A new method for removing mixed noises

Abstract

We first introduce a similarity assumption to describe the similarity phenomenon in natural images, and establish a similarity principle which supplies a simple mathematical justification for the non-local means filter in removing Gaussian noises. Using the similarity principe in an adapted way, we then propose a new algorithm, called mixed noise filter (MNF) to remove simultaneously a mixture of Gaussian and random impulse noises. Our experiments show that our new filter improves significantly the trilateral filter in removing mixed noises, and that it is as efficient as the non-local means filter in removing Gaussian noises, and as good as the trilateral filter in removing random impulse noises.

A Patch-Based Approach for Removing Impulse or Mixed Gaussian-Impulse Noise

“…. , x n denote the centers of the patches that achieve the n smallest values of the distance D to the noisy patch P: 2 distance corresponds to blue curves, the trimmed distance D trimmed to green curves, the weighted distance D weighted to red curves and the "impulse-controlled" (IC) distance used by [32] to indigo curves. See the text for some comments on these graphics.…”

“…We make n vary from 1 to 40 and we plot the number N D (n) of "well-selected" patches as a function of n. We ran this experiment for four different distances between patches: the 2 distance (blue curves), the trimmed distance D trimmed (green curves), the weighted distance D weighted defined in Equation (3.5) (red curves) and the "impulse-controlled" (IC) distance used by [32] (indigo curves). This last distance is also a weighted 2 distance but where the weights are now pixel-dependent and related to the noise detector ROAD [25] (see Section 5.1 for a more detailed description of ROAD).…”

“…From left to right: the original patch (marked by a white window of size 7 × 7 pixels and its neighborhood V ), a noisy version of the image (p = 0.2 and σ = 10), and the mean number of selected patches for the different distances when σ = 10, p = 0.2 (third column) and p = 0.5 (fourth column). The 2 distance corresponds to blue curves, the trimmed distance D trimmed to green curves, the weighted distance D weighted to red curves and the "impulse-controlled" (IC) distance used by [32] to indigo curves. See the text for some comments on these graphics.…”

“…Indeed, the IC distance of [32] is rather empirically defined, and relies on several parameters whose influence is not easy to interpret in practice. Conversely, the weighted distance has a simple definition and only relies on the value of p. We will see in Section 5.1 how the noise ratio p can be efficiently estimated.…”

Adaptive Nonlinear Filter using Main Texture Direction for Mixed Noise in Color Image Processing

“…Many filters have been proposed for the removal of the noise. For instances, the classical standard median filter (SMF), the switching bilateral filter (SBF) [5] , the high performance filter (HPF) [6] , the spatially adaptive denoising algorithm (SADA) [7] and the new method for removing mixed noises (MNF) [8] , although these filters can remove the noise effectively, they fail to preserve image features and have higher computational complexity, like MNF and SBF.…”