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.Comment: 16 pages, 8 figure

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D_s spectrum and leptonic decays with Fermilab heavy quarks and improved staggered light quarks

We present preliminary results for the D_s meson spectrum and decay constants in unquenched lattice QCD. Simulations are carried out with 2+1 dynamical quarks using gauge configurations generated by the MILC collaboration. We use the ``asqtad'' a^2 improved staggered action for the light quarks, and the clover heavy quark action with the Fermilab interpretation. We compare our spectrum results with the newly discovered 0+ and 1+ states in the D_s system.Comment: 3pp. Presented at 21st International Symposium on Lattice Field Theory (LATTICE 2003), Tsukuba, Ibaraki, Japan, 15-19 Jul 200

Development and clinical validation of real-time artificial intelligence diagnostic companion for fetal ultrasound examination

OBJECTIVE: Prenatal diagnosis of a rare disease on ultrasound relies on a physician's ability to remember an intractable amount of knowledge. We developed a real-time decision support system (DSS) that suggests, at each step of the examination, the next phenotypic feature to assess, optimizing the diagnostic pathway to the smallest number of possible diagnoses. The objective of this study was to evaluate the performance of this real-time DSS using clinical data. METHODS: This validation study was conducted on a database of 549 perinatal phenotypes collected from two referral centers (one in France and one in the UK). Inclusion criteria were: at least one anomaly was visible on fetal ultrasound after 11 weeks' gestation; the anomaly was confirmed postnatally; an associated rare disease was confirmed or ruled out based on postnatal/postmortem investigation, including physical examination, genetic testing and imaging; and, when confirmed, the syndrome was known by the DSS software. The cases were assessed retrospectively by the software, using either the full phenotype as a single input, or a stepwise input of phenotypic features, as prompted by the software, mimicking its use in a real-life clinical setting. Adjudication of discordant cases, in which there was disagreement between the DSS output and the postnatally confirmed (‘ascertained’) diagnosis, was performed by a panel of external experts. The proportion of ascertained diagnoses within the software's top-10 differential diagnoses output was evaluated, as well as the sensitivity and specificity of the software to select correctly as its best guess a syndromic or isolated condition. RESULTS: The dataset covered 110/408 (27%) diagnoses within the software's database, yielding a cumulative prevalence of 83%. For syndromic cases, the ascertained diagnosis was within the top-10 list in 93% and 83% of cases using the full-phenotype and stepwise input, respectively, after adjudication. The full-phenotype and stepwise approaches were associated, respectively, with a specificity of 94% and 96% and a sensitivity of 99% and 84%. The stepwise approach required an average of 13 queries to reach the final set of diagnoses. CONCLUSIONS: The DSS showed high performance when applied to real-world data. This validation study suggests that such software can improve perinatal care, efficiently providing complex and otherwise overlooked knowledge to care-providers involved in ultrasound-based prenatal diagnosis. © 2023 The Authors. Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of International Society of Ultrasound in Obstetrics and Gynecology

On an Analytical, Spatially-Varying, Point-Spread-Function

The point spread function (PSF), namely the response of an ultrasound system to a point source, is a powerful measure of the quality of an imaging system. The lack of an analytical formulation inhibits many applications ranging from apodization optimization, array-design, and deconvolution algorithms. We propose to fill this gap through a general PSF derivation that is flexible with respect to the type of transmission (synthetic aperture, plane-wave, diverging-wave etc.), while faithfully capturing the spatially-variant blurring of the Tissue Reflectivity Function as caused by Delay-And-Sum reconstruction. We validate the derived PSF against simulation using Field II, and show that accounting for PSF spatial-variability in sparse- based deconvolution improves reconstruction

Observation of the Askaryan Effect: Coherent Microwave Cherenkov Emission from Charge Asymmetry in High Energy Particle Cascades

We present the first direct experimental evidence for the charge excess in high energy particle showers predicted nearly 40 years ago by Askaryan. We directed bremsstrahlung photons from picosecond pulses of 28.5 GeV electrons at the SLAC Final Focus Test Beam facility into a 3.5 ton silica sand target, producing electromagnetic showers several meters long. A series of antennas spanning 0.3 to 6 GHz were used to detect strong, sub-nanosecond radio frequency pulses produced whenever a shower was present. The measured electric field strengths are consistent with a completely coherent radiation process. The pulses show 100% linear polarization, consistent with the expectations of Cherenkov radiation. The field strength versus depth closely follows the expected particle number density profile of the cascade, consistent with emission from excess charge distributed along the shower. These measurements therefore provide strong support for experiments designed to detect high energy cosmic rays and neutrinos via coherent radio emission from their cascades.Comment: 10 pages, 4 figures. Submitted to Phys. Rev. Let