Abstract—In the information age, numerous data needs to be transferred from one point to another. The bigger the amount of the data, the more the consumption in computation and memory. Due to a limitation of the existing resource, the compression of the data and the reconstruction of the compressed data receive much attention in several research areas. A sparse signal reconstruction problem is considered in this work. The signal can be captured into a vector whose elements can be zeros. Iteratively Reweighted Least Squares (IRLS) is a technique that is designed for extracting the signal vector from the available observation data. In this paper, a new algorithm based on the iteratively reweighted least squares using diagonal regularization method are proposed for sparse image reconstruction. The explicit solution of the IRLS optimization problem is derived and then an alternative IRLS algorithm based on the available solution is proposed. Since the matrix inverse in the iterative computation can be subject to ill condition, a diagonal regularization is proposed to overcome such a problem. Numerical simulation is conducted to illustrate the performance of the new IRLS with the comparison to the former IRLS algorithm. Numerical results indicate that the new IRLS method provides lower signal recovery error than the conventional IRLS approach at the expense of more complexity in terms of more computational time.
 
Keywords—compressed sensing, image reconstruction, iterative reweighted least squares


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