Compressive imaging by generalized total variation minimization

Encouraged by performance enhancement obtained using ℓ_p-minimization (with p <; 1) relative to that of ℓ₁-minimization in compressive sensing, we present an algorithm for the reconstruction of digital images from undersampled measurements, where the concept of conventional TV is extended to a generalized TV (GTV) that involves pth power (with p <; 1) of the discretized gradient of the image. To deal with the nonconvex issue arising from this new formulation, weighted TV (WTV) is introduced and an iterative reweighting technique is applied so that the algorithm is carried out in a convex setting. In addition, the Split Bregman method is reformulated in a major way so as to solve the WTV minimization problem involved. Numerical examples are included to demonstrate significant performance gain by the proposed GTV minimization method.