A class of adaptive filters based on sequential eigen-decomposition of the data covariance matrix is introduced. These new algorithms are completely rank revealing and hence they can perfectly handle the following two relevant data cases where conventional RLS methods fail to provide satisfactory results: 1) highly oversampled "smooth" data with rank deficient or almost rank deficient covariance matrix. 2) Noise-corrupted data where a signal must be separated effectively from superimposed noise. The paper corrects the widely held belief that eigenbased algorithms must be computationally more demanding than conventional RLS techniques. A spatial RLS adaptive filter has a principal complexity of O(N/sup 2/) operations per time step, where N is the filter order. Somewhat ironically, though, the corresponding new eigensubspace or low rank adaptive filter requires only O(Nr) operations per time step where r/spl les/N denotes the numerical rank of the data covariance matrix. Thus eigensubspace adaptive filters can be computationally less or even much less demanding depending on the rank/order ratio r/N or the "compressibility" of the signal. Some high-performance subspace trackers are obtained as by-products of this research. Simulation results confirm the present claims.

A constructive procedure for the design of low rank detectors in the multichannel case of Gaussian detection of known transient signals in noise is described. These detectors consist of two consecutive blocks: a data and noise dependent "compression stage" which maps the significant signal energy into a subspace of minimal dimension followed by a minimal set of subspace matched filters which point in the directions in which the signal is much stronger than the noise.>

A square-root normalized Schur (1917,1986) RLS (recursive least squares) adaptive filter is presented which belongs to the newly developed class of Schur-type algorithms for adaptive filtering and parameter estimation in the serialized data case of RLS processing. Schur-type algorithms can outperform many of the well-known fast adaptive filtering algorithms due to their inherent ability to work with arbitrary recursive windowing of the data. Key features of the square-root Schur RLS adaptive filter are a fully pipelineable structure and excellent numerical properties. A systolic array of CORDIC processors for implementation of the square-root Schur RLS adaptive filter is presented, and its performance is illustrated with a typical example.>

A new form of the recursive Givens reduction (the array of W.M. Gentleman and H.T. Kung, 1981) is discussed. The new algorithm uses a modified Barnwell window in contrast to the classical solution which relies on a simple exponential decay. The modified Barnwell window has much better spectral properties when compared to the exponential window, and hence the new algorithm exhibits a considerably improved steady-state and tracking behavior. It is shown that the recursive Givens reduction based on the modified Barnwell window can be implemented with two conventional exponentially weighted systolic arrays of the Gentleman and Kung type which are operated in parallel with little intermediate processing.>

The design of feed-forward adaptive linear neuron (ADALINE) neural networks can be split into two: (1) designing the first hidden layer which uses linear hyperplanes to partition the continuous amplitude input space into a number of cells, and (2) designing the second and succeeding hidden layers which group the cells to larger decision regions. The design of the first hidden layer and of the Boolean output layer are discussed. The first procedure is basically a vector quantization of the pattern space that linearly separates all training patterns. Each cell in the vector quantization lattice is completely determined by a code address which is generated by the first hidden layer when only a pattern of the training set is supplied to the input of the neural network. The second problem is then to form a closed decision region as a Boolean function of cell addresses. A procedure is devised that minimizes this Boolean function by incorporation of free cells in the lattice, cells that are not addressed by the training patterns. It is shown that the second and succeeding hidden layers in a feed-forward network may therefore be replaced by a simple logical network. An algorithm for the design of this logical network is devised.>

A new type of scene adaptive coder has been developed. It involves a quadtree mean decomposition of the motion-compensated frame-to-frame difference signal followed by a scalar quantization of the local means. As a fundamental property, the new coding algorithm treats the displacement estimation problem and the quadtree construction problem as a unit. The displacement vector and the related quadtree are jointly optimized in order to minimize the direct frame-to-frame update information rate (in bits), which turns up as a new and more adequate cost function in displacement estimation. This guarantees the highest possible data compression ratio at a given quality threshold. Excellent results have been obtained for coding of color image sequences at a rate of 64 kb/s. The quadtree concept entails a much lower computational complexity compared to the conventional motion-compensated transform coder while achieving a subjective image quality that is as good or better than that of the traditional transform-based counterpart.>

The author describes the concept of recursive oblique plane decomposition (ROPD), which circumvents the problem of setting up large-area normal equations for computation of plane parameters in model-based variable-block-size image coding and constitutes the basis for extremely fast model-based adaptive variable-block-size image coding algorithms. He presents an algorithm of this type, where ROPD is embedded in an adaptive bottom-up quadtree segmentation structure. Excellent coding results have been obtained with this technique for a set of typical natural grey-level images. An example of a variable-block-size ROPD coded image is shown.>

A summary is presented of a study on two-dimensional linear prediction models for image sequence processing and its application to change detection and scene coding. The study focused on two-dimensional joint process modeling of interframe relationships, the derivation of computationally efficient matching algorithms, and the implementation of a block-adaptive interframe predictor for use in interframe predictive coding and change detection. In the approach presented, the spatial nonstationarity is handled by an underlying quadtree segmentation structure. A maximum-likelihood criterion and a simpler minimum-variance criterion are discussed as detection and segmentation rules. The results of this research indicate that a constrained joint process model involving only a single gain parameter and a shift parameter is the best tradeoff between performance and computational complexity.>

Quadtrees are a compact hierarchical method of representation of images. The authors present a new type of scene adaptive coder which is based on a quadtree mean decomposition of the motion compensated frame-to-frame difference signal followed by a scalar quantization and variable wordlength encoding of the local sample means. As a fundamental property, the displacement vector is determined in a sense such that the resulting quadtree decomposition attains a minimum in terms of a minimum number of bits required for encoding. This underlying joint optimization of displacement and decomposition has proven excellent results for coding of color image sequences at a rate of 64 kbit/s. The new quadtree scene coder is superior over traditional transform-based concepts and attracts a regular algorithm structure which is well suited to VLSI realization.>

Two versions of the most recently introduced "pure order recursive" LS lattice algorithm are discussed in this paper. An analysis of the round-off error characteristics of the new order recursive lattice method is performed and a comparison is made with the numerical characteristics of the mixed time and order recursive conventional LS lattice algorithm in the pre-windowed case. Theoretical results are verified by fixed-point computer simulation for several types of input data.