Infimal Convolution Regularisation Functionals of BV and $$\varvec{\mathrm {L}}^{\varvec{p}}$$ L p Spaces

Infimal convolution of total generalized variation functionals for dynamic MRI.

PURPOSE To accelerate dynamic MR applications using infimal convolution of total generalized variation functionals (ICTGV) as spatio-temporal regularization for image reconstruction. THEORY AND METHODS ICTGV comprises a new image prior tailored to dynamic data that achieves regularization via optimal local balancing between spatial and temporal regularity. Here it is applied for the first tim...

Infimal Convolution Regularizations with Discrete l1-type Functionals

As first demonstrated by Chambolle and Lions the staircasing effect of the RudinOsher-Fatemi model can be reduced by using infimal convolutions of functionals containing higher order derivatives. In this paper, we examine a modification of such infimal convolutions in a general discrete setting. For the special case of finite difference matrices, we show the relation of our approach to the cont...

On Infimal Convolution of TV-Type Functionals and Applications to Video and Image Reconstruction

The infimal convolution of total (generalized) variation type functionals and its application as regularization for video and image reconstruction is considered. The definition of this particular type of regularization functional is motivated by the need of suitably combining spatial and temporal regularity requirements for video processing. The proposed functional is defined in an infinite dim...

Convolution and Homogeneous Spaces

Optimal Decomposition in Real Interpolation and Duality in Convex Analysis

This thesis is devoted to the study of mathematical properties of exact minimizers for the K–,L–, and E– functionals of the theory of real interpolation. Recently exact minimizers for these functionals have appeared in important results in image processing. In the thesis, we present a geometry of optimal decomposition for L– functional for the couple (`2, X), where space `2 is defined by the st...