On some iterative concepts for image restoration

Several iterative strategies for solving inverse problems in the context of signal and image processing are discussed. Problems for which it is reasonable to assume that the solution has a sparse expansion with respect to a wavelet basis or frame are focused. A variational formulation of the problem is considered and an iteration scheme for which the iterates approximate the solution is constructed. The concrete problem of simultaneously denoising, decomposing, and deblurring a given image, is discussed. The associated variational formulation of the problem contains terms that promote sparsity and smoothness. A natural extension to vector-valued inverse problems is also considered. In the linear case, and under fairly general assumptions on the constraint, its is proved that weak convergence of the iterative scheme always holds.

Duke Scholars

Author Ingrid Daubechies Mathematics