High-Quality Image Reconstruction Characteristic Function for Single-Pixel Compressive Imaging

Fig. 2. Influence differences of single-pixel compressive imaging quality for different objects and different kinds of Hadamard encoding matrices when sampling ratio $η = 0.366$ . (a) Lena target; (b) binary slit shaped target; (c) random grayscale point target

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Fig. 3. Diagram of Gram matrix for Natural Hadamard encoding matrix when sampling ratio $η = 0.366$ and point spread function derived from 2016th row of Gram matrix. (a) Gram matrix; (b) point spread function $F_{P S, G}^{(2016)}$

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Fig. 4. Special positions and reconstruction results for Natural, CC, RD and MP Hadamard encoding matrices when sampling ratio $η = 0.562$ . (a) Special positions; (b) reconstruction results

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Fig. 5. Relationship between four characteristic parameters and sampling ratio $η$ for five kinds of Hadamard encoding matrices. (a) Curves of $μ_{m a x} - η$ ; (b) curves of $μ_{o v e r l a y} - η$ ; (c) curves of $μ_{p a r t_s u m} - η$ ; (d) curves of $s_{s p e c t r u m, c o s} - η$

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Fig. 6. $S_{ε} - η$ curves for five kinds of Hadamard encoding matrices

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Fig. 7. Simulated and experimental demonstration results for five kinds of Hadamard encoding matrices when sampling ratio $η$ is 0.6. (a) Simulated reconstruction results for random grayscale point targets for corresponding sparsity threshold value $S_{ε}$ ; (b) simulated reconstruction results for the same slit shaped target with sparsity S=0.16400; (c) experimental reconstruction results for the same slit shaped target with sparsity S=0.16400

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Fig. 8. Simulated and experimental demonstration results for five kinds of Hadamard encoding matrices when sparsity S is 0.25000. (a) Simulated reconstruction results for random grayscale point targets for corresponding sampling ratio value $η$ ; (b) simulated reconstruction results for the same radial-type target with sampling ratio $η = 0.728$ ; (c) experimental reconstruction results for the same radial-type target with sampling ratio $η = 0.728$

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Fig. 9. Sparsity threshold value $S_{ε}$ and PSNR for four types of encoding matrices when sampling ratio is $η = 0.5$ and $η = 0.7$

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Table 1. Characteristic parameters and sparsity threshold values at different sampling ratio $η$ for Random Hadamard encoding matrix

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Table 1. Characteristic parameters and sparsity threshold values at different sampling ratio $η$ for Random Hadamard encoding matrix

η	$μ_{m a x}$	$μ_{o v e r l a y}$	$μ_{p a r t_s u m}$	$s_{s p e c t r u m, c o s}$	$S_{ε}$
0.05	0.2549	0.4902	0.1610	0.6527	0.00587
0.10	0.1785	0.3521	0.0983	0.6831	0.01220
0.15	0.1270	0.2541	0.0709	0.6989	0.01950
0.20	0.1062	0.2076	0.0562	0.6978	0.02930
0.25	0.0918	0.1816	0.0462	0.7097	0.03910
0.30	0.1010	0.1906	0.0385	0.7262	0.04880
0.35	0.0844	0.1591	0.0328	0.7373	0.06100
0.40	0.0818	0.1587	0.0282	0.7421	0.07570
0.45	0.0711	0.1389	0.0245	0.7509	0.09030
0.50	0.0605	0.1143	0.0213	0.7601	0.11200
0.55	0.0542	0.1057	0.0186	0.7727	0.12900
0.60	0.0476	0.0928	0.0161	0.7860	0.15300
0.65	0.0428	0.0841	0.0141	0.8001	0.17200
0.70	0.0359	0.0712	0.0121	0.8151	0.20000
0.75	0.0319	0.0638	0.0104	0.8402	0.24200
0.80	0.0299	0.0568	0.0087	0.8617	0.27600
0.85	0.0233	0.0448	0.0071	0.8858	0.39100
0.90	0.0184	0.0369	0.0055	0.9190	0.51300
0.95	0.0136	0.0267	0.0037	0.9574	0.69600

