysis would help clarify their individual and joint effects on performance.\n3. From the experimental setup, it appears that a separate model is trained for each dataset. The authors are encouraged to report or discuss the training cost.", "was_revised": true, "final_justification": "The authors have addressed my concerns raised during the review stage. I consider this to be an above-average paper and therefore maintain my original rating.", "rebuttal": "Thank you for your review. We will reply to your questions in order.\n1. To address your concerns regarding the inference efficiency of FRN, we further provide a comparison of the inference time and memory cost required by each method for processing a single image (Taking a single sample from the CAVE dataset as an example.):\n\nMethod | Time(S)$\\\\downarrow$ | Mem.(G)$\\\\downarrow$\n-------|-------|-------\nHSACS | 2.39 | 0.208 \nHSRNet | 0.94 | 0.031 \nSSRNet | 1.03 | 0.016 \nAWAN | $\\textbf{0.89}$ | 0.413 \nMST++ | 1.08 | 0.028 \nLTRN | 1.94 | 0.015 \nMSFN | 3.69 | 0.069 \n$\\\\textbf{FRN}$ | 0.92 | $\\textbf{0.010}$ \n\nIt can be observed that FRN has the second fastest inference speed after AWAN and the lowest memory cost.\n\n2. Thank you for your constructive comments. Regarding the contributions of the fractal recursion, we provide a 'w/o' configuration in Table 3, which means reconstructing the HSI from the RGB image in one step (without using fractal recursion). It can be observed that all metrics drop significantly on the CAVE dataset (with PSNR decreasing by $1.18$ dB).\n\nAs for your suggestion on conducting a component-wise analysis of BAMamba, we attempted to replace the atomic generator with MSFN. The results on the CAVE dataset are as follows:\n\nConfig | PSNR$\\\\uparrow$ | RMSE$\\\\downarrow$ | UIQI$\\\\uparrow$ | SSIM$\\\\uparrow$\n-------|-------|-------|-------|-------\nMSFN | 40.0611 | 3.9624 | 0.8890 | 0.9866\n$\\\\textbf{BAMamba}$ | $\\\\textbf{41.0522}$ | $\\\\textbf{3.6243}$ | $\\\\textbf{0.9010}$ | $\\\\textbf{0.9900}$\n\nIt can be found that BAMamba outperforms MSFN, achieving a $0.99$ dB higher PSNR on the CAVE dataset. When comparing the contributions of fractal recursion and BAMamba in a component-wise manner, we observe that the former contributes more significantly. We attribute this to the fact that fractal recursion serves as a general strategy that fundamentally reduces the difficulty of solving the ill-posed problem. In contrast, the latter (a deep neural network for HSI reconstruction) may be more prone to overfitting due to potential limitations in its design.\n\n3. We trained BAMamba separately on the two datasets, and all experiments were conducted on a single NVIDIA RTX 4090 GPU. The specific training details are provided in Section 4.1. The default setting for epochs is $300$. The training time on the CAVE dataset was $1.58$ hours with a memory cost of $12.8$ GB, while the training time on the Harvard dataset was $13$ hours with a memory cost of $12.8$ GB.\n\n4. In fact, we later identified this experimental gap and further conducted experiments by setting the recursion levels to $M=6$ and $n=2$. The results on the CAVE dataset are as follows:\nConfig | PSNR$\\\\uparrow$ | RMSE$\\\\downarrow$ | UIQI$\\\\uparrow$ | SSIM$\\\\uparrow$\n--------|--------|--------|--------|--------\n$\\\\textbf{M=5}$ | $\\\\textbf{41.0522}$ | $\\\\textbf{3.6243}$ | $\\\\textbf{0.9010}$ | $\\\\textbf{0.9900}$\n$M=6$ | 41.0233 | 3.6441 | 0.9005 | 0.9887\n\nDeeper recursion introduced more redundant information into the reconstruction output, leading to a decline in reconstruction performance.\n\n5. Same as Question 2.\n\n6. We will release our code on GitHub."