Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a generic wavelet frame based image restoration model, called the "general model", which includes most of the existing wavelet frame based models as special cases. Moreover, the general model also includes examples that are new to the literature. Motivated by our earlier studies [1-3], We provide an asymptotic analysis of the general model as image resolution goes to infinity, which establishes a connection between the general model in discrete setting and a new variatonal model in continuum setting. The variational model also includes some of the existing variational models as special cases, such as the total generalized variational model proposed by [4]. In the end, we introduce an algorithm solving the general model and present one numerical simulation as an example.
Code (0)
등록된 구현이 없습니다.
Tasks
Image RestorationSimilar Papers 제목 키워드 기반
An Edge Driven Wavelet Frame Model for Image Restoration
Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images a…
DeblurringImage InpaintingImage RestorationSupport Driven Wavelet Frame-based Image Deblurring
The wavelet frame systems have been playing an active role in image restoration and many other image processing fields over the past decades, owing to the good capability of sparsely approximating piece-wise smooth funct…
DeblurringImage DeblurringImage RestorationSelf-LearningAll-in-One Image Restoration via Causal-Deconfounding Wavelet-Disentangled Prompt Network
Image restoration represents a promising approach for addressing the inherent defects of image content distortion. Standard image restoration approaches suffer from high storage cost and the requirement towards the known…
Image RestorationUnified Image Restoration and Enhancement: Degradation Calibrated Cycle Reconstruction Diffusion Model
Image restoration and enhancement are pivotal for numerous computer vision applications, yet unifying these tasks efficiently remains a significant challenge. Inspired by the iterative refinement capabilities of diffusio…
DenoisingImage DeblurringImage DehazingImage Inpainting+5Universal Face Restoration With Memorized Modulation
Blind face restoration (BFR) is a challenging problem because of the uncertainty of the degradation patterns. This paper proposes a Restoration with Memorized Modulation (RMM) framework for universal BFR in diverse degra…
Blind Face Restoration