|M.Sc Student||Tur Ronen|
|Subject||Innovation Rate Sampling of Pulse Streams with Applications|
in Ultrasound Imaging
|Department||Department of Electrical Engineering||Supervisor||Professor Yonina Eldar|
|Full Thesis text|
One of the most well-known results in sampling theory is that of Shannon-Nyquist, stating that a band-limited signal can be perfectly reconstructed from its samples, as long as the sampling rate is larger than the total bandwidth of the signal. The essence of this result is that it exploits prior knowledge on the signal, identifies its degrees of freedom, and states a condition accompanied by an actual sampling scheme, under which all degrees of freedom can be perfectly determined. Following this result, various signal models have been investigated, and efficient sampling schemes were designed to obtain the signal's degrees of freedom, which uniquely determine it.
In this work we explore a class of signals comprised of a stream of short pulses, which appear in many applications including bio-imaging 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. Applying a carefully designed pre-filter on the signal, prior to sampling, allows perfect reconstruction from minimal rate samples. Unfortunately, for signals with a large number of pulses per unit time, existing sampling schemes are numerically unstable.
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 a minimal number of samples. We then propose a compactly supported class of filters, satisfying this condition. The numerically stable periodic solution is extended to aperiodic finite and infinite streams, although the latter does not operate at the minimal rate. High noise robustness is also demonstrated when the delays are sufficiently separated.
In the absence of minimal rate single-channel schemes for the infinite setting, we exploit the additional flexibility of multichannel sampling and propose noise robust methods, operating at the minimal rate possible, for arbitrary pulse shapes. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in several sampling channels.
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.