}, {"review_id": "SFTqyQncHn", "reviewer": "Reviewer_fsWJ", "summary": "The authors creatively introduce the mathematical concept of fractals into spectral reconstruction by recursively reconstructing atomic spectral cubes, thereby reducing the complexity of the task. Furthermore, to alleviate the computational burden introduced by recursion, the authors adopt an efficient design based on the Mamba architecture. Experimental results validate the effectiveness of the proposed approach.", "questions": "The author needs to provide a more detailed explanation of how M is selected and how the final number of generated channels is determined.", "limitations": "See Weaknesses.", "rating": 6, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:  \n[1] The author skillfully integrates the concept of fractals into spectral reconstruction and effectively leverages the Mamba network to alleviate the computational burden associated with multiple recursive calls.  \n[2] Decomposing the reconstruction of the entire HSI into the reconstruction of multiple atomic cubes, while progressively providing more information (inputs) for subsequent reconstructions and simultaneously reducing the outputs (unknowns), is an interesting idea.  \n[3] Experimental results confirm the effectiveness of FRN.  \n[4] The paper is clearly written and well composed.    \n  \nWeaknesses:  \n[1] The description of the hyperparameter M in Section 4.5 is unclear, and it is also not explained how different values of M ultimately generate a HSI with a fixed number of channels.  \n[2] Section 4.5 lacks further experiments on the Recursive Levels, such as evaluating performance at M=6, to better justify the choice of this hyperparameter.  \n[3] The paper lacks a detailed explanation of the reference channels mentioned in Section 4.5.", "was_revised": true, "final_justification": "The authors have responded clearly and thoroughly to my concerns. They provided detailed clarification on the recursive generation process, including how the hyperparameter M influences the final number of spectral channels. The additional experimental results further support their design choices. Given the solid empirical results, I believe the contribution is stronger than I initially judged.", "rebuttal": "Thank you for your review. \n\n1. We will include an example to more concretely illustrate how the recursive levels M (in Section 4.5) influence the hyperspectral image generation process. As shown in Figure.2 (a), in this paper, we input a 3-channel RGB image into the FRN and generate a $K=31$-channel hyperspectral image. However, the generation process is not an end-to-end operation in the traditional sense. Instead, it requires $M$ stages to complete, with each stage employing the same U-Net style BAMamba model as the atomic reconstruction network. Assuming the default setting of $M=5$, the output size of BAMamba at each stage is fixed to $2 \\\\times H \\\\times W,$ that is, $n=2$ spectral channels (where $M=\\\\log_{n}{K}$). The complete process is as follows:\n\nStage 1 ($1$-call, ($n \\\\times 1=2$)-band generation): \n\n$f(x_r, x_g, x_b) = (x_1, x_2)$; \n\n\nStage 2 ($2$-call, ($n \\\\times 2=4$)-band generation): \n\n$f(x_r, x_g, x_b, x_1) = (x_1, x_2)$, $f(x_r, x_g, x_b, x_2) = (x_3, x_4)$; \n\n\nStage 3 ($4$-call, ($n \\\\times 4=8$)-band generation): \n\n$f(x_r, x_g, x_b, x_1) = (x_1, x_2)$, $f(x_r, x_g, x_b, x_2) = (x_3, x_4)$, $f(x_r, x_g, x_b, x_3) = (x_5, x_6)$, $f(x_r, x_g, x_b, x_4) = (x_7, x_8)$;\n\n\nStage 4 ($8$-call, ($n \\\\times 8=16$)-band generation): \n\n$f(x_r, x_g, x_b, x_1) = (x_1, x_2)$, $f(x_r, x_g, x_b, x_2) = (x_3, x_4)$, $f(x_r, x_g, x_b, x_3) = (x_5, x_6)$, $f(x_r, x_g, x_b, x_4) = (x_7, x_8)$, $f(x_r, x_g, x_b, x_5) = (x_9, x_{10})$, $f(x_r, x_g, x_b, x_6) = (x_{11}, x_{12})$, $f(x_r, x_g, x_b, x_7) = (x_{13}, x_{14})$, $f(x_r, x_g, x_b, x_8) = (x_{15}, x_{16})$;\n\n\nStage 5 ($16$-call, ($n \\\\times 16=32$)-band generation): \n\n$f(x_r, x_g, x_b, x_1) = (x_1, x_2)$, $f(x_r, x_g, x_b, x_2) = (x_3, x_4)$, $\\\\cdots$, $f(x_r, x_g, x_b, x_{15}) = (x_{29}, x_{30})$, $f(x_r, x_g, x_b, x_{16}) = (x_{31}, x_{32})$.\n\n\nThe value of $M$ and the number of spectral channels in the HSI must satisfy the condition that $n^M$ is closest to $K$. This ensures that the FRN can generate a sufficient number of spectral bands without introducing excessive redundant outputs. For example, when $M=5$, the FRN ultimately produces $32$ channels ($>31$), and the extra final channel will be removed.