We propose a fast and scalablepolyatomic Frank-Wolfe (P-FW)algorithm for the resolution of high-dimensional LASSO regression problems. This algorithm improves upon traditional Frank-Wolfe methods by considering generalized greedy steps withpolyatomic(i.e.linear combinations of multiple atoms) update directions, hence allowing for a more efficient exploration of the search space. To preserve sparsity of the intermediate iterates, we re-optimize the LASSO problem over the set of selected atoms at each iteration. For efficiency reasons, the accuracy of this re-optimization step is relatively low for early iterations and gradually increases with the iteration count. We provide convergence guarantees for our algorithm and validate it in simulated compressed sensing setups. Our experiments reveal that P-FW outperforms state-of-the-art methods in terms of runtime, both for FW methods and optimal first-order proximal gradient methods such as theFast Iterative Soft-Thresholding Algorithm (FISTA).

Stochastic Maximum Likelihood (SML) is a popular direction of arrival (DOA) estimation technique in array signal processing. It is a parametric method that jointly estimates signal and instrument noise by maximum likelihood, achieving excellent statistical performance. Some drawbacks are the computational overhead as well as the limitation to a point-source data model with fewer sources than sensors. In this work, we propose a Sieved Maximum Likelihood (SiML) method. It uses a general functional data model, allowing an unrestricted number of arbitrarily-shaped sources to be recovered. To this end, we leverage functional analysis tools and express the data in terms of an infinite-dimensional sampling operator acting on a Gaussian random function. We show that SiML is computationally more efficient than traditional SML, resilient to noise, and results in much better accuracy than spectral-based methods.

The starting point for deconvolution methods in radio astronomy is an estimate of the sky intensity called a dirty image. These methods rely on the telescope point-spread function so as to remove artefacts which pollute it. In this work, we show that the intensity field is only a partial summary statistic of the matched filtered interferometric data, which we prove is spatially correlated on the celestial sphere. This allows us to define a sky covariance function. This previously unexplored quantity brings us additional information that can be leveraged in the process of removing dirty image artefacts. We demonstrate this using a novel unsupervised learning method. The problem is formulated on a graph: each pixel interpreted as a node, linked by edges weighted according to their spatial correlation. We then use spectral clustering to separate the artefacts in groups, and identify physical sources within them.

We propose a recurrent neural-network for real-time reconstruction of acoustic camera spherical maps. The network, dubbed DeepWave, is both physically and algorithmically motivated: its recurrent architecture mimics iterative solvers from convex optimisation, and its parsimonious parametrisation is based on the natural structure of acoustic imaging problems. Each network layer applies successive filtering, biasing and activation steps to its input, which can be interpreted as generalised deblurring and sparsification steps. To comply with the irregular geometry of spherical maps, filtering operations are implemented efficiently by means of graph signal processing techniques. Unlike commonly-used imaging network architectures, DeepWave is moreover capable of directly processing the complex-valued raw microphone correlations, learning how to optimally back-project these into a spherical map. We propose moreover a smart physically-inspired initialisation scheme that attains much faster training and higher performance than random initialisation. Our real-data experiments show DeepWave has similar computational speed to the state-of-the-art delay-and-sum imager with vastly superior resolution. While developed primarily for acoustic cameras, DeepWave could easily be adapted to neighbouring signal processing fields, such as radio astronomy, radar and sonar.

Delay-And-Sum (DAS), the state-of-art in ultrasound imaging, is known to be sub-optimal, resulting in low resolution and contrast. Most proposed improvements involve ad-hoc re-weighting, or hit computational bottlenecks given real-time requirements. This paper takes a fresh perspective on the problem, leveraging a functional framework to obtain a regularized least-squares estimate of the tissue reflectivity function. An explicit solution is derived, which - for specific cases - can be efficiently implemented, making it suitable for real-time imaging. In our formulation, DAS appears as a back-projection without any optimal properties. We illustrate the framework through first a one-dimensional set-up, and then a two-dimensional extension with Synthetic Aperture Focusing Technique (SAFT). The one-dimensional simulations show a 77% resolution improvement with respect to DAS, which artificially limits the available bandwidth. On a standard performance-assessment phantom, simulations show that SAFT depth resolution can be improved by 71%.

