RBSRICNN: Raw Burst Super-Resolution through
Iterative Convolutional Neural Network
Rao Muhammad Umer
Department of Computer Science
University of Udine
engr.raoumer943@gmail.com

Christian Micheloni
Department of Computer Science
University of Udine
christian.micheloni@uniud.it

Abstract
Modern digital cameras and smartphones mostly rely on image signal processing(ISP) pipelines to produce realistic colored RGB images. However, comparedto DSLR cameras, low-quality images are usually obtained in many portablemobile devices with compact camera sensors due to their physical limitations.
The low-quality images have multiple degradations i.e., sub-pixel shift due tocamera motion, mosaick patterns due to camera color filter array, low-resolution
due to smaller camera sensors, and the rest information are corrupted by the noise.
Such degradations limit the performance of current Single Image Super-resolution(SISR) methods in recovering high-resolution (HR) image details from a single lowresolution (LR) image. In this work, we propose a Raw Burst Super-Resolution
Iterative Convolutional Neural Network (RBSRICNN1 ) that follows the burst
photography pipeline as a whole by a forward (physical) model. The proposed
Burst SR scheme solves the problem with classical image regularization, convex
optimization, and deep learning techniques, compared to existing black-box datadriven methods. The proposed network produces the final output by an iterativerefinement of the intermediate SR estimates. We demonstrate the effectiveness of
our proposed approach in quantitative and qualitative experiments that generalize
robustly to real LR burst inputs with onl synthetic burst data available for training.

1

Introduction

The Burst Super-resolution is the task of fusing several low-resolution (LR) frames to produce a single
high-resolution (HR) image. It is a fundamental low-level vision and image processing problem withvarious practical applications in satellite imaging, deforestation, environment and climate changemonitoring, mobile photography, video enhancement, and security and surveillance imaging as well.
In the last decade, most of the photos have been taken using built-in smartphone cameras, where theresulting low-quality images are inevitable and undesirable due to their physical limitations. Since
the mobile cameras are small and versatile due to their compact camera sensors, there are several key
limitations [6] of the mobile phone cameras as compared to a DSLRs i.e.small sensor size, limited
aperture, noise (i.e.photon shot and read noise) and limited dynamic range, limited depth of field
due to fixed aperture, limited zoom and color sub-sampling. As a result, the image quality is notcomparable with that of DSLR cameras. Therefore, the focus is shifted towards software solutions to
mitigate cameras hardware limitations.
Mathematically, the Burst SR problem is described as the following forward image observation modelfor degradation process:yi = MHSi (x̃) + ηi ,1

i = 1, . . . , B(1)

Our code and trained models are publicly available at https://github.com/RaoUmer/RBSRICNN

Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021).

where, yi is the i-th observed image of the LR burst B images, M is a mosaicking operator that
corresponds to the CFA (Color Filter Array) of a camera (usually Bayer), H is a down-sampling
operator (i.e.bilinear, bicubic, etc.) that resizes an HR image x̃ by a scaling factor r, Si is an affine
transformation of the coordinate system of the image x̃ (i.e.translation and rotation), and ηi is anadditive heteroskedastic Gaussian noise related to photon shot and read noise. Recovery of the latent
HR image x̃ from the LR burst belongs to the broad spectrum of inverse problems. The operators
M and H are typically ill-conditioned, i.e.singular. Further, this coupled with the presence of thenoise ηi and the affine transformation Si perturbing the measurements leads to an highly ill-posed
nature of an inverse problem, where a unique solution does not exist. Burst photography pipeline
with multi-frame super-resolution (MFSR) is the most common way to deal with such a scenario thatgenerates the HR image from a low-quality burst of raw sensor images.
(a) HR Reference(b) Input LR Bursts(c) Burst SR (Ours)
Numerous works have beenaddressed towards the task of
SISR [16, 25, 36, 37, 35, 24, 38,
31, 29, 27, 40, 23, 13, 9] andreal-world SISR [20, 33, 26, 11,28, 30, 32]. Due to the ill-posed
nature of the SISR problem, theexisting methods have limited
performance to recover high Figure 1: An image from the Zurich RAW to RGB Dataset [15]frequency details through single (testset), where we present (a) the ground truth HR reference
image learned priors. On the image of size 384 × 384 × 3, (b) the input LR bursts of sizeother hand, the MFSR aims to (W × H × C × B) 48 × 48 × 4 × 14, and (c) the Burst SR output
recover the latent HR image using of size 384 × 384 × 3 of our network (RBSRICNN). All images
multiple LR frames by exploiting are converted from raw sensor space to sRGB for visualization
the additional signal information purpose.
due to sub-pixel shifts, comparedto the SISR methods. The recent works [12, 18, 19, 34, 7, 3] have demonstrated the potential of
MFSR methods that aim to fuse multiple LR frames to reconstruct a HR output. However, the deeplearning based Raw Burst SR methods are black-box data-driven approaches with larger model sizedue to not directly model the image formation process, while our proposed scheme (RBSRICNN)
has the merit of interpretability and small model size with good reconstruction results by following
the image observation model as shown in Fig. 1. Our proposed scheme exploits a powerful image
regularization and large-scale optimization techniques by training a deep CNNs in an iterative
manner to produce the final SR output with an iterative refinement of the intermediate SR estimates.
PSNR=36.92
SSIM=0.9545
LPIPS=0.0631