\n\n2. We further provide experimental results for the case of $M=6$ and $n=2$, where the FRN outputs $2^6=64$ channels. These were mapped to $32$ channels by computing the channel-wise mean, and the final extra channel was removed. The evaluation metrics are as follows:\nConfig | PSNR$\\\\uparrow$ | RMSE$\\\\downarrow$ | UIQI$\\\\uparrow$ | SSIM$\\\\uparrow$\n--------|--------|--------|--------|--------\n$\\\\textbf{M=5}$ | $\\\\textbf{41.0522}$ | $\\\\textbf{3.6243}$ | $\\\\textbf{0.9010}$ | $\\\\textbf{0.9900}$\n$M=6$ | 41.0233 | 3.6441 | 0.9005 | 0.9887\n\nDeeper recursion introduced more redundant information into the reconstruction output, leading to a decline in reconstruction performance.\n\n3. In each stage, the input to $f(\\\\cdot)$ includes not only the RGB image but also the intermediate outputs from the previous stage, referred to as \"Spectral Cues\" (as mentioned in Section 4.5). In practice, instead of simply adding one intermediate result from the previous stage as an additional condition to $f(\\\\cdot)$, we compute the Euclidean distances between all intermediate outputs of the previous stage and the current wavelength to be reconstructed by BAMamba. Then, we select the closest channels as additional cues. We found that the reconstruction achieves the best performance when the number of reference channels is set to $4$.\n\n4. The values of $M$ and $n$ are determined such that $n^M$ approximates $31$ ($K$) as closely as possible."}, {"review_id": "7fnQv6pUiA", "reviewer": "Reviewer_5ryr", "summary": "This paper introduces FRN, a network for reconstructing hyperspectral images (HSIs) from RGB images, addressing the limitations of existing methods with a unique approach based on fractal principles and progressive reconstruction. BAMamba, a band-aware state space model, further enhances efficiency and accuracy by filtering out irrelevant information.", "questions": "See weakness.", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths：\n\n1. Progressive reconstruction is a feasible idea and would have been used in scenarios with limited resources.\n\n2. FRN consistently achieves superior performance compared to exsiting methods in both quantitative and qualitative evaluations, reconstructing HSIs with higher accuracy and detail.\n\n3. The recursive design and BAMamba module effectively reduce the computational burden of the reconstruction process, making FRN more efficient and suitable for handling high-dimensional HSI data.\n\nWeaknesses:\n\n1. Fractals are generally adopted in two-dimensional [1] and above spaces. In the one-dimensional space of the spectrum, the fractal does not more sense than simple linear interpolation.\n\n2. The Mamba model has been widely applied in the field of spectral reconstruction, and the related methods[2-7] are not discussed in this paper. From the current manuscript, we cannot find contributions beyond the previous work.\n\n3. The core contributions of this work include two parts: the fractal reconstruction framework and the Mamba-based network module. The former is a progressive reconstruction network, and it is hard to say that it truly surpasses the previous framework design. The latter introduced the Mamba network and made no significant contribution compared with the previous spectral reconstruction work based on Mamba. Therefore, the contribution of this work is very limited.\n\n[1] Fractal generative models, arvix 2025.\n\n[2] MambaHSI: Spatial-spectral mamba for hyperspectral image classification, TRGS 2024.\n\n[3] Spectral-spatial mamba for hyperspectral image classification, arvix 2024.\n\n[4] Dual hyperspectral mamba for efficient spectral compressive imaging, arvix 2024.\n\n[5] VmambaSCI: Dynamic Deep Unfolding Network with Mamba for Compressive Spectral Imaging, MM 2024.\n\n[6] MambaSCI: Efficient Mamba-UNet for Quad-Bayer Patterned Video Snapshot Compressive Imaging, NeurIPS 2024.\n\n[7] Detail Matters: Mamba-Inspired Joint Unfolding Network for Snapshot Spectral Compressive Imaging, AAAI 2025.", "was_revised": true, "final_justification": "The authors did not directly address our main concerns in the reply.  The author's responses merely repeated what they had done, avoiding discussion of some core issues, including the difference between claimed contribution and practical implementation, and the lack of ablation experiments with other methods.