Table 2. Sparsity threshold value $S_{ε}$ and PSNR at different sparsity S for four types of encoding matrices when sampling ratio $η = 0.5$
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Table 2. Sparsity threshold value $S_{ε}$ and PSNR at different sparsity S for four types of encoding matrices when sampling ratio $η = 0.5$
Encoding matrix $S_{ε}$ PSNR /dB
$S = 0.0766$ 0 $S = 0.0988$ 0 $S = 0.1210$ 0
Random Hadamard 0.12100 84.33 75.05 69.21
Bernoulli 0.08250 70.03 65.18 61.18
Orthogonal 0.11500 80.61 72.80 68.24
Gaussian 0.07660 69.53 64.38 60.92

Table 3. Sparsity threshold value $S_{ε}$ , target sparsity S, and PSNR for four types of encoding matrices when sampling ratio $η = 0.7$

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Table 3. Sparsity threshold value $S_{ε}$ , target sparsity S, and PSNR for four types of encoding matrices when sampling ratio $η = 0.7$

Object		Random Hadamard	Bernoulli	Orthogonal	Gaussian
Object 1	spaceS=0.16400	PSNR： 78.24 dBSε=0.22200	PSNR： 63.54 dBSε=0.09200	PSNR： 76.47 dBSε=0.20600	PSNR： 62.64 dBSε=0.09150
	DCTS=0.98300	PSNR： 14.78 dBSε=0.07110	PSNR： 16.21 dBSε=0.10700	PSNR： 16.04 dBSε=0.21100	PSNR： 16.47 dBSε=0.09850
	DWTS=0.89300	PSNR： 17.67 dBSε=0.18100	PSNR： 18.14 dBSε=0.09180	PSNR： 18.64 dBSε=0.21800	PSNR： 18.62 dBSε=0.09650
Object 2	spaceS=0.56300	PSNR： 9.46 dBSε=0.22200	PSNR： 4.71 dBSε=0.09200	PSNR： 8.24 dBSε=0.20600	PSNR： 5.72 dBSε=0.09150
	DCTS=0.15300	PSNR： 9.56 dBSε=0.07110	PSNR： 84.57 dBSε=0.10700	PSNR： 90.78 dBSε=0.21100	PSNR： 81.36 dBSε=0.09850
	DWTS=0.37400	PSNR： 18.73 dBSε=0.18100	PSNR： 64.27 dBSε=0.09180	PSNR： 75.24 dBSε=0.21800	PSNR： 64.18 dBSε=0.09650

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Shichang Ju, Junjie Cai, Wenlin Gong. High-Quality Image Reconstruction Characteristic Function for Single-Pixel Compressive Imaging[J]. Acta Optica Sinica, 2024, 44(7): 0711001

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Paper Information

Category: Imaging Systems

Received: Nov. 6, 2023

Accepted: Jan. 11, 2024

Published Online: Apr. 11, 2024

The Author Email: Gong Wenlin (wlgong@suda.edu.cn)

DOI:10.3788/AOS231741

CSTR:32393.14.AOS231741

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Characteristic parameters and sparsity threshold values at different sampling ratio η for Random Hadamard encoding matrix

Table 1. Characteristic parameters and sparsity threshold values at different sampling ratio η for Random Hadamard encoding matrix

Table 2. Sparsity threshold value Sε and PSNR at different sparsity S for four types of encoding matrices when sampling ratio η=0.5

Table 2. Sparsity threshold value Sε and PSNR at different sparsity S for four types of encoding matrices when sampling ratio η=0.5

Table 3. Sparsity threshold value Sε, target sparsity S, and PSNR for four types of encoding matrices when sampling ratio η=0.7

Table 3. Sparsity threshold value Sε, target sparsity S, and PSNR for four types of encoding matrices when sampling ratio η=0.7

Table 1. Characteristic parameters and sparsity threshold values at different sampling ratio $η$ for Random Hadamard encoding matrix

Table 1. Characteristic parameters and sparsity threshold values at different sampling ratio $η$ for Random Hadamard encoding matrix

Table 2. Sparsity threshold value $S_{ε}$ and PSNR at different sparsity S for four types of encoding matrices when sampling ratio $η = 0.5$

Table 2. Sparsity threshold value $S_{ε}$ and PSNR at different sparsity S for four types of encoding matrices when sampling ratio $η = 0.5$

Table 3. Sparsity threshold value $S_{ε}$ , target sparsity S, and PSNR for four types of encoding matrices when sampling ratio $η = 0.7$

Table 3. Sparsity threshold value $S_{ε}$ , target sparsity S, and PSNR for four types of encoding matrices when sampling ratio $η = 0.7$