  This paper considers the problem of signal denoising using a sparse
tight-frame analysis prior. The L1 norm has been extensively used as a
regularizer to promote sparsity; however, it tends to under-estimate non-zero
values of the underlying signal. To more accurately estimate non-zero values,
we propose the use of a non-convex regularizer, chosen so as to ensure
convexity of the objective function. The convexity of the objective function is
ensured by constraining the parameter of the non-convex penalty. We use ADMM to
obtain a solution and show how to guarantee that ADMM converges to the global
optimum of the objective function. We illustrate the proposed method for 1D and
2D signal denoising.

Computer Vision and Pattern Recognition;Optimization and Control