\n\n1. Although the authors claimed that this work is a fractal-based recursive method and emphasized that it is the first time to introduce the concept of fractals to the spectral reconstruction task, there is no real relationship between this work and fractal-based design. It's just a basic recursive network; the only connection is that they both use a recursive process.\n\n2. The authors seem not to understand the difference between the self-ablation experiment and the comparative ablation experiment. The self-ablation experiment aims to demonstrate that incremental improvements are effective. This does not show any advantages of the proposed method over existing designs. \n\nIn summary, this work indeed has some innovation, but they are overclaimed and not solid. (And there have already been a large number of mamba-based works in spectral reconstruction fields, which are not referred to.)  The experiments also fail to demonstrate what real improvements this design has over other existing methods, rather than simple baselines.", "rebuttal": "Thank you for your review.\n1. In fact, the authors of [1] did not state that \"fractals are generally adopted in two-dimensional and above spaces.\" The core of fractals lies in the \"$\\\\textbf{self-similarity}$\" inherent in both $\\\\textbf{the data and the model}$. For hyperspectral image (HSI) data, the strong correlation between adjacent spectral bands precisely indicates the presence of self-similarity along the spectral dimension. The HSI reconstruction task is essentially an ill-posed problem of generating many more bands (e.g., 31-channel HSI) from a few bands (e.g., RGB 3-channel image). This task can be decomposed into the reconstruction of atomic bands, and the networks involved in each sub-process also possess structural self-similarity. Therefore, the fractal concept is very well matched to the task addressed in this paper.\n\n2. These Mamba-based spectral reconstruction methods have not explored the impact of SSM on spectral reconstruction from the perspective of $\\\\textbf{redundant information removal}$. Redundant information among spectral bands is one of the key factors hindering reconstruction performance. The band-aware mask introduced in BAMamba is a unique design in this paper aimed at addressing this issue. This scheme enables Mamba to learn more compact spectral and spatial correlations. Furthermore, existing studies typically stack multiple SSM layers to improve network performance, which weakens the inherent advantage of SSM’s low computational complexity. In contrast, the introduction of the mask reduces the involvement of irrelevant information in computations, further enhancing $\\\\textbf{inference efficiency}$. Experimental results also validate the effectiveness of this scheme in both reconstruction quality and efficiency. Therefore, BAMamba’s design demonstrates clear innovation over previous approaches from the perspective of $\\\\textbf{task understanding}$.\n\n3. The progressively designed spectral reconstruction network based on fractal principles represents $\\\\textbf{a novel paradigm}$ for spectral reconstruction. It fundamentally reduces the difficulty of solving the ill-posed problem, which was $\\\\textbf{not addressed by previous methods}$. Experimentally, our method significantly outperforms prior approaches, and we believe it will provide valuable references for the community. On the other hand, by leveraging the physical or statistical characteristics of HSI data, this paper employs SSM as a backbone component to reduce the resource consumption required for processing high-dimensional data. Additionally, by introducing a mask, redundant information interference is partially eliminated, further improving the model’s inference efficiency and mitigating the negative effects caused by recursive calls.\n\n[1] Fractal generative models, arvix 2025."