  This paper studies regularized least square recovery of signals whose
samples' prior distributions are nonidentical, e.g., signals with time-variant
sparsity. For this model, Bayesian framework suggests to regularize the least
squares term with an asymmetric penalty. We investigate this problem in two
respects: First, we characterize the asymptotic performance via the replica
method and then discuss algorithmic approaches to the problem. Invoking the
asymptotic characterization of the performance, we propose a tuning strategy to
optimally tune the algorithmic approaches for recovery. To demonstrate
applications of the results, the particular example of BPSK recovery is
investigated and the efficiency of the proposed strategy is depicted in the
shadow of results available in the literature
