Adaptive frame-based color image denoising

Shen, Yi; Han, Bin; Braverman, Elena

doi:10.1016/j.acha.2015.04.001

Cited by 11 publications

(7 citation statements)

References 23 publications

(60 reference statements)

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“…Frame theory is a relatively emerging area in pure as well as applied mathematics research and approximation. It has been applied in a wide range of applications in signal processing [13], image denoising [14], and computational physics and biology [15]. Interested readers should consult the references therein to get a complete picture.…”

Section: Preliminary Resultsmentioning

confidence: 99%

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A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle

Mohammad

2019

Symmetry

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In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.

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Section: Preliminary Resultsmentioning

confidence: 99%

“…Note that, evaluating the values in Equation (14) and by considering the Haar framelet system, we are able to determine the values of j, k for which the representation in Equation 11is accurate. This is done by avoiding the inner products that have zero values.…”

Section: Solving Fredholm Integral Equation Via Tight Frameletsmentioning

confidence: 99%

A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle

Mohammad

2019

Symmetry

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“…In addition, the effectiveness of modified fuzzy set filter is further analyzed by using the performance metrics like NMSE, MSSIM, and UIQI [31,32], which are mathematically given in the equations (8), (9), (10), and (11).…”

Section: Performance Measurementioning

confidence: 99%

“…The existing denoising methods are categorized into two types such as nonlocal self-similarity based methods and conventional local prior based methods. Mostly, the existing methods concentrate only on local priors, so their performances are inadequate [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Robust Gaussian Noise Detection and Removal in Color Images using Modified Fuzzy Set Filter

Suneetha¹,

Reddy

2020

Journal of Intelligent Systems

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In the data collection phase, the digital images are captured using sensors that often contaminated by noise (undesired random signal). In digital image processing task, enhancing the image quality and reducing the noise is a central process. Image denoising effectively preserves the image edges to a higher extend in the flat regions. Several adaptive filters (median filter, Gaussian filter, fuzzy filter, etc.) have been utilized to improve the smoothness of digital image, but these filters failed to preserve the image edges while removing noise. In this paper, a modified fuzzy set filter has been proposed to eliminate noise for restoring the digital image. Usually in fuzzy set filter, sixteen fuzzy rules are generated to find the noisy pixels in the digital image. In modified fuzzy set filter, a set of twenty-four fuzzy rules are generated with additional four pixel locations for determining the noisy pixels in the digital image. The additional eight fuzzy rules ease the process of finding the image pixels,whether it required averaging or not. In this scenario, the input digital images were collected from the underwater photography fish dataset. The efficiency of the modified fuzzy set filter was evaluated by varying degrees of Gaussian noise (0.01, 0.03, and 0.1 levels of Gaussian noise). For performance evaluation, Structural Similarity (SSIM), Mean Structural Similarity (MSSIM), Mean Square Error (MSE), Normalized Mean Square Error (NMSE), Universal Image Quality Index (UIQI), Peak Signal to Noise Ratio (PSNR), and Visual Information Fidelity (VIF) were used. The experimental results showed that the modified fuzzy set filter improved PSNR value up to 2-3 dB, MSSIM up to 0.12-0.03, and NMSE value up to 0.38-0.1 compared to the traditional filtering techniques.

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“…Its main is to eliminate noise while preserving edges and features of an image. Many techniques have been proposed and studied for Gaussian noise removal from natural images, e.g., [22], [35], [42], [18], [19], [4], [14], [37], [8], [21], [5], [20], [47], [15], [16], [24], [7], [49], [38], [6], [17], [27], [3]. In particular, some algorithms also were proposed for binary image denoising in the literature [2], [9], [11], [23], [39].…”

mentioning

confidence: 99%

Piecewise constant signal and image denoising using a selective averaging method with multiple neighbors

Wang¹,

Wu²,

Deng³

2019

Inverse Problems &Amp; Imaging

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Piecewise constant signals and images are an important kind of data. Typical examples include bar code signals, logos, cartoons, QR codes (Quick Response codes), and text images, which are widely used in both general commercial and automotive industry use. One previous work called a general selective averaging method (GSAM) was introduced to remove noise from them. It chooses homogeneous neighbors from the two closest pixels (one pixel at each side) to update the current pixel. One limitation is that it suffered from appearing sparse noisy pixels in the denoised result when the noise level is high. In this paper, we try to solve this problem by proposing a selective averaging method with multiple neighbors. To update the intensity value at each pixel, the proposed algorithm averages more homogeneous neighbors selected from a large domain, which is based on the property of the local geometry of signals and images. This greatly reduces sparse noisy pixels left in the final result by GSAM. Similarly, our method adopts the Neumann boundary condition at edges, and thus preserves edges well. In 1D case, some theoretical results are given to guarantee the convergence of our algorithm. In 2D case, except eliminating additive Gaussian noise, this algorithm can be used for restoring noisy images corrupted by speckle noise. Intensive experiments on both gray and color image denoising demonstrate that the proposed method is quite effective for piecewise constant image denoising and achieves superior performance visually and quantitatively.

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Adaptive frame-based color image denoising

Cited by 11 publications

References 23 publications

A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle

A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle

Robust Gaussian Noise Detection and Removal in Color Images using Modified Fuzzy Set Filter

Piecewise constant signal and image denoising using a selective averaging method with multiple neighbors

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