Estimation error bounds for frame denoising

Alyson K. Fletcher; Kannan Ramchandran

doi:10.1117/12.507260

13 November 2003 Estimation error bounds for frame denoising

Proceedings Volume 5207, Wavelets: Applications in Signal and Image Processing X; (2003) https://doi.org/10.1117/12.507260
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

A subspace-based method for denoising with a frame works as follows: If a signal is known to have a sparse representation with respect to the frame, the signal can be estimated from a noise-corrupted observation of the signal by finding the best sparse approximation to the observation. The ability to remove noise in this manner depends on the frame being designed to efficiently represent the signal while it inefficiently represents the noise. This paper gives bounds to show how inefficiently white Gaussian noise is represented by sparse linear combinations of frame vectors. The bounds hold for any frame so they are generally loose for frames designed to represent structured signals. Nevertheless, the bounds can be combined with knowledge of the approximation efficiency of a given family of frames for a given signal class to study the merit of frame redundancy for denoising.

Citation Download Citation

Alyson K. Fletcher and Kannan Ramchandran "Estimation error bounds for frame denoising", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); https://doi.org/10.1117/12.507260

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