Abstract: This paper describes a method for AWGN (Additive White Gaussian Noise) variance estimation in noisy stochastic signals, referred to as Multiplicative-Noising Variance Estimation (MNVE). The aim was to develop an estimation algorithm with minimal number of assumptions on the original signal structure. The provided MATLAB simulation and results analysis of the method applied on speech signals showed more accuracy than standardized AR (autoregressive) modeling noise estimation technique. In addition, great performance was observed on very low signal-to-noise ratios, which in general represents the worst case scenario for signal denoising methods. High execution time appears to be the only disadvantage of MNVE. After close examination of all the observed features of the proposed algorithm, it was concluded it is worth of exploring and that with some further adjustments and improvements can be enviably powerful.
Abstract: Suppose KY and KX are large sets of observed and
reference signals, respectively, each containing N signals. Is it possible to construct a filter F : KY → KX that requires a priori
information only on few signals, p N, from KX but performs better than the known filters based on a priori information on every
reference signal from KX? It is shown that the positive answer is
achievable under quite unrestrictive assumptions. The device behind
the proposed method is based on a special extension of the piecewise
linear interpolation technique to the case of random signal sets. The proposed technique provides a single filter to process any signal from
the arbitrarily large signal set. The filter is determined in terms of pseudo-inverse matrices so that it always exists.
Abstract: We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.
Abstract: We study a new technique for optimal data compression
subject to conditions of causality and different types of memory. The
technique is based on the assumption that some information about
compressed data can be obtained from a solution of the associated
problem without constraints of causality and memory. This allows
us to consider two separate problem related to compression and decompression
subject to those constraints. Their solutions are given
and the analysis of the associated errors is provided.
Abstract: A theory for optimal filtering of infinite sets of random
signals is presented. There are several new distinctive features of the
proposed approach. First, a single optimal filter for processing any
signal from a given infinite signal set is provided. Second, the filter is
presented in the special form of a sum with p terms where each term
is represented as a combination of three operations. Each operation
is a special stage of the filtering aimed at facilitating the associated
numerical work. Third, an iterative scheme is implemented into the
filter structure to provide an improvement in the filter performance at
each step of the scheme. The final step of the scheme concerns signal
compression and decompression. This step is based on the solution of
a new rank-constrained matrix approximation problem. The solution
to the matrix problem is described in this paper. A rigorous error
analysis is given for the new filter.