Towards theoretically-founded learning-based denoising

Wenda Zhou, Shirin Jalali

2019 (modified: 05 Nov 2023)ISIT 2019Readers: Everyone

Abstract: Denoising a stationary process (X i ) i∈Z corrupted by additive white Gaussian noise (Z i ) i∈Z , i.e., recovering Xn from Y n = X n + Z n , is a classic and fundamental problem in information theory and statistical signal processing. Theoretically-founded and computationally-efficient denoising algorithms which are applicable to general sources are yet to be found. In a Bayesian setup, given the distribution of X n , a minimum mean square error (MMSE) denoiser computes E[X n |Y n ]. However, for general sources, computing E[X n |Y n ] is computationally very challenging, if not infeasible. In this paper, starting from a Bayesian setup, a novel denoiser, namely, quantized maximum a posteriori (Q-MAP) denoiser, is proposed and its asymptotic performance is analyzed. Both for memoryless sources, and for structured first-order Markov sources, it is shown that, asymptotically, as σ 2 (noise variance) converges to zero, 1/σ 2 E[(X i -X Q-MAP ) 2 ] converges to the information dimension of the source. For the studied memoryless sources, this limit is known to be optimal. A key advantage of the QMAP denoiser is that, unlike a MMSE denoiser, it highlights the key properties of the source distribution that are to be used in its denoising. This naturally leads to a learning-based denoising algorithm. Using ImageNet database for training, initial simulation results exploring the performance of such a learning-based denoiser in image denoising are presented.

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