cs.CVSep 20, 2026

Blind Deconvolution of Binary and Pattern Images with Pixel Intensity Constraints and Sparse Gradient Prior

Authors: Qinghua Zhang, Xuesong Yang, Liangtian He, Liang-jian Deng, Jun Liu

Organizations: Laboratory of Mathematics and Complex Systems (Ministry of Education of China), the School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China · School of Mathematical Sciences, and Anhui University Center for Applied Mathematics, Anhui University, Hefei, 230601, P. R. China · School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, P. R. China · Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Blind image deconvolution (BID) is a prominent research topic in the field of imaging sciences, given its significant practical applications. Most existing model-based BID methods focus on natural images, incorporating appropriate prior knowledge about both the underlying image and the blur kernel. However, for certain classes of images, such as barcodes, text, and patterns, pixels can only take very limited values, a specific prior that is often overlooked in the literature. In this article, we introduce a novel pixel intensity constraint to leverage this important information, improving recovery performance for these specialized image classes. Specifically, we propose a unified framework for blind binary and pattern image deconvolution that incorporates both the pixel intensity constraint and a gradient sparsity regularizer. Numerical experiments demonstrate that our method outperforms many existing BID techniques, achieving superior results in terms of both visual quality and quantitative metrics.

Figures & tables

Figure 1: An illustrative example of the two-valued binary image and the multi-valued pattern images. (a) Binary image and (b) its pixel intensity histogram. (c) Pattern image and (d) its pixel intensity histogram.
Figure 2: A visual comparison of binary fingerprint images. (c) Pan et al.’s method [ 40 ] emphasizes the sparsity prior of intensity in the latent image, while (d) Wen et al.’s method [ 35 ] focuses on the extreme channel prior, and (e) Lv et al.’s method [ 39 ] leverages the binary intensity prior. It is evident that (f) our method outperforms these approaches by effectively reducing artifacts while better preserving structural details. (For improved visualization, the estimated kernels are displayed in the lower right corner of the final recovered images.)
Figure 3: An illustrative example of the pixel intensity distribution of xref\mathbf{x}^{\mathrm{ref}} . The pixel intensity histograms of (a) binary reference image xref\mathbf{x}^{\mathrm{ref}} (recovered by [ 21 ] ) and (b) pattern reference image xref\mathbf{x}^{\mathrm{ref}} (recovered by [ 40 ] ). The clustering number ss (i.e., the number of different pixel values in the image) can be approximated by the number of peaks in the histogram.
Figure 4: All test images: eight binary images (a-h) and four pattern images (i-l).
Figure 5: All test kernels are from the research conducted by Levin et al. [ 49 ] .
Figure 6: Quantitative evaluations on 8 binary images of different blur kernels, it can be observed that our method performs competitively against other competing methods.
MethodPSNR ↑\uparrowSSIM ↑\uparrow
Pan et al. [ 40 ]24.150.8973
Chen et al. [ 34 ]24.260.8955
Ren et al. [ 21 ]28.430.9114
Wen et al. [ 35 ]24.590.8863
Lv et al. [ 39 ]24.520.8869
Lv* et al. [ 39 ]25.390.8984
Table 1: Quantitative results (average PSNR/SSIM) of binary image deblurring.
Figure 7: The visual quality and quantitative results (PSNR/SSIM) of different methods on “im2”. (a) Ground truth, (b) Blurred image, (c) Pan et al. [ 40 ] , (d) Chen et al. [ 34 ] , (e) Ren et al. [ 21 ] , (f) Wen et al. [ 35 ] , (g) Lv et al. [ 39 ] , (h) Lv* et al. [ 39 ] , (i) Ours, (j) Ours*.
Figure 8: The visual quality and quantitative results (PSNR/SSIM) of different methods on “im6”. (a) Ground truth, (b) Blurred image, (c) Pan et al. [ 40 ] , (d) Chen et al. [ 34 ] , (e) Ren et al. [ 21 ] , (f) Wen et al. [ 35 ] , (g) Lv et al. [ 39 ] , (h) Lv* et al. [ 39 ] , (i) Ours, (j) Ours*.
Figure 9: Quantitative evaluations on 4 pattern images of different blur kernels. It can be observed that our method performs comparably against other competing methods.
MethodPSNR ↑\uparrowSSIM ↑\uparrow
Pan et al. [ 40 ]30.640.9644
Chen et al. [ 34 ]32.080.9768
Ren et al. [ 21 ]37.240.9827
Wen et al. [ 35 ]33.970.9798
Lv et al. [ 39 ]32.570.9761
Lv* et al. [ 39 ]33.200.9784
Table 2: Quantitative results (average PSNR/SSIM) of pattern image deblurring.
Figure 10: The visual quality and quantitative results (PSNR/SSIM) of different methods on “im10”. (a) Ground truth, (b) Blurred image, (c) Pan et al. [ 40 ] , (d) Chen et al. [ 34 ] , (e) Ren et al. [ 21 ] , (f) Wen et al. [ 35 ] , (g) Lv et al. [ 39 ] , (h) Lv* et al. [ 39 ] , (i) Ours, (j) Ours*.
Figure 11: The visual quality and quantitative results (PSNR/SSIM) of different methods on “im12”. (a) Ground truth, (b) Blurred image, (c) Pan et al. [ 40 ] , (d) Chen et al. [ 34 ] , (e) Ren et al. [ 21 ] , (f) Wen et al. [ 35 ] , (g) Lv et al. [ 39 ] , (h) Lv* et al. [ 39 ] , (i) Ours, (j) Ours*.
Image (kernel)im1 (ker1)im2 (ker2)im3 (ker3)im4 (ker4)
Pan et al. [ 40 ]19.46/0.925030.70/0.962910.09/0.668718.80/0.7715
Chen et al. [ 34 ]24.86/0.956629.92/0.913117.39/0.938319.43/0.6768
Ren et al. [ 21 ]20.97/0.951929.28/0.816319.03/0.958021.75/0.7839
Wen et al. [ 35 ]11.72/0.755045.75/0.999927.61/0.995120.27/0.9051
Lv et al. [ 39 ]32.69/0.984728.82/0.910315.76/0.889121.90/0.7866
Lv* et al. [ 39 ]34.54/0.993032.41/0.991420.06/0.970222.78/0.8653
Table 3: Quantitative results (PSNR/SSIM) of blurry and noisy (BSNR = 40 dB) binary image deblurring.
Image (kernel)im5 (ker5)im6 (ker6)im7 (ker7)im8 (ker8)
Pan et al. [ 40 ]31.70/0.843624.33/0.972623.37/0.942232.63/0.9919
Chen et al. [ 34 ]29.86/0.892623.88/0.937822.25/0.916926.66/0.9582
Ren et al. [ 21 ]31.80/0.928425.91/0.983623.33/0.945831.74/0.9904
Wen et al. [ 35 ]40.63/0.932528.96/0.992924.40/0.967327.39/0.9885
Lv et al. [ 39 ]31.57/0.927326.53/0.985823.62/0.946928.16/0.9876
Lv* et al. [ 39 ]33.27/0.977628.09/0.989524.21/0.948828.68/0.9689
Table 4: Quantitative results (PSNR/SSIM) of blurry and noisy (BSNR = 30 dB) binary image deblurring.
Figure 12: The convergence behavior of our proposed algorithm. The test set contains 12 images (im1-im12) that are blurred with kernel “ker1”. Note that the PSNR values and the kernel similarity are evaluated at the finest image scale.
Figure 13: The evolution of SSIM values with the parameter ss . (a) Test image: “im2” (with an ideal value s=2s=2 ), blur kernel: ker2. (b) Test image: “im12” (with an ideal value s=7s=7 ), blur kernel: ker2.
Image size256×256256\times 256450×450450\times 450600×600600\times 600
Pan et al. [ 40 ]13.2842.0794.23
Chen et al. [ 34 ]53.66147.87288.39
Wen et al. [ 35 ]12.6020.3731.33
Lv et al. [ 39 ]16.4845.2683.26
Ours10.3832.6659.83
Table 5: Average running time (in seconds) comparisons. The kernel size is 35×3535\times 35 .
Figure 14: The statistical property comparison between the blurry image and recovery results. (a) Blurred image and (b) the histograms of its intensity, (c) Recovery result of Pan et al. [ 40 ] and (d) the histogram of its intensity, (e) Recovery result of Lv* et al. [ 39 ] and (f) the histogram of its intensity, (g) Recovery result of ours* and (h) the histogram of its intensity.
Figure 15: Ablation study on binary image “im3” (PSNR/SSIM). (a) Input, (b) Ours* without pixel intensity constraint, (c) Ours* without gradient sparsity prior, (d) Ours* with non-blind deblurring algorithm [ 39 ] , (e) Ours*.
Test imageim4im7im10
True pixel intensities0 and 10 and 10.1137,0.2980,0.8863
K-Means estimation0.0063 and 0.99450.0073 and 0.99700.1209,0.2910,0.8782
Table 6: The comparison between distinct pixel values estimated by K-Means method and the ground truth (blur kernel: ker1).
Figure 16: Comparisons of [ 34 ] with and without the pixel intensity constraint. (a) Ground truth, (b) Blurred image, (c) Result of [ 34 ] , (d) Result of [ 34 ] with our pixel intensity constraint, (e) Ground truth, (f) Blurred image, (g) Result of [ 34 ] , (h) Result of [ 34 ] with our pixel intensity constraint.
More in this topic

