HVOX: Scalable Interferometric Synthesis and Analysis of Spherical Sky Maps

Analysis and synthesis are key steps of the radio-interferometric imaging process, serving as a bridge between visibility and sky domains. They can be expressed as partial Fourier transforms involving a large number of non-uniform frequencies and spherically-constrained spatial coordinates. Due to the data non-uniformity, these partial Fourier transforms are computationally expensive and represent a serious bottleneck in the image reconstruction process. The W-gridding algorithm achieves log-linear complexity for both steps by applying a series of 2D non-uniform FFTs (NUFFT) to the data sliced along the so-called $w$ frequency coordinate. A major drawback of this method however is its restriction to direction-cosine meshes, which are fundamentally ill-suited for large field of views. This paper introduces the HVOX gridder, a novel algorithm for analysis/synthesis based on a 3D-NUFFT. Unlike W-gridding, the latter is compatible with arbitrary spherical meshes such as the popular HEALPix scheme for spherical data processing. The 3D-NUFFT allows one to optimally select the size of the inner FFTs, in particular the number of W-planes. This results in a better performing and auto-tuned algorithm, with controlled accuracy guarantees backed by strong results from approximation theory. To cope with the challenging scale of next-generation radio telescopes, we propose moreover a chunked evaluation strategy: by partitioning the visibility and sky domains, the 3D-NUFFT is decomposed into sub-problems which execute in parallel, while simultaneously cutting memory requirements. Our benchmarking results demonstrate the scalability of HVOX for both SKA and LOFAR, considering state-of-the-art challenging imaging setups. HVOX is moreover computationally competitive with W-gridder, despite the absence of domain-specific optimizations in our implementation

BIPP: An efficient HPC implementation of the Bluebild algorithm for radio astronomy

The Bluebild algorithm is a new technique for image synthesis in radio astronomy which forms a least-squares estimate of the sky intensity function using the theory of sampling and interpolation operators. We present an HPC implementation of the Bluebild algorithm for radio-interferometric imaging: Bluebild Imaging++ (BIPP). BIPP is a spherical imager that leverages functional PCA to decompose the sky into distinct energy levels. The library features interfaces to C++, C and Python and is designed with seamless GPU acceleration in mind. We evaluate the accuracy and performance of BIPP on simulated observations of the upcoming Square Kilometer Array Observatory and real data from the Low-Frequency Array (LOFAR) telescope. We find that BIPP offers accurate wide-field imaging with no need for a w-term approximation and has comparable execution time with respect to the interferometric imaging libraries CASA and WSClean. Futhermore, due to the energy level decomposition, images produced with BIPP can reveal information about faint and diffuse structures before any cleaning iterations. The source code of BIPP is publicly released.Comment: 18 pages, 12 figure

Hardware And Software For Reproducible Research In Audio Array Signal Processing

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

Optimization Notes

While optimization is well studied for real-valued functions $f : \mathbb{R}^{N} \to \mathbb{R}$, many physical problems are (partially) specified in terms of complex-valued functions $f_{c} : \mathbb{C}^{N} \to \mathbb{C}^{M}$. Current optimization packages have limited support for such functions. In particular it is unclear how to define algorithmic differentiation w.r.t. complex-valued functions and arguments. This document is a collection of working notes on the topic

Fourier Tools

The FFT algorithm is a key pillar of modern numerical computing. This document is a collection of working notes on FFT-based algorithms. Efficient implementations of the former are made available through the pyFFS package

DeepWave : a recurrent neural-network for real-time acoustic imaging

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

LenslessPiCam: A Hardware and Software Platform for Lensless Computational Imaging with a Raspberry Pi

Lensless imaging seeks to replace/remove the lens in a conventional imaging system. The earliest cameras were in fact lensless, relying on long exposure times to form images on the other end of a small aperture in a darkened room/container (camera obscura). The introduction of a lens allowed for more light throughput and therefore shorter exposure times, while retaining sharp focus. The incorporation of digital sensors readily enabled the use of computational imaging techniques to post-process and enhance raw images (e.g. via deblurring, inpainting, denoising, sharpening). Recently, imaging scientists have started leveraging computational imaging as an integral part of lensless imaging systems, allowing them to form viewable images from the highly multiplexed raw measurements of lensless cameras (see [5] and references therein for a comprehensive treatment of lensless imaging). This represents a real paradigm shift in camera system design as there is more flexibility to cater the hardware to the application at hand (e.g. lightweight or flat designs). This increased flexibility comes however at the price of a more demanding post-processing of the raw digital recordings and a tighter integration of sensing and computation, often difficult to achieve in practice due to inefficient interactions between the various communities of scientists involved. With LenslessPiCam, we provide an easily accessible hardware and software framework to enable researchers, hobbyists, and students to implement and explore practical and computational aspects of lensless imaging. We also provide detailed guides and exercises so that LenslessPiCam can be used as an educational resource, and point to results from our graduate-level signal processing course

DeepWave: A Recurrent Neural-Network for Real-Time Acoustic Imaging

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