Approximation Theory of Wavelet Frame Based Image Restoration
Jian-Feng Cai, Jae Kyu Choi, Jianbin Yang
TL;DR
This paper provides an error analysis for a wavelet frame based image restoration method, linking discrete image errors to function approximation errors, and focusing on minimal wavelet coefficient solutions.
Contribution
It introduces an error estimate for wavelet frame based image restoration and connects discrete errors to underlying function approximation.
Findings
Error bounds for the wavelet frame based restoration method
Connection between discrete image errors and function approximation
Analysis of minimal wavelet coefficient solutions
Abstract
In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which has the minimal -norm of the canonical wavelet frame coefficients among all possible solutions. Then we further connect the error estimate for the discrete model to the approximation to the underlying function from which the underlying image comes.
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Taxonomy
TopicsImage and Signal Denoising Methods · Advanced Image Processing Techniques · Sparse and Compressive Sensing Techniques