Salt and Pepper Noise Removal with Noise Detection and a Patch-Based Sparse Representation

Abstract

Images may be corrupted by salt and pepper impulse noise due to noisy sensors or channel transmission errors. A denoising method by detecting noise candidates and enforcing image sparsity with a patch-based sparse representation is proposed. First, noise candidates are detected and an initial guide image is obtained via an adaptive median filtering; second, a patch-based sparse representation is learnt from this guide image; third, a weighted 1 -1 regularization method is proposed to penalize the noise candidates heavier than the rest of pixels. An alternating direction minimization algorithm is derived to solve the regularization model. Experiments are conducted for 30%∼90% impulse noise levels, and the simulation results demonstrate that the proposed method outperforms total variation and Wavelet in terms of preserving edges and structural similarity to the noise-free images.

Improvement of quantized adaptive switching median filter for impulse noise reduction in gray-scale digital images

“…Create a 3 × 3 square region, defined by (j,k) = (y-1,x-1) to (y+1,x+1). If the pixel is noise-free pixel (α 1 (j,k)=0), add this pixel to h 3 , i.e., noise-free pixel (α 1 (j 1 ,k)=0) and remove them from h 7 , i.e., h 7 (D(j 1 ,k))←h 7 (D(j 1 ,k))-1 At the bottom row (i.e., j 2 =y+3), find noise-free pixel (α 1 (j 2 ,k)=0) and add them to h 7 , i.e., h 7 (D(j 2 ,k))←h 7 (D(j 2 ,k))+1…”

“…This type of impulse noise can severely degrade the quality of the image, which * Correspondence: haidi_ibrahim@ieee.org may affect subsequent processes such as segmentation, detection, and classification, due to information lost [2]. Therefore, a noise reduction technique is required to improve the quality of the image [2,7].…”

Salt and Pepper Noise Removal with Multi-Class Dictionary Learning and L0 Norm Regularizations

“…Recently, the transform domain sparsity is incorporated into sparse image reconstruction models [6][7][8] to significantly improve the image quality. The improvement on denoising, however, is still unsatisfactory since the sparsity is limited by pre-defined dictionaries or transforms which may not capture different image structures [8][9][10][11].…”

“…The state-of-the-art approaches introduce the adaptive dictionary learning [8][9][10][11] to provide sparser representations, leading to boosted performance for salt and pepper noise removal. However, the commonly used redundant dictionary learning algorithm, K-SVD [12], is relatively time consuming [13], which may slow down the iterative image reconstruction [8,9,14,15] or lose optimal sparsity when partial image patches are used for fast training [12].…”

“…the finite difference, a basic form of total variations (TV) [18,30] that models the piece-wise constant signals, and wavelets which characterize the piecewise smooth signals [6]. To better captures the image features, a dictionary [8,9] or transform [10,11] may be adaptively trained from the noisy image itself. Unlike the typical dictionary learning, which is time consuming in the iterative image reconstruction [8,9], the recently-proposed PANO not only saves the training time (only several seconds) but also provides adaptively sparse representation to the image by learning the self-similarity [11].…”