Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal, time-invariant, and satisfy the fading memory property and second, that a subset of this class is universal in the category of fading memory filters with stochastic almost surely uniformly bounded inputs. This means that any discrete-time filter that satisfies the fading memory property with random inputs of that type can be uniformly approximated by elements in the non-homogeneous state-affine family.Comment: 41 page

On a fast bilateral filtering formulation using functional rearrangements

We introduce an exact reformulation of a broad class of neighborhood filters, among which the bilateral filters, in terms of two functional rearrangements: the decreasing and the relative rearrangements. Independently of the image spatial dimension (one-dimensional signal, image, volume of images, etc.), we reformulate these filters as integral operators defined in a one-dimensional space corresponding to the level sets measures. We prove the equivalence between the usual pixel-based version and the rearranged version of the filter. When restricted to the discrete setting, our reformulation of bilateral filters extends previous results for the so-called fast bilateral filtering. We, in addition, prove that the solution of the discrete setting, understood as constant-wise interpolators, converges to the solution of the continuous setting. Finally, we numerically illustrate computational aspects concerning quality approximation and execution time provided by the rearranged formulation.Comment: 29 pages, Journal of Mathematical Imaging and Vision, 2015. arXiv admin note: substantial text overlap with arXiv:1406.712

Systematic approach to nonlinear filtering associated with aggregation operators. Part 1. SISO-filters

There are various methods to help restore an image from noisy distortions. Each technique has its advantages and disadvantages. Selecting the appropriate method plays a major role in getting the desired image. Noise removal or noise reduction can be done on an image by linear or nonlinear filtering. The more popular linear technique is based on average (on mean) linear operators. Denoising via linear filters normally does not perform satisfactorily since both noise and edges contain high frequencies. Therefore, any practical denoising model has to be nonlinear. In this work, we introduce and analyze a new class of nonlinear SISO-filters that have their roots in aggregation operator theory. We show that a large body of non-linear filters proposed to date constitute a proper subset of aggregation filters. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No. 17-07-00886 and by Ural State Forest Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"

How Predictable are Temperature-series Undergoing Noise-controlled Dynamics in the Mediterranean

Mediterranean is thought to be sensitive to global climate change, but its future interdecadal variability is uncertain for many climate models. A study was made of the variability of the winter temperature over the Mediterranean Sub-regional Area (MSA), employing a reconstructed temperature series covering the period 1698 to 2010. This paper describes the transformed winter temperature data performed via Empirical Mode Decomposition for the purposes of noise reduction and statistical modeling. This emerging approach is discussed to account for the internal dependence structure of natural climate variability

Hierarchical morphological segmentation for image sequence coding

This paper deals with a hierarchical morphological segmentation algorithm for image sequence coding. Mathematical morphology is very attractive for this purpose because it efficiently deals with geometrical features such as size, shape, contrast, or connectivity that can be considered as segmentation-oriented features. The algorithm follows a top-down procedure. It first takes into account the global information and produces a coarse segmentation, that is, with a small number of regions. Then, the segmentation quality is improved by introducing regions corresponding to more local information. The algorithm, considering sequences as being functions on a 3-D space, directly segments 3-D regions. A 3-D approach is used to get a segmentation that is stable in time and to directly solve the region correspondence problem. Each segmentation stage relies on four basic steps: simplification, marker extraction, decision, and quality estimation. The simplification removes information from the sequence to make it easier to segment. Morphological filters based on partial reconstruction are proven to be very efficient for this purpose, especially in the case of sequences. The marker extraction identifies the presence of homogeneous 3-D regions. It is based on constrained flat region labeling and morphological contrast extraction. The goal of the decision is to precisely locate the contours of regions detected by the marker extraction. This decision is performed by a modified watershed algorithm. Finally, the quality estimation concentrates on the coding residue, all the information about the 3-D regions that have not been properly segmented and therefore coded. The procedure allows the introduction of the texture and contour coding schemes within the segmentation algorithm. The coding residue is transmitted to the next segmentation stage to improve the segmentation and coding quality. Finally, segmentation and coding examples are presented to show the validity and interest of the coding approach.Peer ReviewedPostprint (published version

Solving the Selesnick-Burrus Filter Design Equations Using Computational Algebra and Algebraic Geometry

In a recent paper, I. Selesnick and C.S. Burrus developed a design method for maximally flat FIR low-pass digital filters with reduced group delay. Their approach leads to a system of polynomial equations depending on three integer design parameters $K,L,M$. In certain cases (their ``Region I''), Selesnick and Burrus were able to derive solutions using only linear algebra; for the remaining cases ("Region II''), they proposed using Gr\"obner bases. This paper introduces a different method, based on multipolynomial resultants, for analyzing and solving the Selesnick-Burrus design equations. The results of calculations are presented, and some patterns concerning the number of solutions as a function of the design parameters are proved.Comment: 34 pages, 2 .eps figure

CMOS design of chaotic oscillators using state variables: a monolithic Chua's circuit

This paper presents design considerations for monolithic implementation of piecewise-linear (PWL) dynamic systems in CMOS technology. Starting from a review of available CMOS circuit primitives and their respective merits and drawbacks, the paper proposes a synthesis approach for PWL dynamic systems, based on state-variable methods, and identifies the associated analog operators. The GmC approach, combining quasi-linear VCCS's, PWL VCCS's, and capacitors is then explored regarding the implementation of these operators. CMOS basic building blocks for the realization of the quasi-linear VCCS's and PWL VCCS's are presented and applied to design a Chua's circuit IC. The influence of GmC parasitics on the performance of dynamic PWL systems is illustrated through this example. Measured chaotic attractors from a Chua's circuit prototype are given. The prototype has been fabricated in a 2.4- mu m double-poly n-well CMOS technology, and occupies 0.35 mm/sup 2/, with a power consumption of 1.6 mW for a +or-2.5-V symmetric supply. Measurements show bifurcation toward a double-scroll Chua's attractor by changing a bias current