Parameter tuning using asynchronous parallel pattern search in sparse signal reconstruction

Parameter tuning is an important but often overlooked step in signal recovery problems. For instance, the regularization parameter in compressed sensing dictates the sparsity of the approximate signal reconstruction. More recently, there has been evidence that non-convex ℓp quasi-norm minimization, where 0 < p < 1, leads to an improvement in reconstruction over existing models that use convex regularization. However, these methods rely on good estimates of the value of not only p (the choice of norm) but also on the value of the penalty regularization parameter. This paper describes a method for choosing suitable parameters. The method involves creating a score to determine the effectiveness of the choice of parameters by partially reconstructing the signal. We then efficiently search through different combinations of parameters using a pattern search approach that exploits parallelism and asynchronicity to find the pair with the optimal score. We demonstrate the efficiency and accuracy of the proposed method through numerical experiments.