2

Proposed Methodology

2.1

Problem Formulation

By referencing to the image observation model (1), the recovery of x from yi mostly relies on thevariational approach by combining the observations and prior knowledge, and the solution is obtainedby minimizing the following objective function:x̂ = arg minxB
1 X
kyi − MHSi (x)k22 + λR(x),22σ B i=1(2)where the first term corresponds to the data fidelity term that measures the closeness of the solution
to the observations, while the second term (i.e.R(x)) corresponds to the regularization term that
encodes any priors knowledge about the GT image, and λ is the trade-off parameter that governs thecompromise between the data fidelity and the regularizer term. The Eq. (2) can be also written in thefollowing form:
J(x) = arg minx1ky − Axk22 + λR(x),2σ 2 B(3)

where the A=MHS corresponds to the camera response. In the next section 2.2, we employ a proper
optimization strategy to find the solution that minimizes the objective function (3) to get the required
latent HR image.
2

Eq.(6)

x2

x(k)

z(k)

ResnetDecoderResnetEncoderx1 z(1)

DecoderResnetEncoderz(0)Decoderx0

Encoder

ERDx(K)(SR output)yi(LR Bursts)
Eq.(7)

Eq.(7)

Eq.(7)

Figure 2: Visualizes the structure of the our proposed iterative Raw Burst SR scheme. Given an
LR burst images (yi ), each network’s stage produces a new estimate x(k+1) from the previous step
estimate x(k) . A single optimizer is used for all network stages with shared structures and parameters.
2.2

Optimization Scheme

In the Majorization-Minimization (MM) [14, 10, 21] framework, an iterative algorithm for solving
the minimization problem x̂ = arg min J(x) takes the form x(k+1) = arg min Q(x; x(k) ), wherexx

Q(x; x(k) ) is the majorizer of the function J(x) at a fixed point x(k) by satisfying the following
two conditions: Q(x; x(k) ) > J(x), ∀x 6= x(k) and Q(x(k) ; x(k) ) = J(x(k) ). We need to upperbound the J(x) by a suitable majorizer Q(x; x(k) ) in order to get the required solution. Insteadof minimizing the actual objective function (3) due to its complexity, we minimize the majorizer
function Q(.) to produce the next solution estimate x(k+1) . By satisfying the above two properties ofthe majorizer function, iteratively minimizing Q(.; x(k) ) also decreases the actual objective function
J(.) [14]. We write a quadratic majorizer for the complete objective function (3) as the followingform:
1ky − Axk22 + g(x, x(k) ),2σ 2 B

(4)

T h
i

1 
x − x(k)αI − AT A x − x(k) ,
2
2σ B

(5)

˜ x(k) ) =d(x;To start an estimate x(k) , we have:g(x, x(k) ) =˜ ·) is a distance function between x and x(k) . To get a valid majorizer, we need to satisfy thewhere d(·,above two conditions such as g(x, y) > 0, ∀x 6= y and g(x, x) = 0. This suggests that αI − AT A
must be a positive definite matrix, which only holds if α > kAT Ak2 ⇒ α ≥ B. Finally, we proceedwith the following formulation to iteratively minimize the quadratic majorizer function Q(.) as:(k)x̂= arg min Q(x; x

(k)



