Sparse Approach in Filtering of Color Images Corrupted by Mixture Noises VOLODYMYR PONOMARYOV 1* ,ALFREDO PALACIOS-ENRIQUEZ 1 1 ESIME-Culhuan, Instituto Politecnico Nacional, 04430, Col. San Fco Culhuacan, Mexico-city, MEXICO Abstract. A novel filtering approach is presented in denoising in the color images contaminated by mixture of additive-impulsive noises. Novel framework consists of three principal stages: impulsive noise suppression that is performed detecting pixels corrupted by impulsive noise and then, filtering found spikes by a variant of median filter; during second stage, original additive noise suppression filter is employed in Wavelet transform domain via a sparse representation and 3D-filtering; finally, non- desirable effects obtained in an image during previous stages are processed to correct fine details. In case of multiplicative noise suppression, the designed denoising scheme uses 3D homomorphic sparse processing stage and post-filtering procedure. Evaluation of novel approach in denoising complex distortions has been performed using objective criteria (PSNR and SSIM measures) and subjective perception via human visual system confirming their better performance in comparison with state-of-the- art techniques. Keywords: Signal processing, Image Processing, Filtering of Color Images, Mixture Noises Received: February 11, 2020. Revised: April 11, 2020. Accepted: April 29, 2020. Published: May 6, 2020. 1 Introduction The fundamental problem in image processing consists in reducing a noise while preserving the most of image features. The presence of random digital noise in an image reduces the performance of different systems such as pattern recognition, diagnostics, object control, etc. Principal difficulties in any filtering technique are that a processing procedure should perform suppression of noise, meanwhile the fine details, edges, and texture properties can be unchanged. The complex and changing structure of real images does not allow the corrupted image details to be efficiently identified and filtered. If fine details of an image are distorted, these drawbacks could cause misinterpretation during medical diagnosis, incorrect classification of objects in the satellite images, erroneous detection of obstacles by autonomous robots, errors in telemedicine applications, etc. [1]. During image acquisition, additive or multiplicative noise can be present, and during its transmission or acquisition, further contamination may be caused by impulsive noise. Images may be corrupted by interference and imperfections in the channel or the reception equipment. Additionally, digital cameras can introduce noise, electronic interference or errors in data acquisition [2]. The most common type of noise additive one is usually assumed to be Gaussian random process nad (i,j) where all pixels in an image are corrupted. Other type of noise is multiplicative (speckle) one that is usual for coherent sensors such as ultrasound or radar sensors [3]. The most common model of mixed noise used is a combination of additive noise, usually, Gaussian and random impulsive noise n im (i,j). The corrupted image E(i,j) in such type of noises can be represented as follows: . p y probabilit , j) (i, n p - 1 y probabilit ), , ( ) , ( ) , ( im im im      j i n j i e j i E ad (1) In case of multiplicative noise ) , ( j i  , the corrupted image E(i,j ) is presented as folllows: ) , ( ) , ( ) , ( ) , ( j i n j i e j i j i E ad     . (1a) 2 Related Works The restoration of corrupted images by a mixture of different type of noises requires novel approaches, because a lot of existing techniques developed for additive noise suppression are not capable to eliminate the artefacts produced by impulsive noise or other type noise. There are several filtering techniques for Gaussian additive noise elimination where among them, there exist different techniques based on search of a group of pixels called as reference block. Jain [4] proposed a technique based on WT that is applied to some patches with a chosen degree of similarity. Filtering is performed for each sub-band wavelet by obtaining a threshold that adapts to the conditions of each a neighborhood. Lukin [5] proposed an adaptive filter based on an assessment of the image locality via filtering by DCT to obtain a neighborhood and to estimate the local variance, then using it to distinguish homogeneous and heterogeneous areas. Bahoura [6] proposed a signal denoising technique based on wavelet with a thresholding function, which is applied to the wavelet coefficients. Jin [7] introduced new non-local operators to interpret the filter as a regularization of the Dirichlet’s functional. Smoothing WSEAS TRANSACTIONS on SIGNAL PROCESSING DOI: 10.37394/232014.2020.16.10 Volodymyr Ponomaryov, Alfredo Palacios-Enriquez E-ISSN: 2224-3488 81 Volume 16, 2020