Practical Bounds on Image Denoising: From Estimation to Information

Abstract

Abstract-Recently, in a previous work, we proposed a way to bound how well any given image can be denoised. The bound was computed directly from the noise-free image that was assumed to be available. In this work, we extend the formulation to the more practical case where no ground truth is available. We show that the parameters of the bounds, namely the cluster covariances and level of redundancy for patches in the image, can be estimated directly from the noise corrupted image. Further, we analyze the bounds formulation to show that these two parameters are interdependent and they, along with the bounds formulation as a whole, have a nice information-theoretic interpretation as well. The results are verified through a variety of well-motivated experiments.Index Terms-Bayesian Cramér-Rao lower bound, image clustering, image denoising, image patch model, mutual information, Rényi entropy, Shannon entropy.

Patch-Based Near-Optimal Image Denoising

“…In the last decade, many such methods have been proposed, leading to considerable improvement in denoising performance. In [1] and [2], we studied the problem from an estimation theory perspective to quantify the fundamental limits of denoising. The insights gained from that study are applied to develop a theoretically sound denoising method in this paper.…”

“…In this paper, we propose a new denoising filter motivated by our statistical analysis of the performance bounds for patchbased methods [1], [2]. The contributions of our paper are as follows: We design a patch-based statistically motivated redundancy exploiting the Wiener filter, where the parameters of the method are learned from both geometrically and photometrically similar patches.…”

“…For example, the collaborative Wiener filter used in BM3D [12] works in the DCT domain where an estimate of the ground truth (signal-to-noise ratio) is obtained through an initial filtering of the image. Our spatial domain method is motivated by our analysis of the image denoising bounds [1], [2]. In our framework, graphically illustrated in Fig.…”

A New Approach to Image Denoising by Patch-Based Algorithm

“…In the last decade, many such methods have been recommended, lead to extensive enhancement in denoising performance. In [1] and [2], we studied the dispute from an estimation theory aspect to compute the fundamental limits of denoising. The insights gained from that study are applied to promote a hypothetically sound denoising method in this paper.…”

“…The data points with an identical patch to the central patch will have larger weights in the average as recently proposed by Buades [7], [8] who defined the purported non-local means filter as [58]). It stands observing that, if the size of the patch is reduced to one pixel, the non-local means filter, also controlled by a small number of smoothing parameters and, is closely equivalent to (2). As in [30], [31], [36], we also use narrow image patches (e.g., 7x7 or 9x9 patches) to enumerate the particular weights therefore they allow capture regional geometric patterns and texels seen in image s. Moreover, we adaptively determine a window (neighborhood) that probably large to balance the accuracy of approximation and the stochastic error, at each spatial position [34].…”