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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>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.