Faculty Bibliography

We investigate a subband adaptive version of the popular iterative shrinkage/thresholding algorithm that takes different update steps and thresholds for each subband. In particular, we provide a condition that ensures convergence and discuss why making the algorithm subband adaptive accelerates the convergence. We also give an algorithm to select appropriate update steps and thresholds for when the distortion operator is linear and time invariant. The results in this paper may be regarded as extensions of the recent work by Vonesch and Unser.

Although most of its popular applications have been in discrete-time signal processing for over two decades, wavelet transform theory offers a methodology to generate continuous-time compact support orthogonal filter banks through the design of discrete-time finite length filter banks with multiple time and frequency resolutions. In this paper, we first highlight inherently built-in approximation errors of discrete-time signal processing techniques employing wavelet transform framework. Then, we present an overview of emerging analog signal processing applications of wavelet transform along with its still active research topics in more matured discrete-time processing applications. It is shown that analog wavelet transform is successfully implemented in biomedical signal processing for design of low-power pacemakers and also in ultra-wideband (UWB) wireless communications. The engineering details of analog circuit implementation for these continuous-time wavelet transform applications are provided for further studies. We expect a flurry of new research and technology development activities in the coming years utilizing still promising and almost untapped analog wavelet transform and multiresolution signal representation techniques. © 2009 Elsevier B.V. All rights reserved.

This paper describes an iterative algorithm for the design of a constant-modulus finite-duration chirp-like signal having a notch in its frequency spectrum. Frequency-notched signals with good pulse compression properties are needed in wide-band radar systems that must avoid radiating into frequency bands assigned to other systems (e. g. communication and navigation systems). The algorithm is computationally efficient and provides explicit control of the notch frequency and notch order.

This paper proposes the separation of signal components based on resonance. The method relies on several recent developments in sparse signal processing: morphological component analysis (MCA), the rational-dilation wavelet transform (RADWT), and fast algorithms for l(1)-norm regularized linear inverse problems (for example, SALSA). The RADWT allows one to extract signal components according to resonance characteristics because the RADWT allows the Q-factor (frequency resolution) of the wavelet transform to be varied. The sought decomposition can not be accomplished by frequency-based filtering. An example illustrates the method.

The detection of moving objects on the ground by airborne radar is one application of space-time adaptive processing (STAP). The goal is to estimate the position and velocity of objects. This paper considers the problem as a linear inverse problem and uses l(1)-norm regularization to promote sparsity in the solution. It is proposed that the angle-Doppler plane be explicitly segmented into the clutter ridge component and a non-clutter-ridge component. We propose that the second component be modeled as sparse - as the moving objects are assumed to be well isolated in the angle-Doppler plane.

Imaging of cardiac perfusion with MR is a challenging area of research especially due to the motion of the heart and limited time of data acquisition. Compressed sensing is a popular signal estimation method recently adopted by researchers in MRI which can improve the spatial and/or temporal resolution of the acquired images by reducing the number of necessary samples for image reconstruction. This paper focuses on performance of temporal regularization with total variation and wavelets in compressed sensing. The impact of the choice of regularization parameters on the image quality and the temporal variation of intensity in region of interests (ROIs) are discussed. It is found that selecting the regularization parameter so as to optimize the quality of the reconstructed image sequence as a whole, leads to erroneous reconstruction of certain regions due to over regularization.

We investigate the frame bounds of iterated non-perfect reconstruction filter banks. We provide frame bounds valid for iterated FBs with an arbitrary number of stages using the frame bounds of the underlying frame on the real line. Conversely, given the frame bounds of the iterated FB, we derive bounds for the underlying wavelet frame. (C) 2009 Elsevier Inc. All rights reserved.

The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Q-factor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied. The new wavelet transform can attain higher Q-factors (desirable for processing oscillatory signals) or the same low Q-factor of the dyadic wavelet transform. The new wavelet transform is modestly over-complete and based on rational dilations. Like the dyadic wavelet transform, it is an easily invertible 'constant-Q' discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for L(2) (R). The wavelet can be made to resemble a Gabor function and can hence have good concentration in the time-frequency plane. The construction of the new wavelet transform depends on the judicious use of both the transform's redundancy and the flexibility allowed by frequency-domain filter design.