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.

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1991 - 19923

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Author: search.filters.author.Berman, ZeevSubject: search.filters.subject.signal processing

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    Generalizations and Properties of the Multiscale Maxima and Zero-Crossings Representations
    (1992) Berman, Zeev; Baras, John S.; ISR
    The analysis of a discrete multiscale edge representation is considered. A general signal description, called an inherently bounded Adaptive Quasi Linear Representation (AQLR), motivated by two important examples, namely, the wavelet maxima representation, and the wavelet zero-crossings representation, is introduced. This thesis addresses the questions of uniqueness, stability, and reconstruction. It is shown, that the dyadic wavelet maxima (zero-crossings) representation is, in general, nonunique. 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. Two reconstruction algorithms, based on the minimization of an appropriate cost function, are proposed. The first is based on the integration of the gradient of the cost function; the second is a standard steepest descent algorithm. Both algorithms are shown to converge. The last part of this dissertation describes possible modifications in the basic multiscale maxima representations. The main idea is to preserve the structure of the inherently bounded AQLR, while allowing a trade-off between reconstruction quality and amount of information required for representation. In particular, it is shown how quantization can be considered as an integral part of the representation.
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    A Theory of Adaptive Quasi Linear Representations
    (1992) Berman, Zeev; Baras, John S.; ISR
    The 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.
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    The Uniqueness Question of Discrete Wavelet Maxima Representation
    (1991) Berman, Zeev; ISR
    In this paper, we analyze the discrete wavelet maxima representation from the reconstruction point of view. Assuming finite data length and using the finite dimensional linear space approach we present necessary and sufficient conditions for the given representation to be unique. The algorithm which tests for uniqueness is shown. A general form of a solution to the reconstruction problem is described. The above results are valid for any bank of linear filters where the outputs are sampled at extreme values. For illustration we show two wavelet transform examples. The first is the common unique-representation case. The second is an interesting examples of family of sequences which have the same maxima representation. that is, we show an example of a non-unique discrete wavelet maxima representation.