Optimization Method for Sensing Matrix Based on Transfer Learning

Zhaoyang Mao; Lan Li; Wei Wei

doi:10.3788/LOP202158.1410021

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 14 >Page 1410021 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 14, 1410021 (2021)

Optimization Method for Sensing Matrix Based on Transfer Learning

Zhaoyang Mao, Lan Li^*, and Wei Wei

Author Affiliations

School of Science, Xi’an Shiyou University, Xi’an, Shaanxi 710065, China

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DOI: 10.3788/LOP202158.1410021 Cite this Article Set citation alerts

Zhaoyang Mao, Lan Li, Wei Wei. Optimization Method for Sensing Matrix Based on Transfer Learning[J]. Laser & Optoelectronics Progress, 2021, 58(14): 1410021 Copy Citation Text

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Fig. 1. Histogram of the off-diagonal entries in the Gram matrix. (a) Random Gaussian matrix; (b) EIG method; (c) Elad method; (d) our method

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Fig. 2. Reconstruction errors of OMP and BP algorithm

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Fig. 3. Reconstructed images at different sampling rates. (a) Original image; (b) sampling rate is 0.3; (c) sampling rate is 0.4; (d) sampling rate is 0.5

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Algorithm 1:transfer learning optimization of the sparse base
Input:signal x,wavelet basic Ψ₀,sparse matrix Ψ⁽⁰⁾,maximum number of iterations I_max,soft threshold parameters λfor z=1∶I_maxcalculating sparsity coefficient s⁽^z⁾ by Eq. (12)singular value decomposition of s⁽^z⁾x^T+βΨ₀ is performed to obtain UΣV^Tupdate Ψ⁽^z⁾by Eq. (17)end forOutput:Ψ=Ψ^(z)

Table 1. Transfer learning optimization of the sparse base

Algorithm 2: construction of measurement matrix Φ

Input: measurement matrix Φ, sparse matrix Ψ, iterative threshold εInitialization: Gaussian random matrix Φ, A=ΦΨwhile halting criterion false doG=

{\tilde{A}}^{T} \tilde{A}

,eigenvalue decomposition G=VHV^T

\hat{H}

←diag

(H)

\sqrt[]{n / m}

\hat{A}

\hat{H}

V^Tε₀=

(\hat{A})

sum of non-diagonal elements if

|ε_{0} - [\sum {(n / m)}^{2} - n]| < ε

\hat{Φ}

\hat{A}

Ψ^-1 return Φ←

\hat{Φ}

Output: measurement matrix Φ

Table 2. Process of constructing measurement matrix

Method	Sampling rate					Peppers
Gaussian	0.2	5.963	4.325	4.242	3.904	4.720	4.630
	0.4	22.666	21.972	24.398	25.243	23.405	23.536
	0.6	27.669	25.889	29.622	30.254	28.283	28.343
EIG	0.2	6.422	4.051	4.447	3.926	4.319	4.633
	0.4	23.420	22.167	25.384	25.358	23.735	24.012
	0.6	29.378	27.508	31.941	31.966	30.269	30.212
Elad	0.2	5.284	4.987	3.035	4.245	5.438	4.597
	0.4	22.065	22.065	25.824	25.816	23.479	23.849
	0.6	29.378	27.322	31.412	31.966	29.826	29.980
Ours	0.2	7.325	5.424	4.700	4.757	4.650	5.371
	0.4	23.111	22.317	25.271	25.858	23.715	24.054
	0.6	29.695	27.629	31.974	32.044	30.387	30.346

Table 3. PSNR of images reconstructed by 4 methods unit: dB

Method	Barbara	Boats	House	Lena	Peppers
Gaussian	1.593	1.559	1.514	1.568	1.499
EIG	1.860	1.785	1.725	1.737	1.727
Elad	6.024	6.263	6.032	6.082	6.051
Ours	2.082	2.120	2.066	2.096	2.097

Table 4. Running time of 4 methods unit: s

Zhaoyang Mao, Lan Li, Wei Wei. Optimization Method for Sensing Matrix Based on Transfer Learning[J]. Laser & Optoelectronics Progress, 2021, 58(14): 1410021

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