基于非局部低秩和加權(quán)全變分的圖像壓縮感知重構(gòu)算法

趙輝; 張靜; 張樂; 劉瑩莉; 張?zhí)祢U

doi:10.11999/JEIT180828

基于非局部低秩和加權(quán)全變分的圖像壓縮感知重構(gòu)算法

doi: 10.11999/JEIT180828

1.
重慶郵電大學(xué)通信與信息工程學(xué)院? ?重慶? ?400065
2.
重慶郵電大學(xué)信號與信息處理重慶市重點實驗室? ?重慶? ?400065

基金項目: 國家自然科學(xué)基金(61671095)

詳細信息

作者簡介:
趙輝：女，1980年生，教授，碩士生導(dǎo)師，研究方向為信號與圖像處理

張靜：女，1992年生，碩士生，研究方向為信號與圖像處理

張樂：女，1993年生，碩士生，研究方向為信號與圖像處理

劉瑩莉：女，1994年生，碩士生，研究方向為信號與圖像處理

張?zhí)祢U：男，1971年生，博士后，教授，研究方向為通信信號的調(diào)制解調(diào)、盲處理、語音信號處理、神經(jīng)網(wǎng)絡(luò)實現(xiàn)以及FPGA, VLSI實現(xiàn)

通訊作者:
趙輝　zhaohui@cqupt.edu.cn

中圖分類號: TP391.41
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出版歷程
- 收稿日期: 2018-08-22
- 修回日期: 2019-01-28
- 網(wǎng)絡(luò)出版日期: 2019-02-25
- 刊出日期: 2019-08-01

Compressed Sensing Image Restoration Based on Non-local Low Rank and Weighted Total Variation

1.
School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2.
Chongqing Key Laboratory of Signal and Information Processing, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Funds: The National Natural Science Foundation of China (61671095)

摘要

摘要: 為準確有效地實現(xiàn)自然圖像的壓縮感知(CS)重構(gòu)，該文提出一種基于圖像非局部低秩(NLR)和加權(quán)全變分(WTV)的CS重構(gòu)算法。該算法考慮圖像的非局部自相似性(NSS)和局部光滑特性，對傳統(tǒng)的全變分(TV)模型進行改進，只對圖像的高頻分量設(shè)置權(quán)重，并用一種差分曲率的邊緣檢測算子來構(gòu)造權(quán)重系數(shù)。此外，算法以改進的TV模型與NLR模型為約束構(gòu)建優(yōu)化模型，并分別采用光滑非凸函數(shù)和軟閾值函數(shù)來求解低秩和全變分優(yōu)化問題，很好地利用了圖像的自身性質(zhì)，保護了圖像的細節(jié)信息，并提高了算法的抗噪性和適應(yīng)性。仿真結(jié)果表明，與基于NLR的CS算法相比，相同采樣率下，該文所提算法的峰值信噪比最高可提高2.49 dB，且抗噪性更強，驗證了算法的有效性。
- 壓縮感知 /
- 圖像重構(gòu) /
- 非局部低秩 /
- 加權(quán)全變分
Abstract: In order to reconstruct natural image from Compressed Sensing(CS) measurements accurately and effectively, a CS image reconstruction algorithm based on Non-local Low Rank(NLR) and Weighted Total Variation(WTV) is proposed. The proposed algorithm considers the Non-local Self-Similarity(NSS) and local smoothness in the image and improves the traditional TV model, in which only the weights of image’s high-frequency components are set and constructed with a differential curvature edge detection operator. Besides, the optimization model of the proposed algorithm is built with constraints of the improved TV and the non-local low rank model, and a non-convex smooth function and a soft thresholding function are utilized to solve low rank and TV optimization problems respectively. By taking advantage of them, the proposed method makes full use of the property of image, and therefore conserves the details of image and is more robust and adaptable. Experimental results show that, compared with the CS reconstruction algorithm via non-local low rank, at the same sampling rate, the Peak Signal to Noise Ratio(PSNR) of the proposed method increases by 2.49 dB at most and the proposed method is more robust, which proves the effectiveness of the proposed algorithm.
- Compressed Sensing(CS) /
- Image reconstruction /
- Non-local Low Rank(NLR) /
- Weighted Total Variation(WTV)

