Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
Browse
10 results
Search Results
Item Efficient Implementation of Controllers for Large Scale Linear Systems via Wavelet Packet Transforms(1998) Kantor, George A.; Krishnaprasad, Perinkulam S.; ISR; CDCSSIn this paper we present a method of efficiently implementing controllers for linear systems with large numbers of sensors and actuators. It is well known that singular value decomposition can be used to diagonalize any real matrix. Here, we use orthogonal transforms from the wavelet packet to "approximate" SVD of the plant matrix. This yields alternatebases for the input and output vector which allow for feedback control using local information. This fact allows for the efficient computation of a feedback control law in the alternate bases. Since the wavelet packet transforms are also computationally efficient,this method provides a good alternative to direct implementation of a controller matrix for large systems.This paper was presented at the 32nd CISS, March 18-21, 1998.
Item Wavelet-Based Hierarchical Organization of Large Image Databases: ISAR and Face Recognition(1998) Baras, John S.; Wolk, S.; ISRWe present a method for constructing efficient hierarchical organization of image databases for fast recognition and classification. The method combines a wavelet preprocessor with a Tree-Structured-Vector-Quantization for clustering. We show results of application of the method to ISAR data from ships and to face recognition based on photograph databases. In the ISAR case we show how the method constructs a multi-resolution aspect graph for each target.This paper was presented at the "SPIE's 12th Annual International Symposium on Aerospace/Defense Sensing, Simulation, and Controls (Aerosense'98)", April 13-17, 1998, Orlando, Florida. Item Neural Modelling with Wavelets and Application in Adaptive/Learning Control(1995) Kugarajah, Tharmarajah; Krishnaprasad, P.S.; ISRSpatio-spectral properties of the Wavelet Transform provide a useful theoretical framework to investigate the structure of neural networks. A few researchers (Pati & Krishnaprasad, Zhang & Benveniste) have investigated the connection between neural networks and wavelet transforms. However, a number of issues remain unresolved especially when the connection is considered in the multidimensional case. In our work, we resolve these issues by extensions based on some theorems of Daubechies related to wavelet frames and provide a frame-work to analyze local learning in neural-networks.We also provide a constructive procedure to build networks based on wavelet theory. Moreover, cognizant of the problems usually encountered in practical implementations of these ideas, we develop a heuristic methodology, inspired by similar work in the area of Radial Basis Function (RBF) networks (Moody & Darken, Platt), to build a network sequentially on-line as well as off-line.
We show some connections of our method to some existing methods such as Projection Pursuit Regression (Friedman), Hyper Basis Functions (Poggio & Girosi) and other methods that have been proposed in the literature on neural- networks as well as statistics. In particular, some classes of wavelets can also be derived from the regularization theoretical framework given by Poggio & Girosi.
Finally, we choose direct nonlinear adaptive control to demonstrate the utility of the network in the context of local learning. Stability analysis is carried out within a standard Lyapunov formulation. Simulation studies show the effectiveness of these methods. We compare and contrast these methods with some recent results obtained by other researchers using Back Propagation (Feed-Forward) Networks, and Gaussian Networks.
Item Existence and Construction of Optimal Wavelet Basis for Signal Representation(1994) Zhuang, Y.; Baras, John S.; ISR; CSHCNWe study the problem of choosing the optimal wavelet basis with compact support for signal representation and provide a general algorithm for computing the optimal wavelet basis. We first briefly review the multiresolution property of wavelet decomposition and the conditions for generating a basis of compactly supported discrete wavelets in terms of properties of quadrature mirror filter (QMF) banks. We then parametrize the mother wavelet and scaling function through a set of real coefficients. We further introduce the concept of decomposition entropy as an information measure to describe the distance between the given signal and its projection onto the subspace spanned by the wavelet basis in which the signal is to be reconstructed. The optimal basis for a given signal is obtained through minimizing this information measure. We have obtained explicitly the sensitivity of dilations and shifts of the mother wavelet with respect to the coefficient set. A systematic approach is developed in this paper to derive the information gradient with respect to the parameter set from a given square integrable signal and a discrete basis of wavelets. The existence of the optimal basis for the wavelets has been proven in this paper. a gradient based optimization algorithm is developed for computing the optimal wavelet basis.Item Optimal Wavelet Basis Selection for Signal Representation(1994) Zhuang, Y.; Baras, John S.; ISR; CSHCNWe study the problem of choosing the optimal wavelet basis with compact support for signal representation and provide a general algorithm for computing the optimal wavelet basis. We first briefly review the multiresolution property of wavelet decomposition and the conditions for generating a basis of compactly supported discrete wavelets in terms of properties of quadrature mirror filter (QMF) banks. We then parametrize the mother wavelet and scaling function through a set of real coefficients. We further introduce the concept of information measure as a distance measure between the signal and its projection onto the subspace spanned by the wavelet basis in which the signal is to be reconstructed. The optimal basis for a given signal is obtained through minimizing this information measure. We