Image Deblurring

Image deblurring restores sharp images from motion, defocus, and other blur by estimating lost detail and modeling image formation.

See all 63 papers

Explore similar work

CardsList

  1. Framelet-Based Blind Image Restoration with Minimax Concave Regularization

    Apr 21, 2026Heng Zhang, Reza Parvaz, Rui YangImage DeblurringImage Restoration

    College of Artificial Intelligence and Big Data, Chongqing Polytechnic University of Electronic Technology, Chongqing,China · Department of Engineering Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Ardabil, Iran

  2. Poisson Image Denoising Using Minimax Concave and Reweighted ℓ1\ell_1 Penalties: Nonblind and Blind Approaches

    Sep 7, 2026Reza ParvazImage DeblurringNonconvex Optimization

    aDepartment of Engineering Sciences, Faculty of Advanced Technologies,Sep University of Mohaghegh Ardabili, Ardabil, Iran

  3. MG-SpaIR: Multi-grade Sparse-guided Implicit Representation for Training-Data-Free Image Restoration

    Jun 30, 2026Jianmin Liao, Lei Huang, Ronglong Fang +3Implicit Neural RepresentationsAll-in-One Image Restoration

    Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, 13210, NY, USA. · Department of Mathematics & Statistics, Old Dominion University, 2300 Engineering & Computational Sciences Building, Norfolk, 23529, VA, USA. · Department of Medical Physical, Memorial Sloan Kettering Cancer Center, 1250 First Avenue, New York, 10065, NY, USA. +1