An adaptive edge-preserving image denoising technique using patch-based weighted-SVD filtering in wavelet domain
Paras Jain1 & Vipin Tyagi1
Received: 21 May 2015 /Revised: 7 December 2015 /Accepted: 9 December 2015 # Springer Science+Business Media New York 2015
Abstract Image denoising has always been one of the standard problems in image processing and computer vision. It is always recommendable for a denoising method to preserve important image features, such as edges, corners, etc., during its execution.
Image denoising methods based on wavelet transforms have been shown their excellence in providing an efficient edge-preserving image denoising, because they provide a suitable basis for separating noisy signal from the image signal. This paper presents a novel edge-preserving image denoising technique based on wavelet transforms. The wavelet domain representation of the noisy image is obtained through its multi-level decomposition into wavelet coefficients by applying a discrete wavelet transform. A patch-based weighted-SVD filtering technique is used to effectively reduce noise while preserving important features of the original image. Experimental results, compared to other approaches, demonstrate that the proposed method achieves very impressive gain in denoising performance.
Keywords Wavelet transform.Singularvaluedecomposition(SVD) .Edgedetection .Adaptive filtering 1 Introduction
In modern times, images and videos have become an integral part of our life.
Applications have been extended from general documentation of events and visual communication to the more serious surveillance and medical fields. This has increased the demand for accurate and visually impressive images. However, digital images may often get corrupted by noise during the process of acquisition and transmission. This
Multimed Tools Appl
DOI 10.1007/s11042-015-3154-8 * Vipin Tyagi email@example.com 1 Jaypee University of Engineering and Technology, Raghogarh, Guna, MP 473226, India form of corruption may degrade the visual quality of the image. The major challenge for a filtering technique is to suppress noise without affecting the important image structures and details.
Several approaches [17, 20, 39] for noise reduction have been proposed in last few decades, many of them are based on linear spatial domain filters. Linear spatial filters (for example,
Gaussian filters ) are simple and easily implementable and usually smooth the data to reduce noise effects; however, they can also result in blurring of important image structures such as edges . Furthermore, most linear filtering techniques proposed so far need some prior knowledge about the noise and the image characteristics. Mostly, such details are not available and may be hard to estimate from the input noisy data.
To overcome these problems of linear filters, filtering based on non-linear edgepreserving methods have become the main stream in the field and research is still going on in this direction . These non-linear edge-preserving filtering methods can preserve the important image features while suppressing the undesirable noise. Some of these techniques are based on partial differential equations (PDE’s) and variational models. For example, non-linear/anisotropic diffusion (AD)  was designed to overcome blurring issues of Gaussian filter  by smoothing the image only in the direction orthogonal to the gradient. The regularization methods based on the total variation (TV) [35, 36] were designed to smooth the homogenous regions of the image but not its edges. In ,
Tomasi and Manduchi proposed a simple, non-iterative and local smoothing filter known as the bilateral filter which smooths images by means of a non-linear combination of nearby image values. The non-local means (NLM)  is the first filter that makes use of the self-similarity in the whole image. NLM obtains a denoised patch by weighted averaging all other patches in the same image. It is an extension of the bilateral filter  in the sense of replacing the Euclidean distance between two pixels with the weighted Euclidean distance between two patches.
While the denoising approaches mentioned so far come under the category of spatial domain denoising methods, a vast section of image denoising literature is devoted to transform domain methods. In , Shao et al. introduced a new taxonomy of state-ofthe-art image denoising techniques which helps us to choose an appropriate technique based on image representation. They have provided a good comparative study on spatial domain, transform domain, and dictionary learning based denoising approaches. Inspired by non-local filtering in , Dabov et al.  proposed a transform-based block-matching and 3D (BM3D) filtering method which has great potential. Recently, the BM4D is proposed as an extension of the BM3D algorithm for denoising of volumetric data .
Qiu et al.  proposed a new edge-preserving smoothing filter, called Linear-Local
SURE (LLSURE) filter based on a local linear model and the principle of Stein’s
Unbiased Risk Estimate (SURE). Singular value decomposition (SVD) is also used for image noise reduction [4, 19, 24, 30, 46]. Cross validation techniques are used for thresholding parameter selection [28, 45]. Bayesian procedures combine inference from data with prior information to estimate thresholding parameters [7, 43]. Furthermore, a different subgroup of transform domain methods which include the wavelet-based denoising methods, exploits the decomposition of the data into a wavelet basis and modifies the wavelet coefficients to denoise the data [2, 8, 11, 22, 23, 26, 32, 40]. In particular, Jain and Tyagi  have proposed very recently a new technique for noise reduction in wavelet domain. They presented a new locally adaptive patch-based (LAPB) thresholding scheme that relies on the aggregation of multiple threshold estimates of a
Multimed Tools Appl wavelet coefficient and involves estimation of thresholding parameters for a coefficient in a local neighborhood.