Shuangjiang Li

In this paper, we study the compressed sensing (CS) image recovery problem. The traditional method divides the image into blocks and treats each block as an independent sub-CS recovery task. This often results in losing global structure of an image. In order to improve the CS recovery result, we propose a nonlocal (NL) estimation step after the initial CS recovery for denoising purpose. The NL estimation is based on the well-known NL means filtering that takes an advantage of self-similarity in images. We formulate the NL estimation as the low-rank matrix approximation problem, where the low-rank matrix is formed by the NL similarity patches. An efficient algorithm, nonlocal Douglas-Rachford (NLDR), based on Douglas-Rachford splitting is developed to solve this low-rank optimization problem constrained by the CS measurements. Experimental results demonstrate that the proposed NLDR algorithm achieves significant performance improvements over the state-of-the-art in CS image recovery.

Hyperspectral images consist of large number of spectral bands but many of which contain redundant information. Therefore, band selection has been a common practice to reduce the dimensionality of the data space for cutting down the computational cost and alleviating from the Hughes phenomenon. This paper presents a new technique for band selection where a sparse representation of the hyperspectral image data is pursued through an existing algorithm, K-SVD, that decomposes the image data into the multiplication of an overcomplete dictionary (or signature matrix) and the coefficient matrix. The coefficient matrix, that possesses the sparsity property, reveals how importantly each band contributes in forming the hyperspectral data. By calculating the histogram of the coefficient matrix, we select the top K bands that appear more frequently than others to serve the need for dimensionality reduction and at the same time preserving the physical meaning of the selected bands. We refer to the proposed band selection algorithm based on sparse representation as SpaBS. Through experimental evaluation, we first use synthetic data to validate the sparsity property of the coefficient matrix. We then apply SpaBS on real hyperspectral data and use classification accuracy as a metric to evaluate its performance. Compared to other unsupervised band selection algorithms like PCA and ICA, SpaBS presents higher classification accuracy with a stable performance.