Predicted multi-variable intelligent matching pursuit algorithm for image sequences reconstruction based on l0 minimization

• We propose a novel method PMIMP for image sequences reconstruction by solving l0 minimization essentially.
• We develop a novel optimization function for image sequences reconstruction without knowing the sparsity level.
• We use the estimated support collection of the previous image as prior information to guide the current image reconstruction.
• We use multi-variable scheme to improve the reconstruction performance significantly with fewer measurements.

In this paper, we study the problem of reconstructing image sequences which satisfy the conditions that (a) the sparsity level is high in the wavelet domain and (b) the sparsity pattern of adjacent images changes very slowly. The idea of the proposed method predicted multi-variable intelligent matching pursuit (PMIMP) algorithm is to use the estimated support collection of the previous image as prior information and then utilize the prior information to guide the current image reconstruction by solving l0l0 minimization. Multi-variable scheme is used to sample image sequences to enhance the guidance of prior information and improve the reconstruction accuracy with fewer measurements. l0l0 minimization is an NP-hard problem that requires exhaustively listing all possibilities of the original signal and is difficult to be achieved by traditional algorithms. To solve it, we take advantage of the intelligent optimization algorithm which is famous for its global searching ability and superior performance in solving combinatorial optimization problems. To improve the reconstruction speed, matching strategies of greedy algorithm, which performs quite well in reconstruction speed, are utilized to design the updating mechanism of PMIMP. As the sparsity level is hard to be estimated in image sequences reconstruction, we propose a novel optimization function which does not need the sparsity level known as a prior. We illustrate the reconstruction performance of our proposed method PMIMP on several image sequences and compare it with the state-of-the-art algorithms. The experimental results demonstrate that PMIMP achieves the best reconstruction performance in both PSNR, SSIM and visual quality with fewer measurements.