(k)
) = d˜ x; x
+ λR(x) =

x

α
k 2
k
kx − z k2 + λR(x) + const. = Prox(λ/ασ2 )R(.) (z ), (6)2σ 2 B

T
T
T(k)where zk =xk +AT (y−Axk )⇒zk =x(k) + B1 B
) (see Fig. 2), and the const. does
i=1 Si H M (yi −MHSi x
not depend on x and thus it is irrelevant to the optimization task. The Prox(.) is the proximal operator
and it is computed as in [29]. Since the Eq. (6) is treated as the objective function of a denoisingproblem where z is the noisy observation, we employ a deep denoising neural network to get therequired solution estimate x̂(k) by unrolling the network into K finite stages. Moreover, in the Eq. (6),
we decouple the degradation operator A from the latent image x and now we need to tackle it with aless complex problem i.e.denoising. For the fast convergence and less computational cost, we adopt
a strategy similar to [18, 29, 19], where the trainable extrapolation weights w(k) are learnt directlyfrom the training data instead of the fixed ones [22].

P

2.3

Network Architecture and Training

The proposed Raw Burst SR scheme is shown in Fig. 2. We unroll the proposed RBSRICNN into
K stages, where each stage computes the refined estimate of the solution. yi is an input Raw
LR burst, x0 is an initial estimate, and xK is the final estimated SR image. We adapt the similar
Encoder-Resnet-Decoder architecture as done in [29]. Due to the iterative nature of our Burst SR
approach, the network parameters are updated by using Truncated Backpropagation Through Time
(TBPTT) algorithm as done in [18, 29] to train our network, where the sequence is unrolled intoa small number of k-steps out of total K and then the back-propagation is performed on the small
3

Table 1: Comparison with others. We compare our method with the common evaluation metrics(PSNR/SSIM/LPIPS). The quantitative SR results (×4 upscale) are shown over the synthetic and real
Burst SR test sets. The arrows indicate if high ↑ or low ↓ values are desired.
Burst SR Method
DeepJoint [12]+RRDB [33]DeepBurstSR [3]
HighRes-net [7]
RBSRICNN (ours)#Params[M]#Conv2d

17.26
5.25
1.11
0.38

371
48
25
12

Synthetic data

Real data

PSNR↑ SSIM↑

LPIPS↓

PSNR↑ SSIM↑ LPIPS↓

33.25
34.48
34.30
37.62

0.195
0.118
0.170
0.166

42.13
45.17
43.99
41.40

0.881
0.905
0.891
0.895

0.957
0.978
0.972
0.952

0.088
0.037
0.051
0.101

Fine-tuned
on Real data
3
3
3
7

k-steps. During the training, we use the following function to minimize the `1 -Loss between theestimated latent SR image (x(k) ) and ground-truth (GT) (x(gt) ) after k-steps as:
N

L = arg min L(Θ) =Θ

1X kkxi − xgt
i k1
2 i=1

(7)

where N is the mini-batch size and Θ are the trainable parameters of our network.

3

Experiments

3.1

Training data and evaluation metrics

We used 46, 839 and 1204 sRGB images from the Zurich RAW to RGB dataset [15] for the training
and the validation, respectively. We generate the synthetic RAW LR bursts with their corresponding
HR using the data generation code in [3], where the sRGB image is first converted to the Raw (linear)sensor space using an inverse camera pipeline [4], then the LR burst is generated by applying randomtranslations and rotations, followed by bilinear downsampling, further mosaicked and corrupted byrandom noise. For the evaluation of our method on the real dataset, we used the BurstSR testset
containing 639 real-world LR bursts, provided in the Burst SR challenge [2]. In the real LR bursts,
each burst sequence contains 14 RAW images captured using a handheld smartphone camera using
identical camera settings (e.g., exposure, ISO) resulting in a small random offset between the images
within the burst. We evaluated the trained model under PSNR, SSIM, and LPIPS [39] metrics. The
quantitative Burst SR results are evaluated on the raw linear sensor space.
3.2

