Constrained Total Variation Minimization for Solving Ill-posed Inverse problem in Fourier or Wavelet Domains

International audienceMany ill-posed inverse problems in signal and image processing may be solved by minimizing the total variation of the data, subject to a constraint. By preserving sharp transitions, the total variation functional provides a probable solution while the constraint ensures that this solution satisfies all the conditions stated by the problem. When the constraint can be formulated in a transform domain, the transformation being linear and orthogonal, the approach may be implemented by a simple and fast algorithm. Examples involving Fourier and Wavelet transforms are presented in the context of JPEG restoration, super-resolution, computerized tomography and denoising via wavelet shrinkage