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Paul Hurley

Publications and source records attributed to Paul Hurley.

12 recordsLinked to original sources
arXiv2026

Optical Linear Systems Framework for Event Sensing and Computational Neuromorphic Imaging

Event vision sensors (neuromorphic cameras) output sparse, asynchronous ON/OFF events triggered by log-intensity threshold crossings, enabling microsecond-scale sensing with high dynamic range and low data bandwidth. As a nonlinear system, this event representation does not readily integrate with the linear forward models that underpin most computational imaging and optical system design. We present a physics-grounded processing pipeline that maps event streams to estimates of per-pixel log-intensity and intensity derivatives, and embeds these measurements in a dynamic linear systems model with a time-varying point spread function. This enables inverse filtering directly from event data, using frequency-domain Wiener deconvolution with a known (or parameterised) dynamic transfer function. We validate the approach in simulation for single and overlapping point sources under modulated defocus, and on real event data from a tunable-focus telescope imaging a star field, demonstrating source localisation and separability. The proposed framework provides a practical bridge between event sensing and model-based computational imaging for dynamic optical systems.

cs.CV↗
arXiv2024

PolyCLEAN: Atomic Optimization for Super-Resolution Imaging and Uncertainty Estimation in Radio Interferometry

Aims: We address two issues for the adoption of convex optimization in radio interferometric imaging. First, a method for a fine resolution setup is proposed which scales naturally in terms of memory usage and reconstruction speed. Second, a new tool to localize a region of uncertainty is developed, paving the way for quantitative imaging in radio interferometry. Methods: The classical $\ell_1$ penalty is used to turn the inverse problem into a sparsity-promoting optimization. For efficient implementation, the so-called Frank-Wolfe algorithm is used together with a \textit{polyatomic} refinement. The algorithm naturally produces sparse images at each iteration, leveraged to reduce memory and computational requirements. In that regard, PolyCLEAN reproduces the numerical behavior of CLEAN while guaranteeing that it solves the minimization problem of interest. Additionally, we introduce the concept of the \textit{dual certificate image}, which appears as a numerical byproduct of the Frank-Wolfe algorithm. This image is proposed as a tool for uncertainty quantification on the location of the recovered sources. Results: PolyCLEAN demonstrates good scalability performance, in particular for fine-resolution grids. On simulations, the Python-based implementation is competitive with the fast numerically-optimized CLEAN solver. This acceleration does not affect image reconstruction quality: PolyCLEAN images are consistent with CLEAN-obtained ones for both point sources and diffuse emission recovery. We also highlight PolyCLEAN reconstruction capabilities on observed radio measurements. Conclusions: PolyCLEAN can be considered as an alternative to CLEAN in the radio interferometric imaging pipeline, as it enables the use of Bayesian priors without impacting the scalability and numerical performance of the imaging method.

astro-ph.IM↗
arXiv2023

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 decomposes the sky into distinct energy levels using functional principal component analysis. These levels can be linearly combined to construct a least-squares estimate of the radio sky, i.e. minimizing the residuals between measured and predicted visibilities. This approach is particularly useful for deconvolution-free imaging or for scientific applications that need to filter specific energy levels. We present an HPC implementation of the Bluebild algorithm for radio-interferometric imaging: Bluebild Imaging++ (BIPP). 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 and has competitive execution time with respect to the interferometric imaging libraries CASA and WSClean for images with $\leq 10^6$ pixels. Furthermore, due to the energy level decomposition, images produced with BIPP can reveal information about faint and diffuse structures before any cleaning iterations. BIPP does not perform any regularization, but we suggest methods to integrate the output of BIPP with CLEAN. The source code of BIPP is publicly released.

astro-ph.IM↗
arXiv2022

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choice would be to work with e.g. the Fourier series (FS) coefficients in order to avoid the additional overhead of translating between the analog and discrete domains. Unfortunately, there exists very little literature and tools for the manipulation of FS coefficients from discrete samples. This paper introduces a Python library called pyFFS for efficient FS coefficient computation, convolution, and interpolation. While the libraries SciPy and NumPy provide efficient functionality for discrete Fourier transform coefficients via the FFT algorithm, pyFFS addresses the computation of FS coefficients through what we call the fast Fourier series (FFS). Moreover, pyFFS includes an FS interpolation method based on the chirp Z-transform that can make it more than an order of magnitude faster than the SciPy equivalent when one wishes to perform interpolation. GPU support through the CuPy library allows for further acceleration, e.g. an order of magnitude faster for computing the 2-D FS coefficients of 1000 x 1000 samples and nearly two orders of magnitude faster for 2-D interpolation. As an application, we discuss the use of pyFFS in Fourier optics. pyFFS is available as an open source package at https://github.com/imagingofthings/pyFFS, with documentation at https://pyffs.readthedocs.io.

cs.MS↗
arXiv2021

SiML: Sieved Maximum Likelihood for Array Signal Processing

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.

