A Sparse Restoration Algorithm Based on Clustered Class Graph Signals

Fig. 2. Recovery effect of different algorithms, when sampling rate is 0.3. (a) Original picture; (b) CBOMP algorithm; (c) OMP algorithm; (d) BP algorithm; (e) CoSaMP algorithm; (f) ROMP algorithm

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Fig. 3. Comparison of PSNR values of five algorithms

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Fig. 4. PSNR value of different block numbers

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Table 0. [in Chinese]

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Table 0. [in Chinese]

Algorithm 3：CBOMP algorithm
Input： $H$ ， $Y = [\underset{y [1]}{\underset{︸}{y^{11}, y^{12}, \dots, y^{1 c_{1}}}}, \dots, \underset{y [i]}{\underset{︸}{y^{i 1}, y^{i 2}, \dots, y^{i c_{i}}}}, \dots, \underset{y [p]}{\underset{︸}{y^{p 1}, \dots, y^{p c_{p}}}}]$ ， $p$ ， $S$ ；
Initialize： $r_{0} = y [i]$ ， $Λ_{0} = \emptyset$ ， $t = 1$ ；
for t=1：512
$λ [i] = a r g m a x_{i} {‖〈r_{0}, H {[i]}^{T}〉‖}_{F}$ ；
$Λ_{t} = Λ_{t - 1} \cup {λ {[i]}_{t}}$ ， $H_{t} = [H_{t - 1}, H_{λ {[i]}_{t}}]$ ；
${\hat{Θ}}_{t} = a r g m i n {‖Y - H_{t} \hat{Θ}‖}_{2}$ ；
$r_{t} = Y - H_{t} {\hat{Θ}}_{t}, t = t + 1$ ；
if $t > S$ break end end
Output： $\hat{Θ}$

Table 0. [in Chinese]

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Table 0. [in Chinese]

Algorithm 2： Clustered classification based on graph signal
Input： $Y = [y^{1}, y^{2}, \dots, y^{N}]$ ， $ε > 0$ ；
Initialize： ${\hat{y}}^{_{1}} = y^{_{1}}$ ， $Λ_{0} = {[0,0, \dots, 0]}^{1 \times N}$ ， $N_{g} = 1$ ， $b = 2$ ；
for $i = 2 : N$
for $j = 1 : N_{g}$ if $D_{I S} (y^{_{i}}, {\hat{y}}^{_{j}}) < ε$ ， ${\hat{y}}^{_{b}} = y^{_{i}}$ ， $Λ^{i} = j$ ， $b = b + 1$ ；
break
if $j = N_{g}$ $N_{g} = N_{g} + 1$ ， $Λ^{i} = N_{g}$ ， ${\hat{y}}^{j + 1} = y^{i}$ ， $b = j + 2$ ； end end
Sort： $\hat{Y}$ ； Output： $\hat{Y} = [{\hat{y}}^{_{1}}, {\hat{y}}^{_{2}}, \dots, {\hat{y}}^{_{N}}]$ ， $Λ_{0}$ ， $N_{g}$ ；

Table 0. [in Chinese]

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Table 0. [in Chinese]

Algorithm 1： Graph filter design
Input： $L$ ， $Φ \in C^{M \times N}$ ， $I$ ， $δ$ ；
Initialize：1. $H = Φ L$ ， $G = {\hat{H}}^{T} \hat{H}$ ， $G = S V S^{T}$ ；
2.Replace all non-zero elements in matrix $V$ with $\frac{n}{m}$ to obtain matrix $\tilde{V}$ ， $\tilde{V} = Z^{T} Z$ ；
3. $G_{0} = S Z^{T} Z S^{T}$ ， $G_{0} = {(H^{0})}^{T} H^{0}$ ；
for i=1：1000
$ε = {‖I_{N} - {H_{i}}^{T} H_{i}‖}_{F}^{2}$
if $ε \leq 0.001$
break
$H^{i + 1} = H^{i} - δ H^{i} [{(H^{i})}^{T} H^{i} - I]$ end end
Output： $H$

Table 1. Comparison of running time of five algorithms
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Table 1. Comparison of running time of five algorithms
Sampling rate Running time /s
CBOMP OMP ROMP CoSaMP BP
0.2 5.17 12.04 7.14 10.43 29.05
0.3 7.34 13.08 9.03 11.26 40.75
0.4 7.10 12.18 9.35 11.33 40.98
0.5 7.24 12.70 9.65 12.03 40.76
0.6 7.13 12.89 10.78 12.87 41.26

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Lan Li, Wei Wei, Mingli Jing, Shasha Pu. A Sparse Restoration Algorithm Based on Clustered Class Graph Signals[J]. Laser & Optoelectronics Progress, 2022, 59(10): 1010008

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