Journal Article•
Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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TL;DR: This paper addresses the above problems to some extend by introducing rotation invariant similarity measures and aims to reduce the computational complexity and preserves the edges by discarding the dissimilar pixels by using a two-level refining approach.
Abstract: Magnetic resonance images are subjected to degradation due to the presence of noise from various sources. For further processing of the MR images and for effective visual analysis, the noise should be removed. Many denoising algorithms have been proposed for enhancing MR images. Preserving the structural details has its own importance in image denoising, and especially for medical images it should not be compromised. For effective image denoising, the data distribution in the images should be known in advance. Data in the magnitude MR images are Rician distributed (if acquired with single coil). Among the recently proposed denoising methods for reducing Rician noise, non-local maximum likelihood estimation method (NLML) proved to be an efficient one. But the superior performance of the NLML is restricted by its high computational complexity and non optimal way of selecting the samples for ML estimation. In this paper we address the above problems to some extend by introducing rotation invariant similarity measures. The proposed method aims to reduce the computational complexity and preserves the edges by discarding the dissimilar pixels by using a two-level refining approach. Comparative analysis of the proposed method with conventional NLML method based on the execution time and quantitative analysis in terms of PSNR, SSIM, FSIM and UIQI shows that the proposed method has an edge over the conventional method.
1 citations
TL;DR: The Ocean Weather Ship Weather Reporter encountered heavy seas over a 4-day period from September 12-15, 1961 as discussed by the authors, and measured the sea state during this period with a shipborne wave recorder at 3-hour intervals.
Abstract: The Ocean Weather Ship Weather Reporter, underway from the United Kingdom to assume her position at station J (near 53°N, 18°W) on the North Atlantic, encountered heavy seas over a 4-day period from September 12–15, 1961. The ship measured the sea state during this period with a shipborne wave recorder at 3-hour intervals. The wave energy spectra are computed from these records and are presented. The upper and lower confidence limits in the estimation of these energy spectra are discussed. Such statistical quantities as the significant wave height and the average period are presented.
1 citations
TL;DR: In this article, the power average of a small number of random samples is presented as a suitable estimate of the mean power content of such a sum of sinusoids of evenly distributed random argument.
01 Jan 1993
Abstract: The Canham model of porous silicon assigns the surprising optical transitions to excitons localised on quantum wires of fluctuating width. We use a topographical model of exciton energetics on such a wire to derive analytical expressions for the resulting absorption and emission band profiles. The fluctuating width of a quantum wire modulates the exciton energy in a random manner. We therefore identify the optical absorption, corresponding to exciton creation at random positions, with the energy spectrum, A(E), of a random function, E(x). Emission of light occurs when excitons decay after relaxing into local minima of E(x): these excitons are localised in a purely classical sense. We obtain the energy spectrum of the local minima, which corresponds to the emission line shape. A calculation of the zeroth and first moments of the emission line allows a straightforward comparison of predicted band profiles with experiment by means of the Stokes’ shift.
TL;DR: In this article, the Laplace transform is replaced by the kernel of the second-kind integral equation of the first-kind in a form where the kernel can be replaced by its Laplace transformation.
Abstract: On solving the Fredholm integral equation of the second-kind in a form where the kernel is replaced by its Laplace transform, we find that our Fredholm-determinant completely agrees with the one we recently derived and is contrary to the one reported in Srinivasan's work. Further, whereas our formalism ensures the physical tenability of the generating-function, a simple analysis of the generating-function due to Srinivasan shows that it leads to untenable results.