have obtained explicitly the sensitivity of dilations and shifts of the mother wavelet with respect to the coefficient set. A systematic approach is developed here to derive the information gradient with respect to the parameter set for a given square integrable signal and the optimal wavelet basis. A gradient based optimazation algorithm is developed in this paper for computing the optimal wavelet basis.Item Analysis and Synthesis of Distributed Systems(1994) Zhuang, Y.; Baras, J.S.; ISRWe first model and analyze distributed systems including distributed sensors and actuators. We then consider identification of distributed systems via adaptive wavelet neural networks (AWNNs) by taking advantage of the multiresolution property of wavelet transforms and the parallel computational structure of neural networks. A new systematic approach is developed in this dissertation to construct an optimal discrete orthonormal wavelet basis with compact support for spanning the subspaces employed for system identification and signal representation. We then apply a backpropagation algorithm to train the network to approximate the system. Filter banks for parameterizing wavelet systems are studied. An analog VLSI implementation architecture of the AWNN is also given in this dissertation. This work is applicable to signal representation and compression under optimal orthonormal wavelet bases in addition to progressive system identification and modeling. We anticipate that this work will find future applications in signal processing and intelligent systems.Item Hierarchical Wavelet Representations of Ship Radar Returns(1993) Baras, John S.; Wolk, S.I.; ISRIn this paper we investigate the problem of efficient representations of large databases of pulsed radar returns in order to economize memory requirements and minimize search time. We use synthetic radar returns from ships as the experimental data. We motivate wavelet multiresolution representations of such returns. We develop a novel algorithm for hierarchically organizing the database, which utilizes a multiresolution wavelet representation working in synergy with a Tree Structured Vector Quantizer (TSVQ), utilized in its clustering mode. The tree structure is induced by the multiresolution decomposition of the pulses. The TSVQ design algorithm is of the "greedy" type. We show by experimental results that the combined algorithm results in data search times that are logarithmic in the number of terminal tree nodes, with negligible performance degradation (as measured by distortion-entropy curves) from the full search vector quantization. Furthermore we show that the combined algorithm provides an efficient indexing scheme (with respect to variations in aspect, elevation and pulsewidth) for radar data which is equivalent to a multiresolution aspect graph or a reduced target model. Promising experimental results are reported using high quality synthetic data.Item Identification of Infinite Dimensional Systems Via Adaptive Wavelet Neural Networks(1993) Zhuang, Y.; Baras, John S.; ISRWe consider identification of distributed systems via adaptive wavelet neural networks (AWNNs). We take advantage of the multiresolution property of wavelet systems and the computational structure of neural networks to approximate the unknown plant successively. A systematic approach is developed in this paper to find the optimal discrete orthonormal wavelet basis with compact support for spanning the subspaces employed for system identification. We then apply backpropagation algorithm to train the network with supervision to emulate the unknown system. This work is applicable to signal representation and compression under the optimal orthonormal wavelet basis in addition to autoregressive system identification and modeling. We anticipate that this work be intuitive for practical applications in the areas of controls and signal processing.Item Affine Frames of Rational Wavelets in H2 (II+)(1992) Pati, Y.C.; Krishnaprasad, Perinkulam S.; ISRIn this paper we investigate frame decompositions of H2(II+) as a method of constructing rational approximations to nonrational transfer functions in H2(II+). The frames of interest are generated from a single analyzing wavelet. We consider the case in which the analyzing wavelet is rational and show that by appropriate grouping of terms in a wavelet expansion, H2(II+) can be decomposed as an infinite sum of a rational transfer functions which are related to one another by dilation and translation. Criteria for selecting a finite number of terms from such an infinite expansion are developed using time-frequency localization properties of wavelets.Item A Theory of Adaptive Quasi Linear Representations(1992) Berman, Zeev; Baras, John S.; ISRThe analysis of the discrete multiscale edge representation is considered. A general signal description, called an inherently bounded Adaptive Quasi Linear Representation (AQLR), motivated by two important examples: the wavelet maxima representation and the wavelet zero-crossing representation, is introduced. This paper addresses the questions of uniqueness, stability, and reconstruction. It is shown, that the dyadic wavelet maxima (zero-crossings) representation is, in general, nonunique. Namely, for all maxima (zero-crossings) representation based on a dyadic wavelet transform, there exists a sequence having a nonunique representation. Nevertheless, these representations are always stable. Using the idea of the inherently bounded AQLR two stability results are proven. For a general perturbation, a global BIBO stability is shown. For a special case, where perturbations are limited to the continuous part of the representation, a Lipschitz condition is satisfied. A reconstruction algorithm, based on the minimization of an appropriate cost function, is proposed. The convergence of the algorithm is guaranteed for all inherently bounded AQLR. In the case, where the representation is based on a wavelet transform, this method yields an efficient, parallel algorithm, especially promising in an analog-hardware implementation.