Xampling in Ultrasound Imaging

Recent developments of new medical treatment techniques put challenging demands on ultrasound imaging systems in terms of both image quality and raw data size. Traditional sampling methods result in very large amounts of data, thus, increasing demands on processing hardware and limiting the exibility in the post-processing stages. In this paper, we apply Compressed Sensing (CS) techniques to analog ultrasound signals, following the recently developed Xampling framework. The result is a system with significantly reduced sampling rates which, in turn, means significantly reduced data size while maintaining the quality of the resulting images.Comment: 17 pages, 9 Figures. Introduced in SPIE Medical Imaging Conference, Orlando Florida, 201

Xampling: Signal Acquisition and Processing in Union of Subspaces

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio

Cognitive Sub-Nyquist Hardware Prototype of a Collocated MIMO Radar

We present the design and hardware implementation of a radar prototype that demonstrates the principle of a sub-Nyquist collocated multiple-input multiple-output (MIMO) radar. The setup allows sampling in both spatial and spectral domains at rates much lower than dictated by the Nyquist sampling theorem. Our prototype realizes an X-band MIMO radar that can be configured to have a maximum of 8 transmit and 10 receive antenna elements. We use frequency division multiplexing (FDM) to achieve the orthogonality of MIMO waveforms and apply the Xampling framework for signal recovery. The prototype also implements a cognitive transmission scheme where each transmit waveform is restricted to those pre-determined subbands of the full signal bandwidth that the receiver samples and processes. Real-time experiments show reasonable recovery performance while operating as a 4x5 thinned random array wherein the combined spatial and spectral sampling factor reduction is 87.5% of that of a filled 8x10 array.Comment: 5 pages, Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa) 201

Multichannel Sampling of Pulse Streams at the Rate of Innovation

We consider minimal-rate sampling schemes for infinite streams of delayed and weighted versions of a known pulse shape. The minimal sampling rate for these parametric signals is referred to as the rate of innovation and is equal to the number of degrees of freedom per unit time. Although sampling of infinite pulse streams was treated in previous works, either the rate of innovation was not achieved, or the pulse shape was limited to Diracs. In this paper we propose a multichannel architecture for sampling pulse streams with arbitrary shape, operating at the rate of innovation. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. This architecture is motivated by recent work on sub-Nyquist sampling of multiband signals. We show that the pulse stream can be recovered from the proposed minimal-rate samples using standard tools taken from spectral estimation in a stable way even at high rates of innovation. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in the sampling channels. The resulting scheme is flexible and exhibits better noise robustness than previous approaches

Joint Transmit and Receive Filter Optimization for Sub-Nyquist Delay-Doppler Estimation

In this article, a framework is presented for the joint optimization of the analog transmit and receive filter with respect to a parameter estimation problem. At the receiver, conventional signal processing systems restrict the two-sided bandwidth of the analog pre-filter $B$ to the rate of the analog-to-digital converter $f_s$ to comply with the well-known Nyquist-Shannon sampling theorem. In contrast, here we consider a transceiver that by design violates the common paradigm $B\leq f_s$. To this end, at the receiver, we allow for a higher pre-filter bandwidth $B>f_s$ and study the achievable parameter estimation accuracy under a fixed sampling rate when the transmit and receive filter are jointly optimized with respect to the Bayesian Cram\'{e}r-Rao lower bound. For the case of delay-Doppler estimation, we propose to approximate the required Fisher information matrix and solve the transceiver design problem by an alternating optimization algorithm. The presented approach allows us to explore the Pareto-optimal region spanned by transmit and receive filters which are favorable under a weighted mean squared error criterion. We also discuss the computational complexity of the obtained transceiver design by visualizing the resulting ambiguity function. Finally, we verify the performance of the optimized designs by Monte-Carlo simulations of a likelihood-based estimator.Comment: 15 pages, 16 figure