2 citations · 5 across the 12 of their papers we have counts for
12 papers
Optimal approximation of a large matrix by a sum of projected linear mappings on prescribed subspaces
Phil Howlett, Anatoli Torokhti
We propose and justify a matrix reduction method for calculating the optimal approximation of an observed matrix by a sum $\sum_{i=1}^p \sum_{j=1}^…
A new technique for compression of data sets
Anatoli Torokhti
Data compression techniques are characterized by four key performance indices which are (i) associated accuracy, (ii) compression ratio, (iii) computational work, and (iv) degree o…
Processing of large sets of stochastic signals: filtering based on piecewise interpolation technique
Anatoli Torokhti
Suppose and are large sets of observed and reference signals, respectively, each containing signals. Is it possible to construct a filter that requires a…
Data Compression: Multi-Term Approach
Pablo Soto-Quiros, Anatoli Torokhti
In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accur…
Second Degree Model for Multi-Compression and Recovery of Distributed Signals
Pablo Soto-Quiros, Anatoli Torokhti, Stanley J. Miklavcic
We study the problem of multi-compression and reconstructing a stochastic signal observed by several independent sensors (or compressors) that transmit compressed information to a…
Extended Principal Component Analysis
Pablo Soto-Quiros, Anatoli Torokhti
Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs t…
Interpolation Estimator for Infinite Sets of Random Vectors
Anatoli Torokhti
We propose an approach to the estimation of infinite sets of random vectors. The problem addressed is as follows. Given two infinite sets of random vectors, find a single estimator…
An optimal linear filter for estimation of random functions in Hilbert space
Phil Howlett, Anatoli Totokhti
Let ${\mbox{$\mbox{\boldmath }$}}$ be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space , and let ${\mbox{$\mbox{\boldmath }$}}…
Best approximations of non-linear mappings: Method of optimal injections
Anatoli Torokhti, Pablo Soto-Quiros
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well dev…
Compression and Recovery of Distributed Random Signals
Alex Grant, Anatoli Torokhti, Pablo Soto-Quiros
We consider the case when a set of spatially distributed sensors make local observations which are noisy versions of a signal of interest. Each sensor transmits compressed informat…
Combined Reduced-Rank Transform
Anatoli Torokhti, Phil Howlett
We propose and justify a new approach to constructing optimal nonlinear transforms of random vectors. We show that the proposed transform improves such characteristics of rank-redu…
Generalized rank-constrained matrix approximations
Shmuel Friedland, Anatoli Torokhti
In this paper we give an explicit solution to the rank constrained matrix approximation in Frobenius norm, which is a generalization of the classical approximation of an m by n mat…