Image denoising as a pre-processing stage is a used to preserve details, edges and global contrast without blurring the corrupted image. Among state-of-the-art algorithms, block shrinkage denoising is an effective and compatible method to suppress additive white Gaussian noise (AWGN). Traditional NeighShrink algorithm can remove the Gaussian noise significantly, but loses the edge information i...

Based on an adequate new Gel’fand triple, we construct the infinite dimensional free Gaussian white noise measure μ using the Bochner-Minlos theorem. Next, we give the chaos decomposition of an L2 space with respect to the measure μ .

To improve the spatial resolution of low resolution image with Gaussian blur and Pepper & salt noise, a blind single-image super resolution reconstruction method is proposed. In the low resolution imaging model, the Gaussian blur, down-sampling, as well as Pepper & Salt noise are all considered. Firstly, the Pepper & Salt noise in the low resolution image is reduced through median filtering met...

Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...

This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic e...

The problem considered in this paper is whether the capacity of a discrete time Gaussian channel is increased by feedback or not. It is well known that the capacity of a white Gaussian channel under the average power constraint is not changed by feedback. In the previous paper [7] we gave some sufficient conditions under which the capacity of a non-white Gaussian channel is increased by feedbac...

We propose a Somewhat Homomorphic Encryption (SHE) scheme based on the Learning With Rounding (LWR) problem. The LWR problem is somewhat similar to the more classical Learning With Errors (LWE) and was proposed as a deterministic variant of it and setting up an LWR instance does not require the generation of gaussian noise. Thus our SHE scheme can be instantiated without the need for expensive ...

We study the sensitivity to noise of |permanent(X)|2 for random real and complex n×n Gaussian matrices X, and show that asymptotically the correlation between the noisy and noiseless outcomes tends to zero when the noise level is ω(1)/n. This suggests that, under certain reasonable noise models, the probability distributions produced by noisy BosonSampling are very sensitive to noise. We also s...

In order to detect correlation of Gaussian signals, linear, rank, and sign correlation are developed. Magnitude of correlation coefficients, significance, and two-sided significance are computed and compared for each test. Programs are written as macro files, in c++, that are run in ROOT. Efficiencies of correlation tests are calculated resulting in a relative length equation, and methods of ac...

The efficacy of a specially constructed Gallager-type errorcorrecting code to communication in a Gaussian channel is being examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite size effects are estimated for comparing the results to the bounds set by Shannon. The cri...