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Regularization of ill-posed problems using (symmetric) Cauchy-like preconditioners

Regularization of ill-posed problems using (symmetric) Cauch...

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SPIE conference on advanced signal processing algorithms, architectures, and implementations viiI

作者： Kilmer, ME Northeastern Univ Dept Elect & Comp Engn Boston MA 02115 USA

ISBN: (纸本)0819429163

In certain applications, the discretization of two-dimensional integral equations can lead to systems involving matrices with block Toeplitz-Toeplitz block structure. Iterative Krylov subspace methods are sometimes employed to find regularized solutions to the related 2D discrete ill-posed problems;however, preconditioners which filter noise are needed to speed convergence to regularized solutions. We describe a preconditioning technique based on the Toeplitz-type structure of the matrix which generalizes the approaches in [1] and [2] to take advantage of symmetry and real arithmetic operations. We use fast sine transforms to transform the original system to a system whose matrix has partially reconstructible Cauchy-like blocks. The preconditioner is a block diagonal, rank m approximation to this matrix, with Cauchy-like blocks each augmented by an identity of appropriate dimension. We note that the initialization cost is in general less than that for the similar 2D preconditioner in [2] which does not take advantage of symmetry. Several examples are given which illustrate the success of our preconditioned methods.

关键词： regularization Toeplitz Cauchy-like minimal residual image processing deblurring

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FPGA-based artificial neural network using CORDIC modules

FPGA-based artificial neural network using CORDIC modules

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conference on advanced signal processing algorithms, architectures, and implementations XVI

作者： Liddicoat, Albert A. Slivovsky, Lynne A. McLenegan, Tim Heyer, Don Calif Polytech State Univ San Luis Obispo Dept Elect Engn San Luis Obispo CA 93407 USA

ISBN: (纸本)0819463922

Artificial neural networks have been used in applications that require complex procedural algorithms and in systems which lack an analytical mathematic model. By designing a large network of computing nodes based on the artificial neuron model, new solutions can be developed for computational problems in fields such as image processing and speech recognition. Neural networks are inherently parallel since each neuron, or node, acts as an autonomous computational element. Artificial neural networks use a mathematical model for each node that processes information from other nodes in the same region. The information processing entails computing a weighted average computation followed by a nonlinear mathematical transformation. Some typical artificial neural network applications use the exponential function or trigonometric functions for the nonlinear transformation. Various simple artificial neural networks have been implemented using a processor to compute the output for each node sequentially. This approach uses sequential processing and does not take advantage of the parallelism of a complex artificial neural network. In this work a hardware-based approach is investigated for artificial neural network applications. A Field Programmable Gate Arrays (FPGAs) is used to implement an artificial neuron using hardware multipliers, adders and CORDIC functional units. In order to create a large scale artificial neural network, area efficient hardware units such as CORDIC units are needed. High performance and low cost bit serial CORDIC implementations are presented. Finally, the FPGA resources and the performance of a hardware-based artificial neuron are presented.

关键词： computer arithmetic field programmable gate arrays (FPGAs) higher-level functions reconfigurable computing digital signal processing and artificial neural networks

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Array processing based on the polarization diversity : the example of a ionospheric radio link

Array processing based on the polarization diversity : the e...

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conference on advanced signal processing algorithms, architectures, and implementations XIV

作者： Ehrel, YM Perrine, C Lemur, D Bourdillon, A Ctr Rech Ecoles Coetquidan F-56381 Guer France Univ Rennes 1 Inst Elect & Telecommun F-35042 Rennes France

ISBN: (纸本)0819454974

The aim of this paper is to present a high data rate transmission system through the ionospheric channel in the HF band (3-30 MHz). The applications expected in this study are image transmission and real-time videoconferencing. Very high rates are required compared to the standard modems (4.8 kbits/s). Therefore. an array processing performs in the multi channel receiving system. Its main originality stands in the development of a compact device of collocated antennas. the spatial responses of which are different one from each other. Besides. synchronization (Zero Crossing Detector) and spatio temporal equalization (L.M.S. algorithm) as well resort to classical and well-tested techniques involving training sequences. An experimental radio link has been under test with a range of 800 km. The corresponding results underlines the improvement of the bit transfer rate which reaches 20 kbits/s (QAM 16 in a 6 kHz bandwidth) or 30 kbits/s (QAM 16 in a 9 kHz bandwidth). Several transmitted images are presented and appear quite consistent with the original..

关键词： ionosphere collocated antennas spatio temporal equalization image compression

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Non-linear signal processing using index calculus DBNS arithmetic

Non-linear signal processing using index calculus DBNS arith...

