Compressed sensing using the sparse prior of signal can reconstruct the originalsignal from far fewer measurements by random projection than Nyquist samples. Thistheory mainly contains three contents: sparse representation, measurement andreconstruction of signal. As for the two-dimentional signal of image, sparsity deteiminesthe quality of the constructed image directly. According to the Meyerâ€™s catoon-texturemodel of image, natural image contains smoothing components, edge and textureinformation. Single sparse represention of image canâ€™t have the same effect for threecomponents of image simultaneously, while morphological component analysis cansparsely represent different components by different transforms. In order to improve thequality of reconstructed image, this paper introduces the idea of morphological componentanalysis to compressed sensing and makes some research in the following aspects:(1) New sparse represention based on Wavelet, Curvelet and Brushlet: 2D-Waveletcan characterize the smoothing component of image for isotropic property of itsorthogonal basis functions. Curvelet can represent edge component sparsely depended onits basis fuctions with varied scales and angles. Brushletâ€™s basis fuctions are sensitive fortexture information because of its vibration. New sparse represention syncretizesadvantages of three image transforms above, and has effectively sparse representions bydifferent tranforms to separate components: soomthing, edge and texture. Aimed at thedisadvantage of the existing algorithm that it has bad recovered quality, this paper studiesreconstructed algorithm based on new sparse representation and proves it can improve thequality of reconstructed image and the ratio of peak signal to noise by protecting detailcomponents.(2) Three reconstructed methods based on new sparse represention: the first isseparate-reconstruct-method, in which separate components from image which depends onmeasurements, then reconstruct original image by shrinkage of coefficients. Second one iscalled fusional method. It combines separation and reconstruction by the same threshold of coefficient. The last one is named reconstruction-fusion-method. In this process, wewould get three recovered images by single sparse represention, and combine informationsof three images into the last reconstructed image. The tests make clear that the threemethods are practiced in recovery and have little difference.(3) Twoâ€“step iterative shrinkage/thresholding algorithm based on total variation:Smoothing and edge of image have total variation sparsity. In the algorithm improved bytotal variation, smoothing and edge would be adjusted. At last, we make use of twoâ€“stepiterative shrinkage/thresholding algorithm with high astringent speed and total variation toreconstruct image of compressed sensing. The results of experiments show that, comparedwith traditional algorithm, our improvements have more effective action in quality ofrecovered image and astringent speed of algorithm. |