Iterative Weighted Maximum Likelihood Denoising With Probabilistic Patch-Based Weights

Abstract

Abstract-Image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation. This paper presents a new approach for image denoising in the case of a known uncorrelated noise model. The proposed filter is an extension of the Non Local means (NL means) algorithm introduced by Buades et al.[1], which performs a weighted average of the values of similar pixels. Pixel similarity is defined in NL means as the Euclidean distance between patches (rectangular windows centered on each two pixels). In this paper a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model. The denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a datadriven way. These weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate. We show that this iterative process noticeably improves the denoising performance, especially in the case of low signal-to-noise ratio images such as Synthetic Aperture Radar (SAR) images. Numerical experiments illustrate that the technique can be successfully applied to the classical case of additive Gaussian noise but also to cases such as multiplicative speckle noise. The proposed denoising technique seems to improve on the state of the art performance in that latter case.

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

“…Note that by the construction of the NL-means matrix D the weights are always computed with respect to the logarithm of the corrupted image. While we were preparing the final version of this paper, we got to know about the parallel work [22] of Deledalle et al, who propose an iterated non-local means filter with probabilistic patch-based weights adapted to SAR images. …”

A non-local approach for SAR and interferometric SAR denoising

“…Both use search windows of size 21×21, patches of size 7×7 and the parameters h and T are set as explained in [8]. The NL-SAR filter has been applied successfully on a single-look amplitude image of the CNES in Toulouse (France) sensed by TerraSAR-X.…”

“…In order to consider the statistical nature of the observed image, we use the probabilistic criterion introduced in [8], where the weights are set to :…”

“…The negation of their logarithm are given in Table 1. A more detailed description of the algorithm can be found in [8,11]. Non-local approaches are known to leave a high variance in regions where there are too few redundant patches.…”

A nonlocal approach for SAR image denoising

“…More recently, speckle reduction techniques based on the "nonlocal" approach have been gaining ground [9,10,11], building upon the nonlocal means algorithm originally proposed in [12]. This approach relies on the observation that most images present clear self-similarities, as most patches repeat almost identically over and over in the image.…”