Srinath Hosur

Wavelet transform domain adaptive FIR filtering

This paper presents and studies two new wavelet transform domain least mean square (LMS) algorithms. The algorithms exploit the special sparse structure of the wavelet transform of wide classes of correlation matrices and their Cholesky factors in order to compute a whitening transformation of the input data in the wavelet domain and minimize computational complexity. The procedures differ in the exact estimates they use and in the way they identify the data dependent whitening transformation. The first approach explicitly computes a sparse estimate of the wavelet domain correlation matrix of the input process. It then computes the Cholesky factor of that matrix and uses its inverse to whiten the input. The complexity of this first approach is O[N log/sup 2/ (N)]. In contrast, the second approach computes a sparse estimate of the Cholesky factor of the wavelet domain correlation matrix of the input process directly. This second approach has a computational complexity of O[N log (N)] floating-point operations. However, it requires a more complex bookkeeping procedure. Both algorithms have a convergence rate that is faster than that of time-domain LMS and discrete Fourier transform (DFT) or discrete cosine transform (DCT)-based LMS procedures. The paper compares the two procedures and analyzes their mean and mean square performance.

Wavelet transform domain LMS algorithm

This paper describes a new wavelet domain RLS algorithm. The algorithm exploits the special sparse structure of the wavelet transform of wide classes of correlation matrices and that of the Cholesky factors of these matrices. Specifically, the algorithm updates a sparse QR factorization of the wavelet domain input data matrix. It then uses these factors to obtain the least-squares (LS) filter coefficients. The computational complexity of the proposed method is O(M log(M)) flops even when the input signal is not a time-series. Its convergence performance is similar to the traditional RLS algorithm. The new algorithm provides a method for trading error performance for lower computational complexity. Simulation results validate the performance of the algorithm.

ULV and generalized ULV subspace tracking adaptive algorithms

Traditional adaptive filters assume that the effective rank of the input signal is the same as the input covariance matrix or the filter length N. Therefore, if the input signal lives in a subspace of dimension less than N, these filters fail to perform satisfactorily. In this paper, we present two new algorithms for adapting only in the dominant signal subspace. The first of these is a low-rank recursive-least-squares (RLS) algorithm that uses a ULV decomposition (Stewart 1992) to track and adapt in the signal subspace. The second adaptive algorithm is a subspace tracking least-mean-squares (LMS) algorithm that uses a generalized ULV (GULV) decomposition, developed in this paper, to track and adapt in subspaces corresponding to several well-conditioned singular value clusters. The algorithm also has an improved convergence speed compared with that of the LMS algorithm. Bounds on the quality of subspaces isolated using the GULV decomposition are derived, and the performance of the adaptive algorithms are analyzed.

Image coding for content-based retrieval

We develop a new coding technique for content-based retrieval of images and text documents which minimizes a weighted sum of the expected compressed file size and query response time. Files are coded into three parts: (1) a header consisting of concatenated query term codewords, (2) locations of the query terms, and (3) the remainder of the file. The coding algorithm specifies the relative position and codeword length of all query terms. Our approach leads to a progressive refinement retrieval by successively reducing the number of searched files as more bits are read. It also supports progressive transmission.

Recent progress in the application of wavelets in surveillance systems

We briefly discuss two approaches for enhancing the resolution enhancement of range-Doppler images (including synthetic aperture radar and inverse synthetic aperture radar images). The first approach can be used in conjunction with current radar systems that use a fixed narrowband waveform to acquire target data. It measures Doppler shifts more accurately than the traditional fast Fourier transform based techniques. It performs well in low signal-to-clutter regimes regardless of the statistical structure of the clutter. The second technique assumes that the radar can transmit different waveforms that are matched to the imaging task under consideration. It is based on the fact that the most accurate reconstruction of a range-Doppler target density function from N waveforms and their echoes is obtained by transmitting the singular functions corresponding to the N largest singular values of two kernels derived from the target density. We discuss two strategies for selecting the radar waveforms. The first strategy uses fixed waveforms that act as approximate singular functions for the kernels corresponding to wide classes of target densities. The second strategy adaptively selects the transmitted waveforms by solving a simultaneous target classification and image reconstruction problem.

Generalized URV subspace tracking LMS algorithm

The convergence rate of the least mean squares (LMS) algorithm is poor whenever the adaptive filter input auto-correlation matrix is ill-conditioned. We propose a new LMS algorithm to alleviate this problem. It uses a data dependent signal transformation. The algorithm tracks the subspaces corresponding to clusters of eigenvalues of the auto-correlation matrix of the input to the adaptive filter, which have the same order of magnitude. The algorithm updates the projection of the tap weights of the adaptive filter onto each subspace using LMS algorithms with different step sizes. The technique also permits adaptation only in those subspaces, which contain strong signal components leading to a lower excess mean squared error (MSE) as compared to traditional algorithms.<<ETX>>

CODING FOR CONTENT-BASED RETRIEVAL

We define a data structure called a web together with an algorithm to choose scale-space atoms for representing an image. The corresponding wavelet coefficients (of the atoms chosen using this method) have useful properties which lead to (i) the definition of a stochastic process for representing images and (ii) an efficient image compression algorithm. The advantage of our image compression algorithm is that the computational requirement is very low. The stochastic process is useful in a theoretical sense because it gives us a framework in which to understand images and certain image compression algorithms.

Adaptive multiuser receiver schemes for antenna arrays

This paper develops a new multiuser detector for antenna arrays. The receiver uses an adaptive multiuser receiver in a multiple sensor environment. Using this receiver, two schemes are proposed for use with antenna arrays. The first scheme is a simple extension of the multiuser detection scheme to a multisensor environment, and has a performance better than the single channel decorrelator detector. The second scheme adaptively implements an array-decorrelator detector, which exploits both spatial and code diversity. It is different from the first scheme in that it uses the array response vector estimates of each user to reduce the correlation between users’s transmitted signal. It therefore, avoids the reduction in performance when signature correlations become significant.

Multiple subspace ULV algorithm and LMS tracking

Publisher Summary The Least Mean Squares (LMS) adaptive algorithm is the most popular algorithm for adaptive filtering because of its simplicity and robustness. However, its main drawback is slow convergence whenever the adaptive filter input auto-correlation matrix is ill-conditioned that is, the eigenvalue spread of this matrix is large. The goal of this chapter is to develop an adaptive signal transformation which can be used to speed up the convergence rate of the LMS algorithm, and at the same time provide a way of adapting only to the strong signal modes, in order to decrease the excess Mean Squared Error (MSE). It uses a data dependent signal transformation. The algorithm tracks the subspaces corresponding to clusters of eigenvalues of the auto-correlation matrix of the input to the adaptive filter, which have the same order of magnitude. The algorithm up-dates the projection of the tap weights of the adaptive filter onto each subspace using LMS algorithms with different step sizes. The technique also permits adaptation only in those subspaces, which contain strong signal components leading to a lower excess MSEas compared to traditional algorithms. The transform should also be able to track the signal behavior in a non-stationary environment. The chapter develops such a data adaptive transform domain LMS algorithm, using a generalization of the rank revealing ULV decomposition.