Supplementary Material for IEEE ICIP 2024

Supplementary Material for IEEE ICIP 2024 A Dictionary Based Approach For Removing Out-Of-Focus Blur
Authors: {aurangau, anil.kokaram}@tcd.ie

Abstract

The field of image deblurring has seen tremendous progress with the rise of deep learning models. These models, albeit efficient, are computationally expensive and energy consuming. Dictionary based learning approaches have shown promising results in image denoising and Single Image Super-Resolution. We propose an extension of the Rapid and Accurate Image Super-Resolution (RAISR) algorithm introduced by Isidoro, Romano and Milanfar for the task of out-of-focus blur removal. We define an image quality index measure which aligns well with the perceptual quality of an image. A metric based blending strategy based on asset allocation strategies is also proposed. Our method demonstrates an average increase of approximately 13% (PSNR) and 10% (SSIM) compared to popular deblurring methods. Furthermore, our blending scheme curtails ringing artefacts post restoration.

Filter Learning Algorithm

Flowchart 1 presents a detailed explanation of the learning technique adapted to the of deblurring.

Flowchart 1: Training Mechanism

Index J

Original Image, J = 1.0	Image Restored with a patch size of 13, J = 0.7031

Blurry Image, J = 0.0	Image Restored with a patch size of 21, J = 0.7796

Results

Tabular Results

Set14[1] and set5[2] were used to measure the performance of our algorithm against popular restoration techniques.

Set14

Algorithm	PSNR (dB)	SSIM
IFAN [3]	23.100	0.653
Restormer [4]	24.566	0.723
NBDNet [5]	27.280	0.754
Landweber [6]	26.263	0.757
NA Landweber	26.291	0.758
PC Landweber	27.732	0.820
Ours	29.287	0.847

Set 5

Algorithm	PSNR (dB)	SSIM
IFAN	25.409	0.789
Restormer	26.645	0.823
NBDNet	31.036	0.869
Landweber	29.011	0.849
NA Landweber	30.019	0.867
PC Landweber	30.715	0.890
Ours	31.999	0.900

Visual Comparison

Original Image	Blurry Image	Restormer [4]

IFAN [3]	NBDNet [5]	Landweber [6]

NA Landweber	PC Landweber	Ours

Average Blur

Size = 3 * 3

Original Image	Blurry Image	Restored Image

Comparison of Moore-Penrose Pseudoinverse and Least Squares Solver

Method Name	PSNR(Original, Restored)	PSNR(Original, Blurry)	PSNR Increase %
Moore-Penrose Pseudoinverse	31.96	24.21	31.98 %
Gradient Based Least-Squares Solver	29.50	24.21	21.82 %
Overall Increase	8.34 %	-	-

Method Name	SSIM(Original, Restored)	SSIM(Original, Blurry)	SSIM Increase %
Moore-Penrose Pseudoinverse	0.9509	0.7857	21.02 %
Gradient Based Least-Squares Solver	0.9100	0.7857	15.82 %
Overall Increase	4.49 %	-	-

Original Image	Blurry Image

Image restored using Least Squares Approach	Image restored using Moore-Penrose Pseudoinverse Approach

Metric Q based blending strategy

Algorithm 1 provides a detailed method for calculating the weighting coefficients $$w = {w_0, w_1, \ldots, w_{{N-1}}}$$

Original Image, Q = 5.3653	Image restored with P=13, Q = 5.2749	Iteration 1, Q = 5.2777

Ringing and effect on Q

Original Image, Q = 4.430	Image with Ringing, Q = 30.0348

References

[1] Roman Zeyde, Michael Elad, and Matan Protter, “On single image scale-up using sparse-representations,” in Curves and Surfaces: 7th International Conference, Avignon, France, June 24-30, 2010, Revised Selected Papers 7. Springer, 2012, pp. 711–730.

[2] Marco Bevilacqua, Aline Roumy, Christine Guillemot, and Marie Line Alberi-Morel, “Low-complexity singleimage super-resolution based on nonnegative neighbor embedding,” 2012.

[3] Junyong Lee, Hyeongseok Son, Jaesung Rim, Sunghyun Cho, and Seungyong Lee, “Iterative filter adaptive network for single image defocus deblurring,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021, pp. 2034–2042.

[4] Syed Waqas Zamir, Aditya Arora, Salman Khan, Munawar Hayat, Fahad Shahbaz Khan, and Ming-Hsuan Yang, “Restormer: Efficient transformer for highresolution image restoration,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 5728–5739.

[5] Liang Chen, Jiawei Zhang, Jinshan Pan, Songnan Lin, Faming Fang, and Jimmy S Ren, “Learning a non-blind deblurring network for night blurry images,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021.

[6] Lizhong Wang, Pierre-Alain Fayolle, and Alexander G Belyaev, “Reverse image filtering with clean and noisy filters,” Signal, Image and Video Processing, vol. 17, no. 2, pp. 333–341, 2023.