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Approximation Theory of Wavelet Frame Based Image Restoration

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arxiv 2208.10416 v1 pith:EDC6A3MH submitted 2022-08-22 math.AP

Approximation Theory of Wavelet Frame Based Image Restoration

Jian-Feng Cai , Jae Kyu Choi , Jianbin Yang This is my paper
classification math.AP
keywords imageerrorframeunderlyingwaveletapproximationdiscreteestimate
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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 $\ell_1$-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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