Compressive sensing via reweighted TV and nonlocal sparsity regularisation

Total variation (TV) regularisation has been widely used for compressive sensing (CS) reconstruction. However, since TV regularisers favour piecewise constant solutions, they tend to produce over‐smoothed image edges. To overcome this drawback, proposed is a novel iteratively reweighted TV regulariser for CS reconstruction. Spatially adaptive weights are computed towards a maximum a posteriori estimation of the image gradients. To exploit the nonlocal redundancy, effective nonlocal sparsity regularisation has also been introduced into the proposed objective function. Experimental results demonstrate that the proposed CS reconstruction method outperforms significantly existing TV‐based CS reconstruction methods.