Sharad Silwal

Analysis, Applied Mathematics, Statistics



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    ABSTRACT: In this expository article we introduce a diagrammatic scheme to represent reverse classes of weights and some of their properties.
    Expositiones Mathematicae 11/2013; 33(1). DOI:10.1016/j.exmath.2013.12.008 · 0.65 Impact Factor
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    ABSTRACT: We introduce a novel approach towards Harnackʼs inequality in the context of spaces of homogeneous type. This approach, based on the so-called critical density property and doubling properties for weights, avoids the explicit use of covering lemmas and BMO.
    Journal of Differential Equations 04/2013; 254(8):3369–3394. DOI:10.1016/j.jde.2013.01.025 · 1.57 Impact Factor
  • Diego Maldonado, Sharad Silwal, Haiyan Wang
    Statistics and its interface 01/2013; 6(1):117-135. DOI:10.4310/SII.2013.v6.n1.a11 · 0.46 Impact Factor
  • Sharad Silwal, Haiyan Wang, Diego Maldonado
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    ABSTRACT: Images encountered in our daily lives typically contain random noise of some level. The human visual system (HVS) has the ability to see through such noises at low level. It is desirable to replicate this ability in an image quality assessment method. Extensive experiments found that well-established full-reference image quality assessment methods, such as mean square error (MSE), structure similarity index (SSIM) by Wang et al. [2004] and peak signalto-noise ratio (PSNR), may poorly mimic the human visual system in this regard. In this article we propose a new full-reference image quality assessment method, namely, wavelet-based non-parametric structure similarity (WNPSSIM) index, based on a non-parametric test of the hypothesis of identical images. The test is conducted on the wavelet domain to take advantage of the belief that wavelet transform provides an alternate representation of image data that is more in sync with the HVS (Field [1999]; Portilla et al. [2003]; Chandler and Hemami [2005]). Experimental comparisons demonstrate that WNPSSIM performs better than some well-known image quality assessment methods when the images involved are corrupted with random noises.
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    Haiyan Wang, Diego Maldonado, Sharad Silwal
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    ABSTRACT: In image processing, image similarity indices evaluate how much structural information is maintained by a processed image in relation to a reference image. Commonly used measures, such as the mean squared error (MSE) and peak signal to noise ratio (PSNR), ignore the spatial information (e.g. redundancy) contained in natural images, which can lead to an inconsistent similarity evaluation from the human visual perception. Recently, a structural similarity measure (SSIM), that quantifies image fidelity through estimation of local correlations scaled by local brightness and contrast comparisons, was introduced by Wang et al. (2004). This correlation-based SSIM outperforms MSE in the similarity assessment of natural images. However, as correlation only measures linear dependence, distortions from multiple sources or nonlinear image processing such as nonlinear filtering can cause SSIM to under- or overestimate the true structural similarity. In this article, we propose a new similarity measure that replaces the correlation and contrast comparisons of SSIM by a term obtained from a nonparametric test that has superior power to capture general dependence, including linear and nonlinear dependence in the conditional mean regression function as a special case. The new similarity measure applied to images from noise contamination, filtering, and watermarking, provides a more consistent image structural fidelity measure than commonly used measures.
    Computational Statistics & Data Analysis 11/2011; 55(11):2925-2936. DOI:10.1016/j.csda.2011.04.021 · 1.15 Impact Factor
  • Sharad Deep Silwal
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    ABSTRACT: This report addresses some mathematical and statistical techniques of image processing and their computational implementation. Fundamental theories have been presented, applied and illustrated with examples. To make the report as self-contained as possible, key terminologies have been defined and some classical results and theorems are stated, in the most part, without proof. Some algorithms and techniques of image processing have been described and substantiated with experimentation using MATLAB. Several ways of estimating original images from noisy image data and their corresponding risks are discussed. Two image processing concepts selected to illustrate computational implementation are: "Bayes classification" and "Wavelet denoising". The discussion of the latter involves introducing a specialized area of mathematics, namely, wavelets. A self-contained theory for wavelets is built by first reviewing basic concepts of Fourier Analysis and then introducing Multi-resolution Analysis and wavelets. For a better understanding of Fourier Analysis techniques in image processing, original solutions to some problems in Fourier Analysis have been worked out. Finally, implementation of the above-mentioned concepts are illustrated with examples and MATLAB codes. Master of Science Masters Department of Statistics Diego M. Maldonado Haiyan Wang

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