SPTM-14.1

Automatic Digital Pre-compensation in IQ Modulators
John D Tuthill (Australian Telecommunications Research Institute), Antonio A Cantoni (Atmosphere Networks)

In digital IQ modulators generating Continuous Phase Frequency Shift Keying (CPFSK) signals, departures from flat-magnitude, linear phase in the pass bands of signal reconstruction filters in the I and Q channels cause ripple in the output signal envelope. Amplitude Modulation (AM) in the signal envelope function produces undesirable sidelobes in the FSK signal spectrum when the signal passes through nonlinear elements in the transmission path. A structure is developed for digitally pre-compensating for the magnitude and phase characteristics of signal reconstruction filters. Optimum digital pre-compensation filters are found using least squares (LS) techniques and we propose a method by which the optimum pre- compensation filters can be estimated using test input signals. This method can be used as part of an automatic compensation process.

SPTM-14.2

TWO-DIMENSIONAL PHASE RETRIEVAL USING A WINDOW FUNCTION
Wooshik Kim (Div. of Elec., Info., and Comm. Eng., Myongji University)

This paper considers two-dimensional phase retrieval using a window function. First, we address the uniqueness and reconstruction of a two-dimensional signal from the Fourier intensities of the three signals: the original signal, the signal windowed by a window w(m,n), and the signal winowed by its complementary window wc(m,n)= 1-w(m,n). Then we consider the phase retrieval without a complementary window. We develop conditions under which a signal can be uniquely specified from the Fourier intensities of the original signal and the windowed signal by w(m,n). We also present a reconstruction algorithm.

SPTM-14.3

A NEW TIME-SCALE ADAPTIVE DENOISING METHOD BASED ON WAVELET SHRINKAGE
Xiao-Ping Zhang, Zhi-Quan Luo (Communications Research Laboratory, McMaster University)

The wavelet shrinkage denoising approach is able to maintain local regularity of a signal while suppressing noise. However, the conventional wavelet shrinkage based methods are not time-scale adaptive to track the local time-scale variation. In this paper, a new time-scale adaptive denoising method for deterministic signal estimation is presented, based on the wavelet shrinkage. A class of smooth shrinkage functions and the local SURE (Stein�s Unbiased Risk Estimate) risk are employed to achieve time-scale adaptive denoising. The system structure and the learning algorithm are developed. The numerical results of our system are presented and compared with the conventional wavelet shrinkage techniques as well as their optimal solutions. Results indicate that the new time-scale adaptive method is superior to the conventional methods. It is also shown that the new method sometimes even achieves better performance than the optimal solution of the conventional wavelet shrinkage techniques.

SPTM-14.4

Sparse Correlation Kernel Reconstruction
Constantine Papageorgiou, Federico Girosi, Tomaso Poggio (MIT Center for Biological and Computational Learning and Artificial Intelligence Laboratory)

This paper presents a new paradigm for signal reconstruction and superresolution, Correlation Kernel Analysis (CKA), that is based on the selection of a sparse set of bases from a large dictionary of class-specific basis functions. The basis functions that we use are the correlation functions of the class of signals we are analyzing. To choose the appropriate features from this large dictionary, we use Support Vector Machine (SVM) regression and compare this to traditional Principal Component Analysis (PCA) for the task of signal reconstruction. The testbed we use in this paper is a set of images of pedestrians. Based on the results presented here, we conclude that, when used with a sparse representation technique, the correlation function is an effective kernel for image reconstruction.

SPTM-14.5

Optimal Generalized Sampling Expansion
Daniel Seidner, Meir Feder (Department of EE-Systems Tel-Aviv University)

This work presents an analysis of Papoulis' Generalized Sampling Expansion (GSE) for a wide-sense stationary signal with a known power spectrum in the presence of quantization noise. We find the necessary and sufficient conditions for a GSE system to produce the minimum mean squared error while using the optimal linear estimation filter. This is actually an extension of the optimal linear equalizer (linear source/channel optimization) to the case of M parallel channels.

SPTM-14.6

Sampling on Unions of Non-Commensurate Lattices Via Complex Interpolation Theory
Stephen D. Casey (American University), Brian M. Sadler (Army Research Laboratory)

Solutions to the analytic Bezout equation associated with certain multichannel deconvolution problems are interpolation problems on unions of non-commensurate lattices. These solutions provide insight into how one can develop general sampling schemes on properly chosen non-commensurate lattices. We will give specific examples of non-comensurate lattices, and use a generalization of B. Ya. Levin's sine-type functions to develop interpolating formulae on these lattices.

SPTM-14.7

Interpolation and Denoising of Nonuniformly Sampled Data Using Wavelet-Domain Processing
Hyeokho Choi, Richard G Baraniuk (Rice University)

In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximum-smoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For signals in the Besov space, the optimization corresponds to convex programming in the wavelet domain; for signals in the Sobolev space, the optimization reduces to a simple weighted least-squares problem. An optional wavelet shrinkage regularization step makes the algorithm suitable for even noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.

SPTM-14.8

Reproducing Kernel Structure and Sampling on Time-Warped Kramer Spaces
Shahrnaz Azizi, Douglas Cochran (Arizona State University)

Given a signal space of functions on the real line, a time-warped signal space consists of all signals that can be formed by composition of signals in the original space with an invertible real-valued function. Clark's theorem shows that signals formed by warping bandlimited signals admit formulae for reconstruction from samples. This paper considers time warping of more general signal spaces in which Kramer's genralized sampling theorem applies and observes that such spaces admit sampling and reconstruction formulae. This observation motivates the question of whether Kramer's theorem applies directly to the warped space, which is answered affirmatively by introduction of a suitable reproducing kernel Hilbert space structure. This result generalizes one of Zeevi, who pointed out that Clark's theorem is a consequence of Kramer's.

SPTM-14.9

Selection of regularisation parameters for total variation denoising
Victor Solo (Macquarie University)

We apply a general procedure of the author to choose penalty parameters in total variation denoising.

SPTM-14.10

Irregular Sampling with Unknown Locations
Pina Marziliano (EPFL, Communications System Division, Audiovisual Communication Laboratory), Martin Vetterli (EECS,Dept. UC Berkeley,USA)

This paper is concerned with finding the locations of an irregularly sampled finite discrete-time band-limited signal. First a geometrical approach is described and is transformed into an optimization problem. Due to the structure of the problem, multiple solutions exist and are shifts of each other. Three methods of solution are suggested: an exhaustive method which finds the exact set of locations; random search method and cyclic coordinate method, both descent methods, which find approximate or exact solutions. The cyclic coordinate method is less likely to fall in a local minimum and proves to be more satisfactory than the random search method in the presence of jitter. A practical example, where a signal is sampled several times with a regular spacing, is also described.

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Last Update: February 4, 1999 Ingo Höntsch