}, {"review_id": "wErbrLSO8Y", "reviewer": "Reviewer_opod", "summary": "The author introduces the concept of fractals into the spectral reconstruction task, treating spectral reconstruction as a progressive process—either predicting from broad to narrow bands or adopting a coarse-to-fine approach to infer the next wavelength. This strategy reduces the overall task complexity and offers a novel perspective. Extensive experiments conducted on different datasets further demonstrate the effectiveness of the proposed approach.", "questions": "The author needs to provide a detailed explanation in Section 4.5 regarding how the reference channels were selected.", "limitations": "See Weaknesses.", "rating": 6, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths：\n\n1.The author is the first to introduce the mathematical concept of fractals into the spectral reconstruction task, formulating it as a progressive process. By constraining the generation of intermediate results, this approach effectively reduces the complexity of the problem and provides a fresh, innovative perspective.\n\n2.The quantitative and visual experiments conducted by the author on different datasets demonstrate the effectiveness of the proposed method, while the ablation studies further confirm the validity and rationality of the core modules.\n\n3.The overall description of the method in this paper is clear and easy to follow.\n\nWeaknesses：\n\n1.While the recursive approach is innovative, it may also introduce additional complexity, potentially limiting its applicability in real-time scenarios.\n\n2.Section 4.1 lacks a description of the training epoch settings, which is crucial for ensuring reproducibility.\n\n3.The paper lacks a detailed explanation of the reference channels discussed in Section 4.5, which may affect the clarity and understanding of the proposed method.", "was_revised": true, "final_justification": "After reviewing the author’s responses to all the reviewers, I find that the author provides a more detailed explanation of the paper’s insight, so I decide to increase my score.", "rebuttal": "Thank you for your review.\n\n1. In fact, since the FRN requires multiple recursive calls to the atomic network, the GFLOPs increase accordingly. Taking this into consideration, we designed the lightweight BAMamba. The comparison of GFLOPs among different methods is as follows:\nMethod | GFLOPs$\\\\downarrow$ \n--------|--------\nHSACS | 82.18\nHSRNet | 3.00\nSSRNet | 1.58\nAWAN | 16.52\nMST++ | 1.46\nLTRN | $\\\\textbf{0.85}$\nMSFN | 2.04\n$\\\\textbf{FRN}$ | 1.45\n\n2. The default setting for epochs is $300$.\n\n3. At each stage, the input to $f(\\\\cdot)$ includes not only the RGB image but also the intermediate outputs from the previous stage, referred to as \"Spectral Cues\". In practice, we select several channels with the smallest Euclidean distances between all intermediate outputs from the previous stage and the current wavelength to be reconstructed by BAMamba, using them as additional cues. We found that the reconstruction results are optimal when the number of reference channels is $4$."}]

Author rebuttal:

Meta-review: This paper introduces FRN, a fractal-inspired recursive network for hyperspectral image reconstruction, complemented by a band-aware Mamba module (BAMamba) to enhance efficiency and accuracy. The key scientific claim is that modeling spectral correlations in a coarse-to-fine recursive manner aligns well with the self-similar, low-rank nature of hyperspectral data, while BAMamba selectively suppresses uninformative regions to improve generalization. Strengths highlighted by reviewers include the novelty of fractal-based recursion in HSI reconstruction, solid empirical results surpassing prior methods, parameter efficiency, and a clear presentation. Weaknesses include limited runtime analysis, incomplete ablations disentangling recursion and BAMamba, and insufficient discussion of related Mamba-based methods. During rebuttal, the authors clarified the recursive design, explained hyperparameter settings (e.g., M), and provided additional analysis on spectral channel generation, which satisfactorily addressed most concerns. Despite some remaining questions on broader comparisons, the overall contribution is innovative, impactful, and well supported by experiments.
Decision: Accept (poster)