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📋📋📋本文目錄如下：🎁🎁🎁

目錄

💥1 概述

📚2 運行結果

🎉3?參考文獻

🌈4 Matlab代碼實現

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💥1 概述

稀疏感知圖像和體數據恢復是一種用于恢復損壞、噪聲或不完整的圖像和體數據的技術。它利用了信號的稀疏性，即信號在某種基礎下可以用較少的非零系數表示，從而實現高質量的恢復。

在進行稀疏感知圖像和體數據恢復的研究時，需要定義一些系統對象。這些對象描述了系統中的各個組成部分和它們之間的關系，有助于實現恢復算法的設計和實現。

系統對象的定義包括以下幾個方面：

1. 輸入數據對象：這個對象描述了輸入的損壞、噪聲或不完整的圖像或體數據。它可以是一個圖像矩陣、一個體數據的三維數組或其他適當的數據結構。

2. 稀疏表示對象：這個對象描述了信號的稀疏表示。它可以是一個稀疏矩陣、一個稀疏系數向量或其他適當的數據結構。稀疏表示對象是恢復算法的關鍵部分，它通過選擇適當的基礎和優化方法來實現信號的稀疏表示。

3. 恢復算法對象：這個對象描述了用于恢復稀疏感知圖像和體數據的算法。它可以是一個迭代算法、一個優化算法或其他適當的算法。恢復算法對象通常包括對輸入數據對象和稀疏表示對象的處理步驟，以及對恢復結果的評估和優化步驟。

4. 輸出數據對象：這個對象描述了恢復后的圖像或體數據。它可以是一個恢復后的圖像矩陣、一個恢復后的體數據的三維數組或其他適當的數據結構。

通過定義這些系統對象，研究人員可以更好地理解稀疏感知圖像和體數據恢復的過程，并設計出高效、準確的恢復算法。這些系統對象的定義還可以為稀疏感知圖像和體數據恢復的實際應用提供指導，例如醫學圖像處理、計算機視覺和圖像壓縮等領域。

📚2 運行結果

?

?部分代碼：

%% Create a step monitor system object
% ISTA iteratively approaches to the optimum solution. In order to 
% observe the intermediate results, the following class can be used:
%
% * saivdr.utility.StepMonitoringSystem% Parameters for StepMonitoringSystem
isverbose = true;  % Verbose mode
isvisible = true;  % Monitor intermediate results
hfig2 = figure(2); % Figure to show the source, observed and result image 
hfig2.Name = 'ISTA-based Image Restoration';% Instantiation of StepMonitoringSystem
import saivdr.utility.StepMonitoringSystem
stepmonitor = StepMonitoringSystem(...'DataType', 'Image',...'SourceImage',   orgImg,...    % Original image'ObservedImage', obsImg,...    % Observed image'IsMSE',         false,...     % Switch for MSE  evaluation'IsPSNR',        true,...      % Switch for PSNR evaluation'IsSSIM',        false,...     % Switch for SSIM evaluation'IsVerbose',     isverbose,... % Switch for verbose mode'IsVisible',     isvisible,... % Switch for display intermediate result'ImageFigureHandle',hfig2);    % Figure handle% Set the object to the ISTA system object
ista.StepMonitor = stepmonitor;%% Perform ISTA-based image restoration
% STEP method of IstaImRestoration system object, _ista_ , executes 
% the ISTA-based image restoration to deblur the observed image.
% As the result, a restored image 
%
% $\hat{\mathbf{u}} = \mathbf{D}\hat{\mathbf{y}}$
%
% is obtained.fprintf('\n ISTA')
resImg = ista.step(obsImg); % STEP method of IstaImRestoration%% Extract the final evaluation  
% The object of StepMonitoringSystem, _stepmonitor_ , stores the 
% evaluation values calculated iteratively in ISTA as a vector. The GET 
% method of _stepmonitor_  can be used to extract the number of iterations
% and the sequence of PSNRs. nItr  = stepmonitor.nItr;
psnrs = stepmonitor.PSNRs;
psnr_ista = psnrs(nItr);%% Perform Wiener filtering
% As a reference, let us show a result of Wiener filter.% Create a step monitor system object for the PSNR evaluation
stepmonitor = StepMonitoringSystem(...'SourceImage',orgImg,...'MaxIter', 1,...'IsMSE',  false,...'IsPSNR', true,...'IsSSIM', false,...'IsVisible', false,...'IsVerbose', isverbose);% Use the same blur kernel as that applied to the observed image, obsImg
blurKernel = blur.BlurKernel;% Estimation of noise to signal ratio
nsr = noise_var/var(orgImg(:));% Wiener filter deconvolution of Image Processing Toolbox
wnfImg = deconvwnr(obsImg, blurKernel, nsr);% Evaluation
fprintf('\n Wiener')
psnr_wfdc = stepmonitor.step(wnfImg); % STEP method of StepMonitoringSystem%% Compare deblurring performances
% In order to compare the deblurring performances between two methods,
% ISTA-based deblurring with NSOLT and Wiener filter, let us show 
% the original, observed and two results in one figure together.hfig3 = figure(3);% Original image x
subplot(2,2,1)
imshow(orgImg)
title('Original image {\bf u}')% Observed image u
subplot(2,2,2)
imshow(obsImg)
title('Observed image {\bf x}')% Result u^ of ISTA 
subplot(2,2,3)
imshow(resImg)
title(['{\bf u}\^ by ISTA  : ' num2str(psnr_ista) ' [dB]'])% Result u^ of Wiener filter
subplot(2,2,4)
imshow(wnfImg)
title(['{\bf u}\^ by Wiener: ' num2str(psnr_wfdc) ' [dB]'])