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conference on advanced signal processing algorithms, architectures, and implementations X

作者： Muscedere, R Jullien, GA Dimitrov, VS Miller, WC Univ Windsor VLSI Res Grp Windsor ON N9B 3P4 Canada

ISBN: (纸本)0819437611

This paper discusses the use of a recently introduced index calculus Double-Base Number System (IDBNS) for representing and processing numbers for non-linear digital signal processing;the target application is a digital hearing aid processor. The IDBNS representation uses 2 orthogonal bases (2 and 3) to represent real numbers with arbitrary precision. By restricting the number of digits to one or two, it is possible to efficiently represent the real number using the indices of the bases rather than the distribution of the digits. In this paper we discuss the use of the two-digit form of this representation (2-IDBNS) to efficiently perform arithmetic associated with the non-linear processing required to correct the usual forms of hearing loss in a digital hearing aid. The non-linear processing takes the form of dynamic range compression as a function of frequency band. Currently developed digital hearing instrument processors require large dynamic range representations (20-24 bits) in order to accurately generate the dynamic range compression associated with typical hearing loss. We show that the natural non-linear representation afforded by the IDBNS provides both a more efficient signal representation and a more efficient technique for processing the dynamic range compression. We pay particular attention to a novel technique of converting from a linear binary input directly to the 2-IDBNS representation using an observation of partial cyclic repetition in the indices along with near unity approximants.

关键词： computer arithmetic non-linear number representation double-base number system hearing loss

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Application of higher-order cepstral techniques in problems of fetal heart signal extraction 6

Application of higher-order cepstral techniques in problems ...

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conference on advanced signal processing algorithms, architectures, and implementations VI

作者： SabryRizk, M Zgallai, W Hardiman, P ORiordan, J CITY UNIV LONDON DEPT ELECT ENGNSIGNAL PROC GRPLONDON EC1V 0HBENGLAND

ISBN: (纸本)0819422347

Recently, cepstral analysis based on second order statistics and homomorphic filtering techniques have been used in the adaptive decomposition of overlapping, or otherwise, and noise contaminated ECG complexes of mothers and fetals obtained by a transabdominal surface electrodes connected to a monitoring instrument, an interface card, and a PC. Differential time delays of fetal heart beats measured from a reference point located on the mother complex after transformation to cepstra domains are first obtained and this is followed by fetal heart rate variability computations. Homomorphic filtering in the complex cepstral domain and the subuent transformation to the time domain results in fetal complex recovery. However, three problems have been identified with second-order based cepstral techniques that needed rectification in this paper. These are (1) errors resulting from the phase unwrapping algorithms and leading to fetal complex perturbation, (2) the unavoidable conversion of noise statistics from Gaussianess to non-Gaussianess due to the highly non-linear nature of homomorphic transform does warrant stringent noise cancellation routines, (3) due to the aforementioned problems in (1) and (2), it is difficult to adaptively optimize windows to include all individual fetal complexes in the time domain based on amplitude thresholding routines in the complex cepstral domain (i.e. the task of `zooming' in on weak fetal complexes requires more processing time). The use of third-order based high resolution differential cepstrum technique results in recovery of the delay of the order of 120 milliseconds.

关键词： advanced signal processing techniques non-linear adaptive filtering differential bicepstral applications non-invasive fetal ECG monitoring

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Low Power implementation of a Turbo-decoder on programmable architectures

Low Power implementation of a Turbo-decoder on programmable ...

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Asia and South Pacific Design Automation conference (ASP-DAC 2001)

作者： Gilbert, F Worm, A Wehn, N Univ Kaiserslautern Dept Elect Engn & Informat Technol Inst Microelect Syst D-67663 Kaiserslautern Germany

ISBN: (纸本)0780366336

Low Power is an extremely important issue for future mobile radio systems. Channel decoders are essential building blocks of base-band signal processing units in mobile terminal architectures. Thus low power implementations of advanced channel decoding techniques are mandatory. In this paper we present a low power implementation of the most sophisticated channel decoding algorithm (Turbo-decoding) on programmable architectures. Low power optimization is performed on two abstraction levels: on system level by the use of an intelligent cancellation technique, on implementation level by the use of dynamic voltage scaling. With these techniques we can reduce the worst case energy consumption to 55% using data of state-of-the-art processors. Our approach is also applicable for hardware implementations. To the best of our knowledge, this is the first in-depth study of low power implementations of Turbo-decoders based on voltage scheduling for third generation wireless systems.

关键词： Bit error rate Channel coding Dynamic voltage scaling Error correction Forward error correction Iterative decoding Processor scheduling Redundancy signal processing algorithms Turbo codes

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Generalized causal moving average (GCMA) smoothing filter for real-time applications

Generalized causal moving average (GCMA) smoothing filter fo...

