2009/03/28 by LianLin Li, Fang Li, Li, Lianlin +1
Computer Science · Engineering · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.0903.4939
openalex publication_date 2009/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the sparsity-constraint optimization. Up to now, many excellent theories, algorithms and software have been developed, for example, the so-called greedy algorithm ant its variants, the sparse Bayesian algorithm, the convex optimization methods, and so on. The formulations for them consist of two terms, in which one is and the other is (, mostly, p=1 is adopted due to good characteristic of the convex function) (NOTE: without the loss of generality, itself is assumed to be sparse). It is noted that all of them specify the sparsity constraint by the second term. Different from them, the developed formulation in this paper consists of two terms where one is with () and the other is . For each iteration the measurement matrix (linear operator) is reweighed by determined by which is obtained in the previous iteration, so the proposed method is called the iteratively reweighed operator algorithm (IROA). Moreover, in order to save the computation time, another reweighed operation has been carried out; in particular, the columns of corresponding to small have been excluded out. Theoretical analysis and numerical simulations have shown that the proposed method overcomes the published algorithms.