Deconvolution ISTA: A solver for multidimensional convolution problems with low computational complexity

Abstract

In this report, we employ the iterative shrinkage-thresholding algorithm (ISTA), which is one of the sparse reconstruction methods, to solve multidimensional circular convolution problems. The novelties of this work are as follows: the derivation of the subgradient and the Lipschitz constant of a multidimensional deconvolution problem;the construction of a sparse reconstruction algorithm to solve the problem;the evaluation of the qualitative ability of the algorithm, especially computational complexities. The proposed method can not only solve the convolution problems but also achieve low computational complexity.