In the framework of block Compressed Sensing (CS), the reconstruction algorithm based on the Smoothed Projected Landweber\n(SPL) iteration can achieve the better rate-distortion performance with a low computational complexity, especially for using the\nPrinciple Components Analysis (PCA) to perform the adaptive hard-thresholding shrinkage. However, during learning the PCA\nmatrix, it affects the reconstruction performance of Landweber iteration to neglect the stationary local structural characteristic of\nimage. To solve the above problem, this paper firstly uses the Granular Computing (GrC) to decompose an image into several\ngranules depending on the structural features of patches. Then, we perform the PCA to learn the sparse representation basis\ncorresponding to each granule. Finally, the hard-thresholding shrinkage is employed to remove the noises in patches. The patches\nin granule have the stationary local structural characteristic, so that our method can effectively improve the performance of hard thresholding\nshrinkage. Experimental results indicate that the reconstructed image by the proposed algorithm has better objective\nquality when compared with several traditional ones. The edge and texture details in the reconstructed image are better preserved,\nwhich guarantees the better visual quality. Besides, our method has still a low computational complexity of reconstruction.
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