stat.AP↗
arXiv2021

CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI

Finite rate of innovation (FRI) is a powerful reconstruction framework enabling the recovery of sparse Dirac streams from uniform low-pass filtered samples. An extension of this framework, called generalised FRI (genFRI), has been recently proposed for handling cases with arbitrary linear measurement models. In this context, signal reconstruction amounts to solving a joint constrained optimisation problem, yielding estimates of both the Fourier series coefficients of the Dirac stream and its so-called annihilating filter, involved in the regularisation term. This optimisation problem is however highly non convex and non linear in the data. Moreover, the proposed numerical solver is computationally intensive and without convergence guarantee. In this work, we propose an implicit formulation of the genFRI problem. To this end, we leverage a novel regularisation term which does not depend explicitly on the unknown annihilating filter yet enforces sufficient structure in the solution for stable recovery. The resulting optimisation problem is still non convex, but simpler since linear in the data and with less unknowns. We solve it by means of a provably convergent proximal gradient descent (PGD) method. Since the proximal step does not admit a simple closed-form expression, we propose an inexact PGD method, coined as Cadzow plug-and-play gradient descent (CPGD). The latter approximates the proximal steps by means of Cadzow denoising, a well-known denoising algorithm in FRI. We provide local fixed-point convergence guarantees for CPGD. Through extensive numerical simulations, we demonstrate the superiority of CPGD against the state-of-the-art in the case of non uniform time samples.

math.OC↗
arXiv2018

Probabilistic Value-Deviation-Bounded Integer Codes for Approximate Communication

When computing systems can tolerate the effects of errors or erasures in their communicated data values, they can trade this tolerance for improved resource efficiency. One method for enabling this tradeoff in the I/O subsystems of computing systems, is to use channel codes that reduce the power needed to send bits on a channel in exchange for bounded errors and erasures on numeric program values---value-deviation-bounded (VDB) codes. Unlike rate distortion codes, which guarantee a bound on the expected value of channel distortion, the probabilistic VDB codes we present guarantee any desired tail distribution on integer distances of words transmitted over a channel. We extend prior work to present tighter upper bounds on the efficiency for VDB codes. We present a new probabilistic VDB encoder that lowers power dissipation in exchange for bounded channel integer distortions. The code we present takes the peculiar approach of changing the channel bit error rate across the ordinal bit positions in a word to reduce power dissipation. We implement the code table generator in a software tool built on the dReal SMT solver and we validate the generated codes using Monte Carlo simulation. We present one realization of hardware to implement the technique, requiring 2 mm$^2$ of circuit board area and dissipating less than 0.5 $μ$W.

cs.IT↗
arXiv2014

Collaborative Randomized Beamforming for Phased Array Radio Interferometers

The Square Kilometre Array (SKA) will form the largest radio telescope ever built and such a huge instrument in the desert poses enormous engineering and logistic challenges. Algorithmic and architectural breakthroughs are needed. Data is collected and processed in groups of antennas before transport for central processing. This processing includes beamforming, primarily so as to reduce the amount of data sent. The principal existing technique points to a region of interest independently of the sky model and how the other stations beamform. We propose a new collaborative beamforming algorithm in order to maximize information captured at the stations (thus reducing the amount of data transported). The method increases the diversity in measurements through randomized beam- forming. We demonstrate through numerical simulation the effectiveness of the method. In particular, we show that randomized beamforming can achieve the same image quality while producing 40% less data when compared to the prevailing method matched beamforming.

astro-ph.IM↗
arXiv2011

Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts

We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask layouts. There, speed is of paramount importance due to the magnitude of the problems to be solved and hence very fast algorithms are needed. We show that by techniques borrowed from computational geometry we are not only able to compute the continuous Haar transform directly, but also to do it quickly. This is achieved by massively pruning the transform tree and thus dramatically decreasing the computational load when the number of vertices is small, as is the case for VLSI layouts. We call this new algorithm the pruned continuous Haar transform. We implement this algorithm and show that for patterns found in VLSI layouts the proposed algorithm was in the worst case as fast as its discrete counterpart and up to 12 times faster.

cs.CE↗
arXiv2010

Fast Continuous Haar and Fourier Transforms of Rectilinear Polygons from VLSI Layouts

We develop the pruned continuous Haar transform and the fast continuous Fourier series, two fast and efficient algorithms for rectilinear polygons. Rectilinear polygons are used in VLSI processes to describe design and mask layouts of integrated circuits. The Fourier representation is at the heart of many of these processes and the Haar transform is expected to play a major role in techniques envisioned to speed up VLSI design. To ensure correct printing of the constantly shrinking transistors and simultaneously handle their increasingly large number, ever more computationally intensive techniques are needed. Therefore, efficient algorithms for the Haar and Fourier transforms are vital. We derive the complexity of both algorithms and compare it to that of discrete transforms traditionally used in VLSI. We find a significant reduction in complexity when the number of vertices of the polygons is small, as is the case in VLSI layouts. This analysis is completed by an implementation and a benchmark of the continuous algorithms and their discrete counterpart. We show that on tested VLSI layouts the pruned continuous Haar transform is 5 to 25 times faster, while the fast continuous Fourier series is 1.5 to 3 times faster.

cs.CE↗
arXiv2007

Codes from Zero-divisors and Units in Group Rings

We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in ideals. We use the result that a group ring is isomorphic to a certain well-defined ring of matrices, and thus every group ring element has an associated matrix. This allows matrix algebra to be used as needed in the study and production of codes, enabling the creation of standard generator and check matrices. Group rings are a fruitful source of units and zero-divisors from which new codes result. Many code properties, such as being LDPC or self-dual, may be expressed as properties within the group ring thus enabling the construction of codes with these properties. The methods are general enabling the construction of codes with many types of group rings. There is no restriction on the ring and thus codes over the integers, over matrix rings or even over group rings themselves are possible and fruitful.

cs.IT↗