Given two n. x n Toeplitz matrices T-1 and T-2, and a vector b epsilon R-n2, consider the linear system Ax = b - eta, where eta epsilon R-n2 is an unknown vector representing the noise and A = T-1 x T-2. Recovering ap...
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ISBN:
(纸本)0819437611
Given two n. x n Toeplitz matrices T-1 and T-2, and a vector b epsilon R-n2, consider the linear system Ax = b - eta, where eta epsilon R-n2 is an unknown vector representing the noise and A = T-1 x T-2. Recovering approximations of a, given A and b, is encountered in image restoration problems. We propose a method for the approximation of the solution a: that has good regularization properties. The algorithm is based on a modified version of Newton's iteration for matrix inversion and relies on the concept of approximate displacement rank. We provide a formal description of the regularization properties of Newton's iteration in terms of filters and determine bounds to the number of iterations that guarantee regularization. The method is extended to deal with more general systems where A = Sigma (h)(i=1) T-1((i)) x T-2((i)). The cost of computing regularized inverses is O(n log n) operations (ops), the cost of solving the system Ax = b is O(n(2) log n) ops. Numerical experiments which show the effectiveness of our algorithm are presented.
Establishing measures for local stationarity is an open problem in the field of time-frequency analysis. One promising theoretical measure, known as the spread, provides a means for quantifying potential correlation b...
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Establishing measures for local stationarity is an open problem in the field of time-frequency analysis. One promising theoretical measure, known as the spread, provides a means for quantifying potential correlation between signal elements. In this paper we investigate the issue of generalizing techniques developed by the authors to better estimate the spread of a signal. Existing techniques estimate the spread as the rectangular region of support of the associated expected ambiguity function oriented parallel to the axes. By applying Radon Transform techniques we can produce a parameterized model which describes the orientation of the region of support providing tighter estimates of the signal spread. Examples are provided that illustrate the enhancement of the new method.
This paper addresses time-frequency (TF) analysis from a statistical signalprocessing perspective, with the goal of developing a general statistical methodology for TF analysis. We review earlier work on statistical ...
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This paper addresses time-frequency (TF) analysis from a statistical signalprocessing perspective, with the goal of developing a general statistical methodology for TF analysis. We review earlier work on statistical models for nonstationary stochastic signals, including frequency modulated locally stationary processes, which have covariance functions which yield nonnegative Wigner distributions. For such processes, time-frequency spectra may be defined without invoking `local-' or `quasi-' stationarity. These results are extended to include general time-varying linear systems and their associated time-frequency spectra. Any time-varying linear system driven by white noise has associated with it a nonnegative time-frequency spectrum. The bilinear class of time-frequency distributions are estimators of this time-frequency spectrum, as are adaptive methods such as positive time-frequency distributions and adaptive multitaper spectrograms. An analysis of the statistical properties of these estimators, including moments and distributional properties, is reviewed.
An architecture is presented for front-end processing in a wideband array system which samples real signals. Such a system may be encountered in cellular telephony, radar, or low SNR digital communications receivers. ...
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An architecture is presented for front-end processing in a wideband array system which samples real signals. Such a system may be encountered in cellular telephony, radar, or low SNR digital communications receivers. The subbanding of data enables system data rate reduction, and creates a narrowband condition for adaptive processing within the subbands. The front-end performs passband filtering, equalization, subband decomposition and adaptive beamforming. The subbanding operation is efficiently implemented using a prototype lowpass finite impulse response (FIR) filter, decomposed into polyphase form, combined with a Fast Fourier Transform (FFT) block and a bank of modulating postmultipliers. If the system acquires real inputs, a single FFT may be used to operate on two channels, but a channel separation network is then required for recovery of individual channel data. A sequence of steps is described based on data transformation techniques that enables a maximally efficient implementation of the processing stages and eliminates the need for channel separation. Operation count is reduced, and several layers of processing are eliminated.
We present a matrix decomposition that can be used to derive features from processes that are described by discrete-time, time-frequency representations. These include, among others, electrocardiograms, brain wave sig...
