  Total variation (TV) regularization has proven effective for a range of
computer vision tasks through its preferential weighting of sharp image edges.
Existing TV-based methods, however, often suffer from the over-smoothing issue
and solution bias caused by the homogeneous penalization. In this paper, we
consider addressing these issues by applying inhomogeneous regularization on
different image components. We formulate the inhomogeneous TV minimization
problem as a convex quadratic constrained linear programming problem. Relying
on this new model, we propose a matching pursuit based total variation
minimization method (MPTV), specifically for image deconvolution. The proposed
MPTV method is essentially a cutting-plane method, which iteratively activates
a subset of nonzero image gradients, and then solves a subproblem focusing on
those activated gradients only. Compared to existing methods, MPTV is less
sensitive to the choice of the trade-off parameter between data fitting and
regularization. Moreover, the inhomogeneity of MPTV alleviates the
over-smoothing and ringing artifacts, and improves the robustness to errors in
blur kernel. Extensive experiments on different tasks demonstrate the
superiority of the proposed method over the current state-of-the-art.
