Image super resolution via multi-regularization combining hybrid Tikhonov-TV prior and deep denoiser prior

In a real scenario, the image is often corrupted by complex degradation, and a lot of useful information is lost, which makes super-resolution (SR) reconstruction seriously ill-posed. To effectively solve such a problem, it is crucial to correctly exploit image prior knowledge. Although existing deep learning-based methods can obtain excellent results, they cannot deal with the complex degradation effectively, which would lead to the loss of texture details and the destruction of edge details. In this paper, an efficient multi-regularization method for SR is proposed, which can simultaneously exploit both internal and external image priors within a unified framework. The hybrid Tikhonov-TV prior and deep denoiser prior are introduced to constrain the reconstruction process. That is, the proposed model combines the superiority of the piecewise-smooth prior and deep prior. Moreover, an adaptive weight parameter is employed to make the hybrid component more detail-preserving. Experimental demonstrate that the proposed method achieves better performance in image detail protection than advanced methods.

I. Introduction

In single-image super-resolution (SISR) problem, the degradation process from HR image to LR image is affected by degradation factors including down-sampling, noise, and blur [1]. This degradation process can be described by the observation model [2], which can be expressed as:

$$\begin{equation*}y=Wx+\sigma \tag{1}\end{equation*}$$ where W represents the system matrix. W=VH, V represents the down-sampling manix, and H represents the blur matrix. represents noise. In fact, the observational model cannot accurately describe the degradation process, which makes SR problem seriously ill-posed.