Training description

We estimate the warp matrix (i.e.Si , refers to the section-2) to align the bursts to the base/reference
frame using the Enhanced Correlation Coefficient (ECC) [8] method as do in [19] for all experiments.
For those bursts whose are not aligned by the ECC method, we keep them in the training and testingdata by making the assumption of the identity matrix. For the training phase, we set the input Raw
burst LR patch sizes as 48 × 48 × 4 with their corresponding Raw HR patch sizes as 384 × 384 × 3 by
the scaling factor ×4. We use the LR burst size of 14. We train the network for 368k iterations witha batch size of 2 using Adam optimizer [17] with parameters β1 = 0.9, β2 = 0.999, and  = 10−8
without weight decay to minimize the loss (7). The learning rate is set to 10−3 for all iterations. We
unroll the proposed network into K stages, where we set K as 10. We implemented our method with
Pytorch 1.7.1. The experiments are performed under Windows 10 with i7-8700 CPU with 32GB
RAM and on NVIDIA GeForce RTX-3090 GPU with 24GB memory. The average running times(image per second on GPU) are 0.3350 and 0.8838 over the synthetic and real testsets, respectively.
3.3

Comparison with the Burst SR methods

We compared our method with existing Burst SR methods including DeepJoint [12]+RRDB [33],DeepBurstSR [3], and HighRes-net [7]. Table 1 compares the quantitative SR results of our methodwith others over the synthetic and real Burst SR testsets. We have achieved good performance on
the synthetic LR burst testset, while, the parameters and depth of our proposed network is much lessthan the other methods. On the real-world LR burst testset, the DeepBurstSR outperforms the others
methods in terms of PSNR/SSIM/LPIPS, while we have a comparable performance, even though
our method is not fine-tuned on the real training data with comparable visual results as shown in
Fig. 3. The fine-tuning [3] increases the performance, but it also further requires significant additional
4

HR GT

Input LR Burst

DeepBurstSR

BSRICNN (Ours)

Figure 3: ×4 SR visual comparison of the proposed RBSRICNN method with the existing Burst SR
methods on the real-world BurstSR [3] testset. All images are converted from the raw sensor space tosRGB for visualization purpose.
labelled training data that is difficult to collect in practice, and it is also more computational expensive
in terms of training time and hardware resources. We also participated in the NTIRE2021 Burst SR
Challenges [2] and our method (MLP_BSR) is ranked among other participants as well.
3.4

Ablation Study

For our ablation study, we compared the impact of different
numbers of input burst frames and iterative steps for the proposed Burst SR method in Table 2. It shows the generalization
ability of our method to the larger input LR bursts and iterative steps, and effective utilization of the information from themultiple LR frames in order to improve burst SR performance.
3.5

Table 2: Ablation study. Impact
of different number of input burst
frames (B) and number of iterative
steps (K). The quantitative results
are reported on the synthetic burst
testset.
Burst Size
(B)
2
4
8
14
16
32

Discussion and Limitation

iterative steps (K = 5)

iterative steps (K = 10)

PSNR↑

SSIM↑

LPIPS↓ PSNR↑SSIM↑LPIPS↓

34.19
34.69
35.09
35.12
35.21
35.23

0.87900.88520.88870.88960.89070.89020.24980.23590.22770.22550.22320.22360.87770.88420.88760.89030.89090.89090.24800.23170.22170.21650.21680.2159

34.12
34.66
34.99
35.30
35.30
35.41

Our proposed method has a close connection to other proximalalgorithms such as ISTA [5] and FISTA [1] that require theexact form of the employed regularizer such as Total Variation / Hessian Schatten-norm [21]. However,in our case, the regularizer is learned implicitly from the training data (i.e.non-convex form) andtherefore we do not have any assumptions regarding the explicit form of the regularizer. Our proposed
algorithm acts as an inexact form of proximal gradient descent steps. Since we are estimating
the warping matrix by using the ECC [8] method to align the observations to the reference frame,
sometimes its estimation is imprecise that will introduce undesirable artifacts to the final SR result.

4

Conclusion

We proposed a deep iterative Burst CNNs for a multi-frame super-resolution task by following the
burst photography pipeline. The proposed burst SR scheme follows the burst physical model andsolves the overall problem through iterative refinement of the intermediate solution estimates to
get the final SR output. The proposed network exploits powerful image regularization, large-scale
optimization, and deep learning techniques for multi-frame image restoration. Our model requires
much less parameters and 2d convolution operation in comparison to other competing methods. Our
method achieves good burst SR results in terms of the synthetic data as well as comparable visualquality of the real-world bursts with respect to the existing approaches.
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