A Sparse Restoration Algorithm Based on Clustered Class Graph Signals

Lan Li; Wei Wei; Mingli Jing; Shasha Pu

doi:10.3788/LOP202259.1010008

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 10 >Page 1010008 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 10, 1010008 (2022)

A Sparse Restoration Algorithm Based on Clustered Class Graph Signals

Lan Li^1、*, Wei Wei¹, Mingli Jing², and Shasha Pu¹

Author Affiliations

¹School of Science, Xi'an Shiyou University, Xi'an 710065, Shaanxi , China

²School of Electronic Engineering, Xi'an Shiyou University, Xi'an 710065, Shaanxi , China

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DOI: 10.3788/LOP202259.1010008 Cite this Article Set citation alerts

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 Copy Citation Text

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Fig. 1. Three types of clustering based on graph signals

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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

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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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]

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]

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 0. [in Chinese]

Sampling rate	Running time /s
Sampling rate	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

Table 1. Comparison of running time of five algorithms

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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