Image Denoising Using a Tight Frame

Shen, Lixin; Papadakis, Manos; Kakadiaris, Ioannis A.; Konstantinidis, I.; Kouri, Donald J.; Hoffman, David K.

doi:10.1109/icassp.2005.1415486

Cited by 18 publications

(16 citation statements)

References 34 publications

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“…We used a we utilize the high performance BLS-GSM method of [28] (using the fully-steerable pyramid) and the standard solution with uniform hard-thresholding (using thresholds optimized as a function of σ w over a training set outside of our simulation set). We refer the reader to [28], [30] for a compilation of many other results in the literature.…”

Section: Simulation Resultsmentioning

confidence: 99%

Weighted Averaging for Denoising With Overcomplete Dictionaries

Guleryuz¹

2007

IEEE Trans. on Image Process.

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We consider the scenario where additive, independent and identically distributed (i.i.d) noise in an image is removed using an overcomplete set of linear transforms and thresholding. Rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates provided by denoising with each of the transforms, we formulate the optimal combination as a conditional linear estimation problem and solve it for optimal estimates. Our approach is independent of the utilized transforms and the thresholding scheme, and as we illustrate using oracle based denoisers, it extends established work by exploiting a separate degree of freedom that is in general not reachable using previous techniques. Our derivation of the optimal estimates specifically relies on the assumption that the utilized transforms provide sparse decompositions. At the same time, our work is robust as it does not require any assumptions about image statistics beyond sparsity. Unlike existing work which tries to devise ever more sophisticated transforms and thresholding algorithms to deal with the myriad types of image singularities, our work uses basic tools to obtain very high performance on singularities by taking better advantage of the sparsity that surrounds them. With well-established transforms we obtain results that are competitive with state-of-the-art methods.

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Section: Simulation Resultsmentioning

confidence: 99%

Weighted Averaging for Denoising With Overcomplete Dictionaries

Guleryuz¹

2007

IEEE Trans. on Image Process.

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“…Our thresholding denoising scheme in the framelet domain is similar to that in the orthonormal wavelet domain [23]. As already pointed out by many authors, see for examples [18,29,35], framelets give better denoising results. (ii) Iterate on n until convergence:…”

Section: Framelet Denoising Schemementioning

confidence: 54%

Restoration of Chopped and Nodded Images by Framelets

Cai¹,

Chan²,

Shen³

et al. 2008

SIAM J. Sci. Comput.

131

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Abstract. In infrared astronomy, an observed image from a chop and nod process can be considered as the result of passing the original image through a highpass filter. Here we propose a restoration algorithm which builds up a tight framelet system that has the highpass filter as one of the framelet filters. Our approach reduces the solution of restoration problem to that of recovering the missing coefficients of the original image in the tight framelet decomposition. The framelet approach provides a natural setting to apply various sophisticated framelet denoising schemes to remove the noise without reducing the intensity of major stars in the image. A proof of the convergence of the algorithm based on convex analysis is also provided. Simulated and real images are tested to illustrate the efficiency of our method over the projected Landweber method.

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“…The reader is referred to [1,10] for the relationship between PDE diffusion and the bilateral filter, another popular method for image denoising. Recently wavelet frames have been successfully used in noise removal [30], image recovery [7,8], image inpainting/restoration [3,4,5], signal classification [9] and medical image analysis [18,25]. Compared with wavelet systems, the elements in a frame system may be linearly dependent; namely, frames can be redundant.…”

Section: Introductionmentioning

confidence: 99%

Correspondence between frame shrinkage and high-order nonlinear diffusion

Jiang

2012

Applied Numerical Mathematics

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Nonlinear diffusion filtering and wavelet/frame shrinkage are two popular methods for signal and image denoising. The relationship between these two methods has been studied recently. In this paper we investigate the correspondence between frame shrinkage and nonlinear diffusion.We show that the frame shrinkage of Ron-Shen's continuous-linear-spline-based tight frame is associated with a fourth-order nonlinear diffusion equation. We derive high-order nonlinear diffusion equations associated with general tight frame shrinkages. These high-order nonlinear diffusion equations are different from the high-order diffusion equations studied in the literature. We also construct two sets of tight frame filter banks which result in the sixth-and eighth-order nonlinear diffusion equations.The correspondence between frame shrinkage and diffusion filtering is useful to design diffusion-inspired shrinkage functions with competitive performance. On the other hand, the study of such a correspondence leads to a new type of diffusion equations and helps to design frame-inspired diffusivity functions. The denoising results with diffusion-inspired shrinkages provided in this paper are promising.

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Image Denoising Using a Tight Frame

Cited by 18 publications

References 34 publications

Weighted Averaging for Denoising With Overcomplete Dictionaries

Weighted Averaging for Denoising With Overcomplete Dictionaries

Restoration of Chopped and Nodded Images by Framelets

Correspondence between frame shrinkage and high-order nonlinear diffusion

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