Vidya Venkatachalam

Nonstationary signal classification using pseudo power signatures: The matrix SVD approach

This paper deals with the problem of classification of nonstationary signals using signatures which are essentially independent of the signal length. This independence is a requirement in common classification problems like stratigraphic analysis, which was a motivation for this research. We achieve this objective by developing the notion of an approximation to the continuous wavelet transform, which is separable in the time and scale parameters, and using it to define power signatures, which essentially characterize the scale energy density, independent of time. We present a simple technique which uses the singular value decomposition to compute such an approximation, and demonstrate through an example how it is used to perform the classification. The proposed classification approach has potential applications in areas like moving target detection, object recognition, oil exploration, and speech processing.

Image classification using pseudo power signatures

Segmentation and classification are important problems with applications in areas like textural analysis and pattern recognition. This paper describes a single-stage approach to solve the image segmentation/classification problem down to the pixel level, using energy density functions based on the wavelet transform. The energy density functions obtained, called pseudo power signatures, are essentially functions of the scale and orientation and are obtained using separable approximations to the 2-D wavelet transform. A significant advantage of these representations is that they are invariant to signal magnitude, and spatial location within the object of interest. Further, they lend themselves to fast and simple classification routines. We provide a complete formulation of the signature determination problem for 2-D, and propose an effective, albeit simple, technique based on a tensor singular value analysis, to solve the problem. We also present an efficient computational algorithm, and a simulation result reflecting the strengths and limitations of this approach.

Detecting periodic behaviour in nonstationary signals

This paper presents results on the multiresolution analysis of nonstationary signals with the objective of detecting underlying periodic phenomena. Wavelet packet analysis with coefficient thresholding is the basis for the detection. The effectiveness of the method is illustrated by analyzing experimental data on sediment electrochemical redox potential in a tidal microcosm. The significance of the technique is that it can extract periodic phenomena from experimental data corrupted by catastrophic and random events, provide a signature of the basic periodic component, and give an estimate of the degree of deviation from periodic behaviour. Consequently, it has potential applications in the analysis of quasi-periodic signals such as electrocardiograms (ECGs), where the determination of the extent of quasi-periodicity is of critical importance.

Nonstationary signal classification using pseudo power signatures

This paper deals with the problem of classification of nonstationary signals using signatures which are essentially independent of the signal length. We develop the notion of a separable approximation to the Continuous Wavelet Transform (CWT) and use it to define a power signature. We present a simple technique which uses the Singular Value Decomposition (SVD) to compute such an approximation, and demonstrate through an example how it is used to perform the classification process. This example serves to show both the effectiveness and the limitations of the approach. Our main result is an alternate approach which develops the idea of using orthogonal projections to refine the approximation process, thus allowing for the definition of better signatures.

Optimal parallel 2-D FIR digital filter with separable terms

This article solves the optimal weighted least mean square (WLMS) filter design problem using sums of separable filters as a sequence of separable filter approximations. An efficient computational algorithm based on necessary conditions is presented. The procedure requires neither the solution of the unconstrained WLMS problem nor the singular value analysis of the ideal filter.

Unsupervised SAR image segmentation using recursive partitioning

We present a new approach to SAR image segmentation based on a Poisson approximation to the SAR amplitude image. It has been established that SAR amplitude images are well approximated using Rayleigh distributions. We show that, with suitable modifications, we can model piecewise homogeneous regions (such as tanks, roads, scrub, etc.) within the SAR amplitude image using a Poisson model that bears a known relation to the underlying Rayleigh distribution. We use the Poisson model to generate an efficient tree-based segmentation algorithm guided by the minimum description length (MDL) criteria. We present a simple fixed tree approach, and a more flexible adaptive recursive partitioning scheme. The segmentation is unsupervised, requiring no prior training, and very simple, efficient, and effective for identifying possible regions of interest (targets). We present simulation results on MSTAR clutter data to demonstrate the performance obtained with this parsing technique.

Enhanced signatures for event classification: the projector approach

The classification of nonstationary signals of unknown duration is of great importance in areas like oil exploration, moving target detection, and pattern recognition. In an earlier work, we provided a solution to this problem, based on the wavelet transform, by defining representations called pseudo power signatures for signal classes which were independent of signal length, and proposed a simple approach using the singular value decomposition to generate these signatures. This paper offers a new approach resulting in more discriminating signatures. The enhanced signatures are obtained by solving a nonlinear minimization problem involving an inverse projection. The problem formulation, solution procedure, and computational algorithm are presented in this work. The efficacy of the projection signatures in separating highly correlated signal classes is demonstrated through a simulation example.

Nonstationary signal enhancement using the wavelet transform

Conventional signal processing typically involves frequency selective techniques which are highly inadequate for nonstationary signals. In this paper, the authors present an approach to perform time-frequency selective processing using the wavelet transform. The approach is motivated by the excellent localization, in both time and frequency, afforded by the wavelet basis functions. Suitably chosen wavelet basis functions are used to characterize the subspace of signals that have a given localized time-frequency support, thus enabling a time-frequency partitioning of signals. A practical implementation scheme using filter banks is also presented, and the effectiveness of the approach over conventional techniques is demonstrated.

Pseudo-power scale signatures: frequency domain approach

Abstract In an earlier work, we introduced a new form of signal representation called the pseudo-power signature (PPS) that was essentially independent of the duration of the signal. The signatures were obtained based on the continuous wavelet transform, and were shown to be reliable and discriminating for classification purposes. In this paper, we take a fresh look at the problem of obtaining PPS by carrying out our analysis in the frequency domain. The main advantages of this approach over our earlier one are that it is more versatile, permits the development of efficient computational algorithms, offers a solution to some unresolved uniqueness problems in our original formulation, and allows the study of the effect of the choice of analyzing wavelet to better aid the classification process.

Parallel and separable 2-D FIR digital filter design

This paper develops a technique to design 2-D filters by approximating an ideal frequency response with sums of separable FIR components. The technique is independent of the nature of the ideal response, and can accommodate the inclusion of a weighting function. This approach gives the designer flexibility in selecting the 1-D filter orders and the number of parallel filters to be used for best results. The problem is presented here for the weighted least squares case and includes a brief analysis of computational complexity. Simulation results are used to demonstrate the effectiveness of this design algorithm.