Decoupled inverse and denoising for image deblurring: Variational BM3D-frame technique

High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude

“…It is demonstrated in [6] and [7], that the BM3D-frames give extraordinary good results for image deblurring problem. In this paper we apply these advanced BM3D-frames for modeling phase and amplitude of u 0 as it is shown in Eqs.…”

“…The algorithm (17)- (18) is a generalization of the decoupled inverse imaging developed in the recent papers [6,7]. It is demonstrated in these papers that the decoupling applied together with the BM3D-frame image modeling results in the imaging which is advanced with respect to that can be achieved using a single-objective optimization.…”

“…It is shown in [5,6] that the analysis and synthesis developed in the BM3D …lter allow the corresponding frame analysis and synthesis interpretation. The BM3D analysis and synthesis operators can be given in the matrix form (3)- (4), linking the image Y 2 R n and the groupwise 3D spectrum vector 2 R m .…”

“…The algorithm searches for …xed-point giving a balance between two quality measures de…ned by these objective functions. This vector optimization, originated in [6,7], decouples the inversion and …ltering operations.…”

“…Second, assuming that phase and amplitude can be spatially varying, continuous or discontinuous, we apply for their modeling (approximation) novel powerful dictionaries known as BM3D-frames [5][6][7]. These frames are derived from the analysis and synthesis procedures of Block Matching 3D (BM3D) …lter, a well-established tool for imaging denoising and other imaging problems [8][9][10].…”