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Abstract - DSP11 |
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DSP11.1 |
Signal Restoration with Controlled Piecewise Monotonicity Constraint J. Lu (Apple Computer, USA) A signal restoration problem can be formulated as a least-squares inversion subject to a constraint that the signal has no more than k piecewise monotonic segments. We refer to the associated constraint as controlled piecewise monotonicity or CPM. We show that this constraint alone is powerful enough to stabilize an ill-posed inversion and enables us to incorporate the knowledge about the waveform geometry of the signal. This leads to a new algorithm for constrained signal restoration. We describe a highly efficient iterative scheme for computing the CPM constrained least-squares restoration. We also present experimental results and discuss issues related to the new algorithm. |
| DSP11.2 |
The Stability af a Direct Method for Superresolution J. Vieira, P. Ferreira (Universidade de Aveiro, Portugal) A direct method for superresolution recently proposed by Walsh and Delaney is further analyzed from the point of view of numerical stability. The method is based on a set of linear equations Ax=b, where A is mxn, and b is a subset (of cardinal n) of the Fourier transform of the object (which has a total of N samples). We give exact and best possible approximate expressions for the determinant of A, when m=n. As a corollary, it is shown that the smallest eigenvalue of A in absolute value satisfies, where (which is independent of N) is explicitly given. The magnitude of the smallest eigenvalue of A becomes increasingly small as N grows, even when the number of unknowns n remains constant. When m>n the singular values of A are studied, and related to the eigenvalues of the matrix of other direct methods. The connection between the method and the other direct methods is clarified. |
| DSP11.3 |
Signal Decomposition Using Adaptive Block Transform Packets J. Horng (Polytechnic University, USA); R. Haddad (New Jersey Institute of Technology, USA) A Block Transform Packet (BTP) is an orthonormal block transform which is constructed from conventional block transform (e.g. DCT) and represents an arbitrary tiling of the time-frequency plane. Unlike the progenitor transforms, the BTP has time-localizabilities and is capable of dealing with non-stationary signals. This paper describes the procedures for signal decomposition using the BTP in an adaptive way. Three examples show the adaptive compression efficiency over DCT. |
| DSP11.4 |
Sub-Nyquist Sampling of Multiband Signals: Perfect Reconstruction and Bounds on Aliasing Error R. Venkataramani, Y. Bresler (University of Illinois, USA) We consider the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. We derive the conditions for exact reconstruction and find an explicit reconstruction formula. Key features of this method are that the sampling rate can be made arbitrarily close to the minimum (Landau) rate and that it can handle classes of multiband signals that are not packable. We compute various bounds on the aliasing error due to mismodeling the spectral support and examine the performance in the presence of additive white sample noise. Finally we provide optimal designs for the reconstruction system. |
| DSP11.5 |
Use of Selected HOS Information for Low-Variance Estimation of Bandlimited Systems with Short Data Records H. Pozidis, A. Petropulu (Drexel University, USA) Although reconstruction of a nonminimum-phase system excited by a stationary non-Gaussian white input is only possible using higher-order statistics (HOS) of the system output, there has been a lot of criticism in the literature against the amount of data required for keeping estimation errors low, and the complexity involved. Recently several attempts for reducing the variance of the HOS estimates have appeared. In the case of bandlimited signals, we have demonstrated via simulations that the estimation variance can be reduced if ``good'' slices, instead of the whole bispectrum, are used. This suggests a potential reduction of variance in the system estimates, without having to resort to long observations. In this paper we justify theoretically the dependence of the system estimate variance on the bispectrum slice, and the criterion of slice selection. We also present simulation results, where the selected-slices approach appears to result in much lower estimation variance, as compared to other entire-bispectrum based approaches, for data lengths as low as 64 samples. |
| DSP11.6 |
1-D Continuous Non-Minimum Phase Retrieval Using the Wavelet Transform A. Bell (Virginia Tech, USA); A. Yagle (University of Michigan, USA) The phase retrieval problem arises when a signal must be reconstructed from only the magnitude of its Fourier transform; if the phase information were also available, the signal could simply be synthesized using the inverse Fourier transform. In continuous phase retrieval, most previous solutions rely on discretizing the problem and then employing an iterative algorithm. We avoid this approximation by using wavelet expansions to transform this uncountably infinite problem into a linear system of equations. The wavelet bases permit a solution by incorporating a priori signal information and they provide a structured system of equations which results in a fast algorithm. Our solutions obviate the stagnation problems associated with iterative algorithms, they are computationally simpler and more stable than previous non-iterative algorithms, and they can accommodate noisy Fourier magnitude information. This paper develops our 1-D continuous, non0-minimum phase retrieval algorithm and illustrates its effectiveness with numerical examples. |
| DSP11.7 |
H-infinity Filtering for Noise Reduction Using a Total Least Squares Estimation Approach J. Shimizu, S. Mitra (University of California, Santa Barbara, USA) A noise reduction algorithm for signals corrupted by additive unknown L2 white noise is proposed using an H-infinity filtering framework. The proposed algorithm consists of two steps: a signal enhancement step and a parameter estimation step, which are iterated at each instant. To weaken the dependence between the signal enhancement step and the parameter estimation step, a total least squares estimation step for the dynamical model parameters needed in the H-infinity filtering is introduced. The effectiveness of the proposed algorithm under low signal-to-noise ratio environments is demonstrated by simulation. |
| DSP11.8 |
Detection and Estimation of Superimposed Signals J. Fuchs (Univ. de Rennes, France) The problem of fitting a small number of superimposed signals to noisy observations is addressed. An approach allowing us to evaluate both the number of signals and their charcateristics is presented. The idea is to search for a parsimonious representation of the data. The parsimony is insured by adding to a maximum likelihood like criterion a regularization term built upon the l1 norm of the weights. Different equivalent formulations of the criterion that is optimised are presented. They lead to appealing physical interpretations. We analyse the performance of the algorithm that has already been successfully applied to different classes of problems. |
| DSP11.9 |
Continuous-Time Reconstruction of Nonuniformly Sampled Signals on a Band-Limited Wavelet Basis L. Nita, J. Oksman (SUPELEC, France) We propose a reconstruction method of continuous-time random signals by fitting nonuniform samples to a band-limited continuous-time wavelet basis. Based on wavelet analysis, our method uses a windowing technique with variable-sized intervals, taking advantage of the nonuniform signal sampling. This method leads to analytical formulas for the reconstructed continuous-time signal, and as well as for its derivatives. This can be very useful to perform a parametric estimation of so-called continuous-time ARMA models adopted for continuous-time random signal modeling. Several parameters like mother wavelet type, time shift interval between consecutive wavelets and resolution levels number can be adapted, function of nature of nonuniformly sampled signal. In this paper, we describe the principle of the proposed reconstruction method and discuss its performances. |
| DSP11.10 |
An Improved Sequential Backward Selection Algorithm for Large-Scale Observation Selection Problems S. Reeves (Auburn University, USA) Some signal reconstruction problems allow for flexibility in the selection of observations and hence the signal formation equation. In such cases, we have the opportunity to determine the best combination of observations before acquiring the data. We analyze the computational complexity of various forms of sequential backward selection (SBS) to select observations. In light of this analysis, we present a computationally improved algorithm for large-scale observation selection problems. |
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