George-Othon Glentis

Efficient least squares adaptive algorithms for FIR transversal filtering

A unified view of algorithms for adaptive transversal FIR filtering and system identification has been presented. Wiener filtering and stochastic approximation are the origins from which all the algorithms have been derived, via a suitable choice of iterative optimization schemes and appropriate design parameters. Following this philosophy, the LMS algorithm and its offspring have been presented and interpreted as stochastic approximations of iterative deterministic steepest descent optimization schemes. On the other hand, the RLS and the quasi-RLS algorithms, like the quasi-Newton, the FNTN, and the affine projection algorithm, have been derived as stochastic approximations of iterative deterministic Newton and quasi-Newton methods. Fast implementations of these methods have been discussed. Block-adaptive, and block-exact adaptive filtering have also been considered. The performance of the adaptive algorithms has been demonstrated by computer simulations.

Efficient algorithms for Volterra system identification

In this paper, nonlinear filtering and identification based on finite-support Volterra models are considered. The Volterra kernels are estimated via input-output statistics or directly in terms of input-output data. It is shown that the normal equations for a finite-support Volterra system excited by zero mean Gaussian input have a unique solution if, and only if, the power spectral process of the input signal is nonzero at least at m distinct frequencies, where m is the memory of the system. A multichannel embedding approach is introduced. A set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format. Efficient algorithms for the estimation of the Volterra parameters are derived for batch, as well as for adaptive processing. An efficient order-recursive method is presented for the determination of the Volterra model structure. The proposed methods are illustrated by simulations.

A Fast Algorithm for APES and Capon Spectral Estimation

In this paper, we derive a novel implementation of some very computationally demanding matched filter-bank-based spectral estimators, namely the amplitude and phase estimator (APES), the amplitude spectrum Capon (ASC) estimator, and the power spectrum Capon (PSC) estimator. Filter-bank-based spectral estimation methods that adopt data-dependent filter banks can provide spectra characterized by a significantly improved resolution compared to classical approaches. However, the computational complexity of the currently available implementation algorithms, is extremely high. A novel technique is introduced that provides efficient algorithms for the computation of the APES, ASC, and PSC spectra. The proposed method is based on suitable displacement representations of all pertinent data matrices, that are subsequently utilized for the computation of the associated complex valued polynomials. The computational complexity of the proposed algorithms is lower than all relevant existing methods.

Efficient Implementation of Iterative Adaptive Approach Spectral Estimation Techniques

This paper presents computationally efficient implementations for several recent algorithms based on the iterative adaptive approach (IAA) for uniformly sampled one- and two-dimensional data sets, considering both the complete data case, and the cases when the data sets are missing samples, either lacking arbitrary locations, or having gaps or periodically reoccurring gaps. By exploiting the methods inherent low displacement rank, together with the development of suitable Gohberg-Semencul representations, and the use of data dependent trigonometric polynomials, the proposed implementations are shown to offer a reduction of the necessary computational complexity by at least one order of magnitude. Numerical simulations together with theoretical complexity measures illustrate the achieved performance gain.

Time-Recursive IAA Spectral Estimation

This letter presents computationally efficient time-updating algorithms of the recent Iterative Adaptive Approach (IAA) spectral estimation technique. By exploiting the inherently low displacement rank, together with the development of suitable Gohberg-Semencul (GS) representations, and the use of data dependent trigonometric polynomials, the proposed time-recursive IAA algorithm offers a reduction of the necessary computational complexity with at least one order of magnitude. The resulting complexity can also be reduced further by allowing for approximate solutions. Numerical simulations together with theoretical complexity measures illustrate the achieved performance gain.

Efficient Algorithms for Adaptive Capon and APES Spectral Estimation

In this paper fast algorithms for adaptive Capon and amplitude and phase estimation (APES) methods for spectral analysis of time varying signals, are derived. Fast, stable, nonrecursive formulae are derived, based on time shifting properties of the pertinent variables. As a consequence, efficient frequency domain recursive least squares (RLS) based, as well as fast RLS based algorithms for the adaptive estimation of the power spectra are developed. Stability issues of the frequency domain estimators are considered, and stabilization procedures are proposed. The computational complexity of the proposed algorithms is lower than relevant existing methods. The performance of the proposed algorithms is demonstrated through extensive simulations.

Non-Parametric High-Resolution SAR Imaging

The development of high-resolution two-dimensional spectral estimation techniques is of notable interest in synthetic aperture radar (SAR) imaging. Typically, data-independent techniques are exploited to form the SAR images, although such approaches will suffer from limited resolution and high sidelobe levels. Recent work on data-adaptive approaches have shown that both the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) algorithm offer excellent performance with high-resolution and low side lobe levels for both complete and incomplete data sets. Regrettably, both algorithms are computationally intensive if applied directly to the phase history data to form the SAR images. To help alleviate this, efficient implementations have also been proposed. In this paper, we further this work, proposing yet further improved implementation strategies, including approaches using the segmented IAA approach and the approximative quasi-Newton technique. Furthermore, we introduce a combined IAA-MAP algorithm as well as a hybrid IAA- and SLIM-based estimation scheme for SAR imaging. The effectiveness of the SAR imaging algorithms and the computational complexities of their fast implementations are demonstrated using the simulated Slicy data set and the experimentally measured GOTCHA data set.

SAR imaging via efficient implementations of sparse ML approaches

High-resolution spectral estimation techniques are of notable interest for synthetic aperture radar (SAR) imaging. Several sparse estimation techniques have been shown to provide significant performance gains as compared to conventional approaches. We consider efficient implementation of the recent iterative sparse maximum likelihood-based approaches (SMLAs). Furthermore, we present approximative fast SMLA formulation using the Quasi-Newton approach, as well as consider hybrid SMLA-MAP algorithms. The effectiveness of the discussed techniques is illustrated using numerical and experimental examples.

Computationally Efficient Time-Recursive IAA-Based Blood Velocity Estimation

High-resolution spectral Doppler is an important and powerful noninvasive tool for estimation of velocities in blood vessels using medical ultrasound scanners. Such estimates are typically formed using an averaged periodogram technique, resulting in well-known limitations in the resulting spectral resolution. Recently, we have proposed techniques to instead form high-resolution data-adaptive estimates exploiting measurements along both depth and emission. The resulting estimates gives noticeably superior velocity estimates as compared to the standard technique, but suffers from a high computational complexity, making it interesting to formulate computationally efficient implementations of the estimators. In this work, by exploiting the rich structure of the iterative adaptive approach (IAA) based estimator, we examine how these estimates can be efficiently implemented in a time-recursive manner using both exact and approximate formulations of the method. The resulting algorithms are shown to reduce the necessary computational load with several orders of magnitude without noticeable loss of performance.

Fast missing-data IAA with application to notched spectrum SAR

Recently, the spectral estimation method known as the iterative adaptive approach (IAA) has been shown to provide higher resolution and lower sidelobes than comparable spectral estimation methods. The computational complexity is higher than methods such as the periodogram (matched filter method). Fast algorithms have been developed that considerably reduce the computational complexity of IAA by using Toeplitz and Vandermonde structures. For the missing-data case, several of these structures are lost, and existing fast algorithms are only efficient when the number of available samples is small. In this work, we consider the case in which the number of missing samples is small. This allows us to use low-rank completion to transform the problem to the structured problem. We compare the computational speed of the algorithm with the state of the art and demonstrate the utility in a frequency-notched synthetic aperture radar imaging problem.