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We present a matrix decomposition that can be used to derive features from processes that are described by discrete-time, time-frequency representations. These include, among others, electrocardiograms, brain wave signals, seismic signals, vibration and shock signals, speech signals for voice recognition, and acoustic transient signals. The new decomposition is based on a transformation of the basis vectors of the singular value decomposition (SVD) which we call transformed singular value decomposition or TSVD. The transformed basis vectors are obtained by forming linear combinations of the original SVD basis vectors in a way such that the means of the transformed vectors are extrema of each other. The TSVD basis vectors are used to identify concentrations of energy density in the discrete-time, time-frequency representation by time and frequency descriptors. That is, descriptors such as the location in time, the spread in time, the location in frequency and the spread in frequency for each principal concentration of energy density can be obtained from the TSVD terms in the matrix decomposition series. Several examples are presented which illustrate the application of the new matrix decomposition for deriving principal time and frequency features from the discrete-time, time-frequency representations of nonstationary processes. Two of the examples illustrate how the derived time and frequency features can be used to classify individual short duration transient signals into respective classes, that is,: (1) automatically classify sonar signals as belonging to one of ten classes, and (2) automatically classify heartbeat signals as belonging to one of two people.
Future wireless systems are required to provide higher data rates, improved spectral efficiency and greater capacity. This can be achieved at the cost of increased signalprocessing complexity. The successful implemen...
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Future wireless systems are required to provide higher data rates, improved spectral efficiency and greater capacity. This can be achieved at the cost of increased signalprocessing complexity. The successful implementation of advancedalgorithms and dedicated hardware architectures to tackle the demanding signalprocessing tasks calls for an integrated development process. It must effectively exploit the many interrelations between the different levels of the design hierarchy and efficiently bridge the gap between system concepts and their VLSI circuit realization. This paper presents the algorithm and architecture level design of interference suppression techniques for advanced wireless receivers based on the use of multiple antenna elements in combination with appropriate signal combining. A systematic approach to architecture exploration is demonstrated which leads to efficient implementations in terms of both power consumption and silicon area.
This paper describes a new digital reprogrammable architecture called Field Programmable On-line oPerators (FPOP). This architecture is a kind of FPGA dedicated to very low-power implementations of numerical algorithm...
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ISBN:
(纸本)0819432938
This paper describes a new digital reprogrammable architecture called Field Programmable On-line oPerators (FPOP). This architecture is a kind of FPGA dedicated to very low-power implementations of numerical algorithms in signalprocessing or digital control applications for embedded or portable systems. FPOP is based on a reprogrammable array of on-line arithmetic operators. On-line arithmetic is a digit-serial arithmetic with most significant digits first using a redundant number system. Because of the small size of the digit-serial operators and the small number of communication wires between the operators, single chip implementation of complex numerical algorithms can be achieved using on-line arithmetic. Furthermore, the digit-level pipeline and the small size of the arithmetic operators lead to high-performance parallel computations. Compared to a standard FPGA, the basic cells in FPOP are arithmetic operators such as adders, subtracters, multipliers, dividers, square-rooters, sine or cosine operators. This granularity level allows very efficient power x delay implementations of most algorithms used in digital control and signalprocessing. The circuit also integrates some analog to digital and digital to analog converters.
This paper presents a robust algorithm for image processing using generalized reaction-diffusion equations. An edge enhancing functional is proposed for image enhancement. A number of super diffusion operators is intr...
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ISBN:
(纸本)0819432938
This paper presents a robust algorithm for image processing using generalized reaction-diffusion equations. An edge enhancing functional is proposed for image enhancement. A number of super diffusion operators is introduced for fast and effective smoothing. Statistical information is utilized for robust edge-stopping and diffusion rate estimation. A unification of computational methods is discussed. The unified computational method is employed for the numerical integration of the generalized reaction-diffusion equations. Computer experiments indicate that the present algorithm is very efficient for edge-detecting and noise-removing.
We present a number of methods that use image and signed processing techniques for removal of noise from a signal. The basic idea is to first construct a time-frequency density of the noisy signal. The time-frequency ...
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ISBN:
(纸本)0819432938
We present a number of methods that use image and signed processing techniques for removal of noise from a signal. The basic idea is to first construct a time-frequency density of the noisy signal. The time-frequency density, which is a function of two variables, can then be treated as an "image", thereby enabling use of image processing methods to remove noise and enhance the image. Having obtained an enhanced time-frequency density, one then reconstructs the signal. Various time frequency-densities are used and also a number of image processing methods are investigated. Examples of human speech and whale sounds are given. In addition, new methods are presented for estimation of signal parameters from the time-frequency density.
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