Innovation Rate Sampling of Pulse Streams With Application to Ultrasound Imaging

Signals comprised of a stream of short pulses appear in many applications including bioimaging and radar. The recent finite rate of innovation framework, has paved the way to low rate sampling of such pulses by noticing that only a small number of parameters per unit time are needed to fully describe these signals. Unfortunately, for high rates of innovation, existing sampling schemes are numerically unstable. In this paper we propose a general sampling approach which leads to stable recovery even in the presence of many pulses. We begin by deriving a condition on the sampling kernel which allows perfect reconstruction of periodic streams from the minimal number of samples. We then design a compactly supported class of filters, satisfying this condition. The periodic solution is extended to finite and infinite streams and is shown to be numerically stable even for a large number of pulses. High noise robustness is also demonstrated when the delays are sufficiently separated. Finally, we process ultrasound imaging data using our techniques and show that substantial rate reduction with respect to traditional ultrasound sampling schemes can be achieved.

[1]  Minh N. Do,et al.  A Theory for Sampling Signals from a Union of Subspaces , 2022 .

[2]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[3]  Yonina C. Eldar,et al.  Beyond bandlimited sampling , 2009, IEEE Signal Processing Magazine.

[4]  Yonina C. Eldar Compressed Sensing of Analog Signals in Shift-Invariant Spaces , 2008, IEEE Transactions on Signal Processing.

[5]  S. Kay Fundamentals of statistical signal processing: estimation theory , 1993 .

[6]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[7]  W. Greub Linear Algebra , 1981 .

[8]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[9]  Yonina C. Eldar,et al.  Xampling: Signal Acquisition and Processing in Union of Subspaces , 2009, IEEE Transactions on Signal Processing.

[10]  Yonina C. Eldar,et al.  Robust Recovery of Signals From a Structured Union of Subspaces , 2008, IEEE Transactions on Information Theory.

[11]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[12]  Martin Vetterli,et al.  Sampling and reconstruction of signals with finite rate of innovation in the presence of noise , 2005, IEEE Transactions on Signal Processing.

[13]  Roxy Senior,et al.  Portable echocardiography: a review , 2006 .

[14]  Yonina C. Eldar,et al.  Time-Delay Estimation From Low-Rate Samples: A Union of Subspaces Approach , 2009, IEEE Transactions on Signal Processing.

[15]  Yonina C. Eldar,et al.  Convex Optimization in Signal Processing and Communications: Optimization techniques in modern sampling theory , 2009 .

[16]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[17]  Georges Bienvenu,et al.  Adaptivity to background noise spatial coherence for high resolution passive methods , 1980, ICASSP.

[18]  C EldarYonina,et al.  Robust recovery of signals from a structured union of subspaces , 2009 .

[19]  Michael Unser,et al.  A Generalized Sampling Method for Finite-Rate-of-Innovation-Signal Reconstruction , 2008, IEEE Signal Processing Letters.

[20]  Yonina C. Eldar,et al.  Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals , 2007, IEEE Transactions on Signal Processing.

[21]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

[22]  Yonina C. Eldar,et al.  Optimization techniques in modern sampling theory , 2010, Convex Optimization in Signal Processing and Communications.

[23]  B. Hofmann-Wellenhof,et al.  Introduction to spectral analysis , 1986 .

[24]  Jim Hefferon,et al.  Linear Algebra , 2012 .

[25]  Thierry Blu,et al.  Extrapolation and Interpolation) , 2022 .

[26]  M. Vetterli,et al.  Sparse Sampling of Signal Innovations , 2008, IEEE Signal Processing Magazine.

[27]  Thierry Blu,et al.  Sampling signals with finite rate of innovation , 2002, IEEE Trans. Signal Process..

[28]  M. Galderisi,et al.  Hand-held echocardiography: its use and usefulness. , 2006, International journal of cardiology.

[29]  Boaz Porat,et al.  A course in digital signal processing , 1996 .