Improved reconstruction in compressive sensing of clustered signals

A new method of compressive sensing reconstruction is presented. The method assumes that the signal to be estimated is both sparse and clustered. These properties are modeled as a modified Laplacian prior in a Bayesian setting, resulting in two penalizing terms in the corresponding unconstrained minimization problem. In the implementation an equivalent constrained minimization problem is solved using quadratic programming. Experiments on images with noisy observations show a significant gain when including the clustered assumption compared to the traditional Least Absolute Shirinkage and Selection Operator (LASSO) approach only penalizing for sparsity. Comparison with other methods highlights that our approach is particularly well suited to clustered signals with little or none variation within the clustered regions, such as two-level images or other binary signals.