Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Performance boost of time-delay reservoir computing by non-resonant clock cycle

The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, until now the interplay of the different timescales has not been investigated thoroughly. In this manuscript, we investigate the effects of a mismatch between the time-delay and the clock cycle for a general model. Typically, these two time scales are considered to be equal. Here we show that the case of equal or resonant time-delay and clock cycle could be actively detrimental and leads to an increase of the approximation error of the reservoir. In particular, we can show that non-resonant ratios of these time scales have maximal memory capacities. We achieve this by translating the periodically driven delay-dynamical system into an equivalent network. Networks that originate from a system with resonant delay-times and clock cycles fail to utilize all of their degrees of freedom, which causes the degradation of their performance

A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels

In this paper, we establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive multiple-input multiple-output MIMO systems employing single-carrier (SC) modulation in time division duplex (TDD) mode by exploiting the joint angle-delay domain channel sparsity in millimeter (mm) wave frequencies. First, based on a generic subspace projection taking the joint angle-delay power profile and user-grouping into account, the reduced rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived for spatially correlated wideband MIMO channels. Second, the statistical pre-beamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction problem and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. Finally, a spatio-temporal domain correlator type reduced rank channel estimator, as an approximation of the RR-MMSE estimate, is obtained by carrying out least square (LS) estimation in a proper reduced dimensional beamspace. It is observed that the proposed techniques show remarkable robustness to the pilot interference (or contamination) with a significant reduction in pilot overhead

Joint PDF modelling of turbulent flow and dispersion in an urban street canyon

The joint probability density function (PDF) of turbulent velocity and concentration of a passive scalar in an urban street canyon is computed using a newly developed particle-in-cell Monte Carlo method. Compared to moment closures, the PDF methodology provides the full one-point one-time PDF of the underlying fields containing all higher moments and correlations. The small-scale mixing of the scalar released from a concentrated source at the street level is modelled by the interaction by exchange with the conditional mean (IECM) model, with a micro-mixing time scale designed for geometrically complex settings. The boundary layer along no-slip walls (building sides and tops) is fully resolved using an elliptic relaxation technique, which captures the high anisotropy and inhomogeneity of the Reynolds stress tensor in these regions. A less computationally intensive technique based on wall functions to represent boundary layers and its effect on the solution are also explored. The calculated statistics are compared to experimental data and large-eddy simulation. The present work can be considered as the first example of computation of the full joint PDF of velocity and a transported passive scalar in an urban setting. The methodology proves successful in providing high level statistical information on the turbulence and pollutant concentration fields in complex urban scenarios.Comment: Accepted in Boundary-Layer Meteorology, Feb. 19, 200

Speckle Reduction and Contrast Enhancement of Echocardiograms via Multiscale Nonlinear Processing

This paper presents an algorithm for speckle reduction and contrast enhancement of echocardiographic images. Within a framework of multiscale wavelet analysis, the authors apply wavelet shrinkage techniques to eliminate noise while preserving the sharpness of salient features. In addition, nonlinear processing of feature energy is carried out to enhance contrast within local structures and along object boundaries. The authors show that the algorithm is capable of not only reducing speckle, but also enhancing features of diagnostic importance, such as myocardial walls in two-dimensional echocardiograms obtained from the parasternal short-axis view. Shrinkage of wavelet coefficients via soft thresholding within finer levels of scale is carried out on coefficients of logarithmically transformed echocardiograms. Enhancement of echocardiographic features is accomplished via nonlinear stretching followed by hard thresholding of wavelet coefficients within selected (midrange) spatial-frequency levels of analysis. The authors formulate the denoising and enhancement problem, introduce a class of dyadic wavelets, and describe their implementation of a dyadic wavelet transform. Their approach for speckle reduction and contrast enhancement was shown to be less affected by pseudo-Gibbs phenomena. The authors show experimentally that this technique produced superior results both qualitatively and quantitatively when compared to results obtained from existing denoising methods alone. A study using a database of clinical echocardiographic images suggests that such denoising and enhancement may improve the overall consistency of expert observers to manually defined borders

Multichannel Speech Separation and Enhancement Using the Convolutive Transfer Function

This paper addresses the problem of speech separation and enhancement from multichannel convolutive and noisy mixtures, \emph{assuming known mixing filters}. We propose to perform the speech separation and enhancement task in the short-time Fourier transform domain, using the convolutive transfer function (CTF) approximation. Compared to time-domain filters, CTF has much less taps, consequently it has less near-common zeros among channels and less computational complexity. The work proposes three speech-source recovery methods, namely: i) the multichannel inverse filtering method, i.e. the multiple input/output inverse theorem (MINT), is exploited in the CTF domain, and for the multi-source case, ii) a beamforming-like multichannel inverse filtering method applying single source MINT and using power minimization, which is suitable whenever the source CTFs are not all known, and iii) a constrained Lasso method, where the sources are recovered by minimizing the $\ell_1$-norm to impose their spectral sparsity, with the constraint that the $\ell_2$-norm fitting cost, between the microphone signals and the mixing model involving the unknown source signals, is less than a tolerance. The noise can be reduced by setting a tolerance onto the noise power. Experiments under various acoustic conditions are carried out to evaluate the three proposed methods. The comparison between them as well as with the baseline methods is presented.Comment: Submitted to IEEE/ACM Transactions on Audio, Speech and Language Processin

Effective Image Restorations Using a Novel Spatial Adaptive Prior

Bayesian or Maximum a posteriori (MAP) approaches can effectively overcome the ill-posed problems of image restoration or deconvolution through incorporating a priori image information. Many restoration methods, such as nonquadratic prior Bayesian restoration and total variation regularization, have been proposed with edge-preserving and noise-removing properties. However, these methods are often inefficient in restoring continuous variation region and suppressing block artifacts. To handle this, this paper proposes a Bayesian restoration approach with a novel spatial adaptive (SA) prior. Through selectively and adaptively incorporating the nonlocal image information into the SA prior model, the proposed method effectively suppress the negative disturbance from irrelevant neighbor pixels, and utilizes the positive regularization from the relevant ones. A two-step restoration algorithm for the proposed approach is also given. Comparative experimentation and analysis demonstrate that, bearing high-quality edge-preserving and noise-removing properties, the proposed restoration also has good deblocking property

Kinetics of a Network of Vortex Loops in He II and a Theory of Superfluid Turbulence

A theory is developed to describe the superfluid turbulence on the base of kinetics of the merging and splitting vortex loops. Because of very frequent reconnections the vortex loops (as a whole) do not live long enough to perform any essential evolution due to the deterministic motion. On the contrary, they rapidly merge and split, and these random recombination processes prevail over other slower dynamic processes. To develop quantitative description we take the vortex loops to have a Brownian structure with the only degree of freedom, which is the length $l$ of the loop. We perform investigation on the base of the Boltzmann type kinetic equation for the distribution function $n(l)$ of number of loops with length $l$. By use of the special ansatz in the collision integral we have found the exact power-like solution to kinetic equation in the stationary case. This solution is not (thermodynamically) equilibrium, but on the contrary, it describes the state with two mutual fluxes of the length (or energy) in space of sizes of the vortex loops. The term flux means just redistribution of length (or energy) among the loops of different sizes due to reconnections. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the turbulent superfluid helium. In particular, we evaluated the mean radius of the curvature and the full rate of the reconnection events. We also studied the evolution of the full length of vortex loops per unit volume-the so-called vortex line density. It is shown this evolution to obey the famous Vinen equation. The properties of the Vinen equation from the point of view of the developed approach had been discussed.Comment: 34 pages, 9 Postscript figures, [aps,preprint,12pt]{revtex4

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)