Finite Rate Of Innovation Framework Research Articles

Axial super-resolution in ultrasound imaging with application to non-destructive evaluation

A fundamental challenge in non-destructive evaluation using ultrasound is to accurately estimate the thicknesses of different layers or cracks present in the object under examination, which implicitly corresponds to accurately localizing the point-sources of the reflections from the measured signal. Conventional signal processing techniques cannot overcome the axial-resolution limit of the ultrasound imaging system determined by the wavelength of the transmitted pulse. In this paper, starting from the solution to the 1-D wave equation, we show that the ultrasound reflections could be effectively modeled as finite-rate-of-innovation (FRI) signals. The FRI modeling approach is a new paradigm in signal processing. Apart from allowing for the signals to be sampled below the Nyquist rate, the FRI framework also transforms the reconstruction problem into one of parametric estimation. We employ high-resolution parametric estimation techniques to solve the problem. We demonstrate axial super-resolution capability (resolution below the theoretical limit) of the proposed technique both on simulated as well as experimental data. A comparison of the FRI technique with time-domain and Fourier-domain sparse recovery techniques shows that the FRI technique is more robust. We also assess the resolvability of the proposed technique under different noise conditions on data simulated using the Field-II software and show that the reconstruction technique is robust to noise. For experimental validation, we consider Teflon sheets and Agarose phantoms of varying thicknesses. The experimental results show that the FRI technique is capable of super-resolving by a factor of three below the theoretical limit.

Modeling the Active Neuron Separation in the Compressed Sensing and Finite Rate of Innovation Framework

In this paper, we present a model for the problem of separating active neurons from their superposition at an array of electrodes in a neural recording setting. In this model, we allow unknown continuous delays between firing neurons and attenuations introduced by the pulses traveling through the medium. Additionally, we show how to utilize this model in the compressed sensing and the finite rate of innovation framework and then present a total of four solutions for the extraction of the pulse shape, number, and activity patterns of active neurons. To support our claims, we present extensive numerical simulations comparing our proposed algorithms with the state of the art.

Comparison of synthetic aperture architectures for miniaturised ultrasound imaging front-ends

BackgroundPoint of care ultrasonography has been the focus of extensive research over the past few decades. Miniaturised, wireless systems have been envisaged for new application areas, such as capsule endoscopy, implantable ultrasound and wearable ultrasound. The hardware constraints of such small-scale systems are severe, and tradeoffs between power consumption, size, data bandwidth and cost must be carefully balanced.MethodsIn this work, two receiver architectures are proposed and compared to address these challenges. Both architectures uniquely combine low-rate sampling with synthetic aperture beamforming to reduce the data bandwidth and system complexity. The first architecture involves the use of quadrature sampling to minimise the signal bandwidth and computational load. Synthetic aperture beamforming (SAB) is carried out using a single-channel, pipelined protocol suitable for implementation on an FPGA/ASIC. The second architecture employs compressive sensing within the finite rate of innovation framework to further reduce the bandwidth. Low-rate signals are transmitted to a computational back-end (computer), which sequentially reconstructs each signal and carries out beamforming.ResultsBoth architectures were tested using a custom hardware front-end and synthetic aperture database to yield B-mode images. The normalised root-mean-squared-error between the quadrature SAB image and the RF reference image was 13% while the compressive SAB error was 22% for the same degree of spatial compounding. The sampling rate is reduced by a factor of 2 (quadrature SAB) and 4.7 (compressive SAB), compared to the RF sampling rate. The quadrature method is implemented on FPGA, with a total power consumption of 4.1 mW, which is comparable to state-of-the-art hardware topologies, but with significantly reduced circuit area.ConclusionsThrough a novel combination of SAB and low-rate sampling techniques, the proposed architectures achieve a significant reduction in data transmission rate, system complexity and digital/analogue circuit area. This allows for aggressive miniaturisation of the imaging front-end in portable imaging applications.

LEAP: Looking beyond pixels with continuous-space EstimAtion of Point sources

Context. Two main classes of imaging algorithms have emerged in radio interferometry: the CLEAN algorithm and its multiple variants, and compressed-sensing inspired methods. They are both discrete in nature, and estimate source locations and intensities on a regular grid. For the traditional CLEAN-based imaging pipeline, the resolution power of the tool is limited by the width of the synthesized beam, which is inversely proportional to the largest baseline. The finite rate of innovation (FRI) framework is a robust method to find the locations of point-sources in a continuum without grid imposition. The continuous formulation makes the FRI recovery performance only dependent on the number of measurements and the number of sources in the sky. FRI can theoretically find sources below the perceived tool resolution. To date, FRI had never been tested in the extreme conditions inherent to radio astronomy: weak signal / high noise, huge data sets, large numbers of sources. Aims. The aims were (i) to adapt FRI to radio astronomy, (ii) verify it can recover sources in radio astronomy conditions with more accurate positioning than CLEAN, and possibly resolve some sources that would otherwise be missed, (iii) show that sources can be found using less data than would otherwise be required to find them, and (v) show that FRI does not lead to an augmented rate of false positives. Methods. We implemented a continuous domain sparse reconstruction algorithm in Python. The angular resolution performance of the new algorithm was assessed under simulation, and with visibility measurements from the LOFAR telescope. Existing catalogs were used to confirm the existence of sources. Results. We adapted the FRI framework to radio interferometry, and showed that it is possible to determine accurate off-grid point source locations and their corresponding intensities. In addition, FRI-based sparse reconstruction required less integration time and smaller baselines to reach a comparable reconstruction quality compared to a conventional method. The achieved angular resolution is higher than the perceived instrument resolution, and very close sources can be reliably distinguished. The proposed approach has cubic complexity in the total number (typically around a few thousand) of uniform Fourier data of the sky image estimated from the reconstruction. It is also demonstrated that the method is robust to the presence of extended-sources, and that false-positives can be addressed by choosing an adequate model order to match the noise level.

Compressed Beamforming in Ultrasound Imaging

Emerging sonography techniques often require increasing the number of transducer elements involved in the imaging process. Consequently, larger amounts of data must be acquired and processed. The significant growth in the amounts of data affects both machinery size and power consumption. Within the classical sampling framework, state of the art systems reduce processing rates by exploiting the bandpass bandwidth of the detected signals. It has been recently shown, that a much more significant sample-rate reduction may be obtained, by treating ultrasound signals within the Finite Rate of Innovation framework. These ideas follow the spirit of Xampling, which combines classic methods from sampling theory with recent developments in Compressed Sensing. Applying such low-rate sampling schemes to individual transducer elements, which detect energy reflected from biological tissues, is limited by the noisy nature of the signals. This often results in erroneous parameter extraction, bringing forward the need to enhance the SNR of the low-rate samples. In our work, we achieve SNR enhancement, by beamforming the sub-Nyquist samples obtained from multiple elements. We refer to this process as "compressed beamforming". Applying it to cardiac ultrasound data, we successfully image macroscopic perturbations, while achieving a nearly eight-fold reduction in sample-rate, compared to standard techniques.

Innovation Rate Sampling of Pulse Streams With Application to Ultrasound Imaging

Signals comprised of a stream of short pulses 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. 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.