HTML全文

圖 1 Barbara仿真效果對比圖

下載: 全尺寸圖片幻燈片

圖 2 Parrots仿真效果對比圖

下載: 全尺寸圖片幻燈片

圖 3 6幅測試圖在不同采樣率下各種算法的PSNR平均值

下載: 全尺寸圖片幻燈片

圖 4 算法測量值含噪的PSNR值比較

下載: 全尺寸圖片幻燈片

表 1 基于非局部低秩和加權(quán)全變分的圖像壓縮感知重構(gòu)算法(NLR-WTV)

　輸入：　從原始圖像${{u}}$采樣得到的壓縮感知測量值${{y}}$

　初始化：${{{u}}_0} = {{{Φ}} ^{\rm{T}}}{{y}}$, ${{a}}$, ${}$, ${{c}}$, ${\lambda _1}$, ${\lambda _2}$, ${\mu _1}$, ${\mu _2}$；

　Outer loop for $k{\rm{ }} = 1, {\rm{ }}2, ·\!·\!·, K$

　　(1) 根據(jù)塊匹配法找到圖像各相似像素點的位置；

　　(2) 根據(jù)式(6)、式(7)和式(8)計算圖像的低頻分量${{{u}}_{\rm{L}}}$和高頻分
量${{{u}}_{\rm{R}}}$；

　　(3) if $k \le {K_{{0}}}$, ${{{w}}_i} = 1$ else 根據(jù)式(9)計算${{{w}}_i}$；end if

　Inner loop for $t{\rm{ }} = 1, {\rm{ }}2, ·\!·\!·, T\;$

　　　　(a) 根據(jù)式(17)計算${{{L}}_i}^{(k + 1)}$；

　　　　(b) 根據(jù)式(19)計算${{{x}}^{(k + 1)}}$；

　　　　(d) 根據(jù)式(25)計算${{{u}}^{(k + 1)}}$；

　　　end for

　　　根據(jù)式(14)更新${{a}}$, ${}$和${{c}}$；

　end for

　輸出：重構(gòu)圖像${ {{ u} } \!\,\!\! { { {\widehat} }= { {{u} }^{(k + 1)} }$

下載: 導(dǎo)出CSV

表 2 不同算法重構(gòu)圖像的PSNR(dB)和SSIM比較

采樣率	算法	性能指標	Monarch	Barbara	Lena	Boats	Parrots	Cameraman
5%	TVAL3	PSNR	20.06	19.79	23.08	22.38	22.87	22.89
	TVAL3	SSIM	0.508	0.412	0.560	0.543	0.593	0.605
	BM3D-CS	PSNR	22.73	21.34	24.12	23.31	24.13	23.76
	BM3D-CS	SSIM	0.642	0.523	0.693	0.610	0.692	0.658
	TVNLR	PSNR	23.02	22.65	25.41	24.79	25.89	24.39
	TVNLR	SSIM	0.751	0.568	0.745	0.696	0.800	0.737
	NLR-CS	PSNR	26.38	27.94	30.64	29.81	31.71	25.38
	NLR-CS	SSIM	0.848	0.830	0.875	0.830	0.885	0.770
	NLR-WTV	PSNR	28.21	29.10	30.83	30.14	32.31	27.87
	NLR-WTV	SSIM	0.883	0.862	0.879	0.857	0.891	0.817

下載: 導(dǎo)出CSV

表 3 算法測量值含噪的SSIM值比較

圖像	算法	15	20	25	30	35
Monarch	NLR-CS	0.374	0.550	0.748	0.874	0.939
Monarch	NLR-WTV	0.387	0.569	0.761	0.890	0.948
Boats	NLR-CS	0.276	0.452	0.672	0.824	0.904
Boats	NLR-WTV	0.281	0.466	0.681	0.844	0.927

下載: 導(dǎo)出CSV

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