Reconstruction in Compressive Sensing Using Affine Scaling Transformations with Variable-p Diversity Measure

The Affine Scaling Transformation (AST) family of algorithms can solve the minimization of the l
_(ples1)
, p-norm-like diversity measure for an underdetermined linear inverse problem. The AST algorithms can therefore be used to solve the sparse signal recovery problem that arises in Compressive Sensing. In this paper, we continue to investigate the application of the iterative AST family of algorithms with a dynamical adjustment of the p parameter to improve convergence speed and signal recovery accuracy. In our previous work we experimentally determined that any p in can give the sparse solution when exact recovery is possible, however, the behavior of the algorithm is highly dependent on this parameter. In addition, the best-approximation error, for those cases where exact recovery is not possible, is also highly dependent on p. Using various criteria, we propose and evaluate some strategies to vary the values of p as a function of the iteration in the AST algorithm. The goal in these strategies for a variable-p AST algorithm is to capture the benefits of the p=0 and the p=1 fixed-p approaches simultaneously.