Super-Resolution of Magnetic Resonance Images via Convex Optimization with Local and Global Prior Regularization and Spectrum Fitting

Abstract EN

Given a low-resolution image, there are many challenges to obtain a super-resolved, high-resolution image.

Many of those approaches try to simultaneously upsample and deblur an image in signal domain.

However, the nature of the super-resolution is to restore high-frequency components in frequency domain rather than upsampling in signal domain.

In that sense, there is a close relationship between super-resolution of an image and extrapolation of the spectrum.

In this study, we propose a novel framework for super-resolution, where the high-frequency components are theoretically restored with respect to the frequency fidelities.

This framework helps to introduce multiple simultaneous regularizers in both signal and frequency domains.

Furthermore, we propose a new super-resolution model where frequency fidelity, low-rank (LR) prior, low total variation (TV) prior, and boundary prior are considered at once.

The proposed method is formulated as a convex optimization problem which can be solved by the alternating direction method of multipliers.

The proposed method is the generalized form of the multiple super-resolution methods such as TV super-resolution, LR and TV super-resolution, and the Gerchberg method.

Experimental results show the utility of the proposed method comparing with some existing methods using both simulational and practical images.