%% Create a step monitor system object
% ISTA iteratively approaches to the optimum solution. In order to?
% observe the intermediate results, the following class can be used:
%
% * saivdr.utility.StepMonitoringSystem

% Parameters for StepMonitoringSystem
isverbose = true; ?% Verbose mode
isvisible = true; ?% Monitor intermediate results
hfig2 = figure(2); % Figure to show the source, observed and result image?
hfig2.Name = 'ISTA-based Image Restoration';

% Instantiation of StepMonitoringSystem
import saivdr.utility.StepMonitoringSystem
stepmonitor = StepMonitoringSystem(...
? ? 'DataType', 'Image',...
? ? 'SourceImage', ? orgImg,... ? ?% Original image
? ? 'ObservedImage', obsImg,... ? ?% Observed image
? ? 'IsMSE', ? ? ? ? false,... ? ? % Switch for MSE ?evaluation
? ? 'IsPSNR', ? ? ? ?true,... ? ? ?% Switch for PSNR evaluation
? ? 'IsSSIM', ? ? ? ?false,... ? ? % Switch for SSIM evaluation
? ? 'IsVerbose', ? ? isverbose,... % Switch for verbose mode
? ? 'IsVisible', ? ? isvisible,... % Switch for display intermediate result
? ? 'ImageFigureHandle',hfig2); ? ?% Figure handle
? ??
% Set the object to the ISTA system object
ista.StepMonitor = stepmonitor;

%% Perform ISTA-based image restoration
% STEP method of IstaImRestoration system object, _ista_ , executes?
% the ISTA-based image restoration to deblur the observed image.
% As the result, a restored image?
%
% $\hat{\mathbf{u}} = \mathbf{D}\hat{\mathbf{y}}$
%
% is obtained.

fprintf('\n ISTA')
resImg = ista.step(obsImg); % STEP method of IstaImRestoration

%% Extract the final evaluation ?
% The object of StepMonitoringSystem, _stepmonitor_ , stores the?
% evaluation values calculated iteratively in ISTA as a vector. The GET?
% method of _stepmonitor_ ?can be used to extract the number of iterations
% and the sequence of PSNRs.?

nItr ?= stepmonitor.nItr;
psnrs = stepmonitor.PSNRs;
psnr_ista = psnrs(nItr);

%% Perform Wiener filtering
% As a reference, let us show a result of Wiener filter.

