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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
💥1 概述
文獻來源：
?壓縮傳感（CS）是最近出現的技術，也是信號和圖像處理中廣泛研究的問題，它提出了一種新的框架，用于以明顯低于奈奎斯特速率的速率同時采樣和壓縮稀疏或可壓縮信號。也許，設計一個反映圖像稀疏先驗信息的有效正則化項在CS圖像恢復中起著至關重要的作用。近年來，局部平滑度和非局部自相似性都導致了CS圖像恢復的先驗稀疏性。本文首先，建立了自適應曲線閾值判據，試圖自適應去除CS恢復過程中恢復圖像中出現的擾動，強加稀疏性。此外，還建立了一種新的稀疏性度量，稱為聯合自適應稀疏性正則化（JASR），該度量在變換域中同時強制執行局部稀疏性和非局部三維稀疏性。然后，提出了一種基于JASR的高保真CS圖像恢復技術——CS-JASR。為了有效地求解所提出的相應優化問題，我們采用了拆分布雷格曼迭代。大量的實驗結果證明了與目前最先進的CS圖像修復方法相比，所提方法的充分性和有效性。
原文摘要：
Compressive sensing (CS) is a recently emerging technique and an extensively studied problem in signal and image processing, which suggests a new framework for the simultaneous sampling and compression of sparse or compressible signals at a rate significantly below the Nyquist rate. Maybe, designing an effective regularization term reflecting the image sparse prior information plays a critical role in CS image restoration. Recently, both local smoothness and nonlocal self-similarity have led to superior sparsity prior for CS image restoration. In this paper, first, an adaptive curvelet thresholding criterion is developed, trying to adaptively remove the perturbations appeared in recovered images during CS recovery process, imposing sparsity. Furthermore, a new sparsity measure called joint adaptive sparsity regularization (JASR) is established, which enforces both local sparsity and nonlocal 3-D sparsity in transform domain, simultaneously. Then, a novel technique for high-fidelity CS image recovery via JASR is proposed-CS-JASR. To efficiently solve the proposed corresponding optimization problem, we employ the split Bregman iterations. Extensive experimental results are reported to attest the adequacy and effectiveness of the proposed method comparing with the current state-of-the-art methods in CS image restoration.
📚2 運行結果
?
可視化代碼：
%%% displaying the images
figure,?
subplot(2,3,1), imagesc(noise), colormap('gray'),
colorbar, title('noise'), axis off
subplot(2,3,4), imagesc(fftshift(noise_FFT_PSD)), colormap('jet'),
colorbar, title('noise FFT-PSD'), axis off
subplot(2,3,2), imagesc(x), colormap('gray'),
colorbar, title('ground-truth'), axis off
subplot(2,3,3), imagesc(z), colormap('gray'),
colorbar, axis off, title(sprintf('noisy image\nPSNR=%0.2fdB',psnr_noisy))
subplot(2,3,5), imagesc(x_est_ksigma), colormap('gray'),
colorbar, axis off, title(sprintf('denoised image using k-sigma\nPSNR=%0.2fdB',psnr_ksigma))
subplot(2,3,6), imagesc(x_est_ACT), colormap('gray'),
colorbar, axis off, title(sprintf('denoised image using ACT\nPSNR=%0.2fdB',psnr_act))
%% ?Auxiliary function for generating Gaussian noise
function ?[noise, noise_FFT_PSD] = generate_Gaussian_noise(SizeX)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% generate_Gaussian_noise creates stationary white/colored Gaussian noise
% with respect to a convolutional kernel selected randomly.
%
%
% FUNCTION INTERFACE:
% ? ? ? ? [noise, noise_FFT_PSD] = generate_Gaussian_noise(SizeX)
%
% ________________________________________________________________________________
% ?INPUT: ? ? ? ?| ?CLASS: ?| DESCRIPTION:
% --------------------------------------------------------------------------------
% ?SizeX ? ? ? ? | (double) | Size of the ground-truth image.
%
%
% ________________________________________________________________________________
% ?OUTPUTS: ? ? ?| ?CLASS: ?| DESCRIPTION:
% --------------------------------------------------------------------------------
% ?noise ? ? ? ? | (double) | generated stationary Guassian noise.
% --------------------------------------------------------------------------------
% ?noise_FFT_PSD | (double) | the noise FFT-PSD (as size as SizeX). ?
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
kernel_type ?= randi([1 14]); % the randomly selected kernel for noise generation
normalizer ? = @(n) (n-mean(n(:)))./std(n(:)); % making the noise zero-mean with unit variance
🎉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。
Compressive Sensing Image Restoration Using Adaptive Curvelet Thresholding and Nonlocal Sparse Regularization | IEEE Journals & Magazine | IEEE Xplore
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