In our demo, we present two hardware platforms for prototyping audio array signal processing. Pyramic is a 48-channel microphone array fitted on an FPGA and Compact Six is a portable microphone array with six microphones, closer to the technical constraints of consumer electronics. A browser based interface was developed that allows the user to interact with the audio stream from the arrays in real time. The software component of this demo is a Python module with implementations of basic audio signal processing blocks and popular techniques like STFT, beamforming, and DoA. Both the hardware design files and the software are open source and freely shared. As part of a collaboration with IBM Research, their beamforming and imaging technologies will also be portrayed. The hardware will be demonstrated through an installation processing the microphone signals into light patterns on a circular LED array. The demo will be interactive and let visitors play with different algorithms for DoA (SRP, FRIDA [1], Bluebild) and beamforming (MVDR, Flexibeam [2]). The availability of an open platform with reference implementations encourages reproducible research and minimizes setup-time when testing and benchmarking new audio array signal processing algorithms. It can also serve as a useful educational tool, providing a means to work with real-life signals.

We propose a method for designing phased-arrays according to a given, analytically-specified, target beam shape. Building on the flexibeam framework, antenna locations are sampled from a probabilistic density function. Naturally scalable with the number of antennas, it is also computationally efficient and numerically stable, as it relies on analytical derivation. We prove that, under mild conditions, the achieved beamshapes converge uniformly to the target beamshapes as the number of antennas increases. We illustrate the technique through a number of examples. For instance, by use of the Laplace filter, beams with extremely fast decay away from the centre of focus are achieved. Some macroscopic observations result. We observe that matched beamforming weights may, for a given layout, achieve beamshapes targeting regions, rather than isolated directions as commonly believed. Additionally, the convergence analysis can be used to forecast the growth of future large phased arrays such as the Square Kilometre Array (SKA).

Radio interferometry usually compensates for high levels of noise in sensor/antenna electronics by throwing data and energy at the problem: observe longer, then store and process it all. Furthermore, only the end image is cleaned, reducing flexibility substantially. We propose instead a method to remove the noise explicitly before imaging. To this end, we developed an algorithm that first decomposes the sensor signals into components using Singular Spectrum Analysis and then cluster these components using graph Laplacian matrix. We show through simulation the potential for radio astronomy, in particular, illustrating the benefit for LOFAR, the low frequency array in Netherlands. From telescopic data to least-squares image estimates, far higher accuracy with low computation cost results without the need for long observation time.

Imaging techniques in radio interferometry often face a significant challenge posed by the large number of antenna signals received, from which the image information needs to be extracted. Beamforming is envisaged to reduce the rate required for transporting data from groups of antennas to a central site for further processing. We propose a novel method for image reconstruction based on the iterative scanning of a region of interest, combined with randomized beamforming. A modified approximate message-passing algorithm is adopted to extract relevant image information from beamformed signals received at the antenna stations. The method is illustrated by simulations, with reference to the LOFAR radio interferometer, and compared with the CLEAN algorithm.

We propose a new, general, method for spatial filtering by beam-forming. The desired filter, specified analytically on an n-dimensional sphere, is extended to n+1-dimensional Euclidean space. A continuous beamforming function is then obtained by the n+1-dimensional Fourier transform of the extended filter. The beamforming weight at a given array element corresponds then to a sample of the function at the array element location., The scheme is a generalisation of focused beamforming on a single point by phase difference alignment. The analytic framework allows tractable, stable determination of beamforming weights, and for clear filter specification. By avoiding approximating a Dirac, desired areas can be covered with reduced side lobes. Multiple areas may be targeted simultaneously. In communications applications, channel information updates can be reduced, and movement accounted for. A WiFi demonstration shows that more flexible beam-shapes can be beneficial for real-life examples, factoring in attenuation.