% Create a step monitor system object for the PSNR evaluation
stepmonitor = StepMonitoringSystem(...
? ? 'SourceImage',orgImg,...
? ? 'MaxIter', 1,...
? ? 'IsMSE', ?false,...
? ? 'IsPSNR', true,...
? ? 'IsSSIM', false,...
? ? 'IsVisible', false,...
? ? 'IsVerbose', isverbose);

% Use the same blur kernel as that applied to the observed image, obsImg
blurKernel = blur.BlurKernel;

% Estimation of noise to signal ratio
nsr = noise_var/var(orgImg(:));

% Wiener filter deconvolution of Image Processing Toolbox
wnfImg = deconvwnr(obsImg, blurKernel, nsr);

% Evaluation
fprintf('\n Wiener')
psnr_wfdc = stepmonitor.step(wnfImg); % STEP method of StepMonitoringSystem

%% Compare deblurring performances
% In order to compare the deblurring performances between two methods,
% ISTA-based deblurring with NSOLT and Wiener filter, let us show?
% the original, observed and two results in one figure together.

hfig3 = figure(3);

% Original image x
subplot(2,2,1)
imshow(orgImg)
title('Original image {\bf u}')

% Observed image u
subplot(2,2,2)
imshow(obsImg)
title('Observed image {\bf x}')

% Result u^ of ISTA?
subplot(2,2,3)
imshow(resImg)
title(['{\bf u}\^ by ISTA ?: ' num2str(psnr_ista) ' [dB]'])

% Result u^ of Wiener filter
subplot(2,2,4)
imshow(wnfImg)
title(['{\bf u}\^ by Wiener: ' num2str(psnr_wfdc) ' [dB]'])

🎉3?參考文獻

文章中一些內容引自網絡，會注明出處或引用為參考文獻，難免有未盡之處，如有不妥，請隨時聯系刪除。

[1]薛明.壓縮感知及稀疏性分解在圖像復原中的應用研究[D].西安電子科技大學,2011.DOI:CNKI:CDMD:2.2010.083018.

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• Genki Fujii, Yuta Yoshida, Shogo Muramatsu, Shunsuke Ono, Samuel Choi, Takeru Ota, Fumiaki Nin, Hiroshi Hibino, "OCT Volumetric Data Restoration with Latent Distribution of Refractive Index," Proc. of 2019 IEEE International Conference on Image Processing (ICIP), pp.764-768, Sept. 2019

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• Shogo Muramatsu, Kosuke Furuya and Naotaka Yuki, "Multidimensional Nonseparable Oversampled Lapped Transforms: Theory and Design," IEEE Trans. on Signal Process., Vol.65, No.5, pp.1251-1264, DOI:10.1109/TSP.2016.2633240, March 2017

• Kota Horiuchi and Shogo Muramatsu, "Fast convolution technique for Non-separable Oversampled Lapped Transforms," Proc. of Asia Pacific Signal and Information Proc. Assoc. Annual Summit and Conf. (APSIPA ASC), Dec. 2016

• Shogo Muramatsu, Masaki Ishii and Zhiyu Chen, "Efficient Parameter Optimization for Example-Based Design of Non-separable Oversampled Lapped Transform," Proc. of 2016 IEEE Intl. Conf. on Image Process. (ICIP), pp.3618-3622, Sept. 2016

• Shogo Muramatsu, "Structured Dictionary Learning with 2-D Non-separable Oversampled Lapped Transform," Proc. of 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.2643-2647, May 2014

• Kousuke Furuya, Shintaro Hara and Shogo Muramatsu, "Boundary Operation of 2-D non-separable Oversampled Lapped Transforms," Proc. of Asia Pacific Signal and Information Proc. Assoc. Annual Summit and Conf. (APSIPA ASC), Nov. 2013

• Shogo Muramatsu and Natsuki Aizawa, "Image Restoration with 2-D Non-separable Oversampled Lapped Transforms," Proc. of 2013 IEEE International Conference on Image Process. (ICIP), pp.1051-1055, Sep. 2013

• Shogo Muramatsu and Natsuki Aizawa, "Lattice Structures for 2-D Non-separable Oversampled Lapped Transforms," Proc. of 2013 IEEE International Conference on Acoustics, Speech and Signal Process. (ICASSP), pp.5632-5636, May 2013

🌈4 Matlab代碼實現