Fused lasso with a non-convex sparsity inducing penalty

The fused lasso problem involves the minimization of the sum of a quadratic, a TV term and an ℓ₁ term. The solution can be obtained by applying a TV denoising filter followed by soft-thresholding. However, soft-thresholding introduces a certain bias to the non-zero coefficients. In order to prevent this bias, we propose to replace the ℓ₁ penalty with a non-convex penalty. We show that the solution can similarly be obtained by applying a modified thresholding function to the result of the TV-denoising filter.