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conference on advanced signal processing algorithms architectures and implementations XIII

作者： Rajagopalan, R Pratt & Whitney Control & Diagnost Syst Propul Syst Anal E Hartford CT 06108 USA

ISBN: (纸本)0819450782

Moving average filters are commonly used in industries for real-time processing of noisy data. Though they perform well in filtering out the noise, they introduce significant lag in the signal. The resulting peak value of the filtered signal at the operating point is likely to be lower due to averaging of higher and lower peak signals in the averaging interval. The generalized moving average smoothing filter by Golay-Savitzky preserves the higher moments and does not suffer from the limitations imposed by the conventional moving average filter. The smoothing strategy is derived from least squares fitting of a lower order polynomial to a number of consecutive points. Due to polynomial curve fitting as opposed to a line fitting in the case of conventional moving average filter, this filter preserves the higher frequency components of the signal and their line width. This paper presents a generalized causal moving average filter deduced using the concepts in Golay-Savitzky smoothing filter for real-time applications. Golay-Savitzky filter is non-causal, relies on the future data that is not available, hence not suitable for real-time applications. Further, the designed causal filter makes use of the filtered data as opposed to the original data in the case of Golay-Savitzky. This approach allows us to conduct frequency response studies to evaluate the quality and the applicability of the filter for various signals in the aircraft engines and other engineering applications. Frequency response studies cannot carried out using the Golay-Savitzky filter. This paper also investigates the performance of various polynomial orders in-reproducing the signal from a noisy data. Some of the performance measures used are bandwidth, overshoots, and lags introduced by the filter. The mathematical technique to extract the signal and deduce the coefficients in off-line is also presented.

关键词： Filtering (signal processing) Electronic filtering signal processing Smoothing Interference (communication) Control systems Digital signal processing Data processing Electromagnetic coupling Nonlinear filtering

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On the regularized solution of block banded block Toeplitz systems

On the regularized solution of block banded block Toeplitz s...

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conference on advanced signal processing algorithms, architectures, and implementations X

作者： Bini, DA Farusi, A Fiorentino, G Meini, B Dipartimento Matemat I-56127 Pisa Italy

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.

关键词： Band Toeplitz systems Newton's iteration regularization displacement rank image processing

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On second-order statistics-based blind equalization of FIR/IIR multiple-input multiple-output channels with common zeros

On second-order statistics-based blind equalization of FIR/I...

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SPIE conference on advanced signal processing algorithms, architectures, and implementations viiI

作者： Tugnait, JK Huang, B Auburn Univ Dept Elect Engn Auburn AL 36849 USA

ISBN: (纸本)0819429163

The problem of blind equalization of MIMO (multiple-input nultiple-output) communications channels is considered using the second-order statistics of the data. Such models arise when a single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth), or when an antenna array is used with or without fractional sampling. We focus on direct design of finite-length MMSE (minimum mean-square error) blind equalizers. We allow infinite impulse response (IIR) channels. Our approaches also work when the "subchannel" transfer functions have common zeros so long as the common zeros are minimum-phase zeros. We only require that the there exist a causal, stable left inverse (not necessarily unique) to the MIMO transfer function and that the leading coefficient matrix of the MIMO channel impulse response have its rank equal to the number of sources. The channel length or model orders need not be known. The sources are recovered up to a unitary mixing matrix and are further 'unmixed' using higher-order statistics of the data. An illustrative simulation example is provided.

关键词： spatio-temporal processing multiple-input multiple-output channels multiaccess systems blind equalization space diversity time diversity fractional sampling

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Application of symmetric redundant residues for fast and reliable arithmetic

Application of symmetric redundant residues for fast and rel...

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conference on advanced signal processing algorithms, architectures and implementations XII

作者： Parhami, B Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA

ISBN: (纸本)0819445584

Despite difficulties in general division, magnitude comparison, and sign detection, residue number system arithmetic has been used for many special-purpose systems in light of its parallelism and modularity for the most common arithmetic operations of addition/subtraction and multiplication. Computation in RNS requires modular reduction, both for the initial conversion from binary to RNS and after each operation to bring the result back to within a valid residue range. Use of redundant residues simplifies this critical operation, leading to even faster arithmetic. One type of redundant mod-m residue, that keeps the representational redundancy to the minimum of 1 bit per residue, has the nearly symmetric range [-m, m) and allows two values for each pseudoresidue: (m) or (m) - m. We study the extent of simplification and speed-up in the modular reduction process afforded by such redundant residues and discuss its potential implications to the design of RNS arithmetic circuits. In particular, we show that besides cost and performance benefits, introduction of error checking and fault tolerance in arithmetic computations is facilitated when such redundant residues are used.

关键词： computer arithmetic error code modular reduction parallel processing redundant representation RNS

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