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Ultrasound imaging, despite its widespread use in medicine, often suffers from various sources of noise and artifacts that impact the signal-to-noise ratio and overall image quality. Enhancing ultrasound images requires a delicate balance between contrast, resolution, and speckle preservation. This paper introduces a novel approach that integrates adaptive beamforming with denoising diffusion-based variance imaging to address this challenge. By applying Eigenspace-Based Minimum Variance (EBMV) beamforming and employing a denoising diffusion model fine-tuned on ultrasound data, our method computes the variance across multiple diffusion-denoised samples to produce high-quality despeckled images. This approach leverages both the inherent multiplicative noise of ultrasound and the stochastic nature of diffusion models. Experimental results on a publicly available dataset demonstrate the effectiveness of our method in achieving superior image reconstructions from single plane-wave acquisitions. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/IUS2024_Diffusion., Comment: Accepted by the IEEE International Ultrasonics Symposium (IUS) 2024

We review recent mathematical results concerning the high-frequency solutions to the Einstein vacuum equations and the limits of these solutions. In particular, we focus on two conjectures of Burnett, which attempt to give an exact characterization of high-frequency limits of vacuum spacetimes as solutions to the Einstein-massless Vlasov system. Some open problems and future directions are discussed., Comment: 34 pages, review article

Despite today's prevalence of ultrasound imaging in medicine, ultrasound signal-to-noise ratio is still affected by several sources of noise and artefacts. Moreover, enhancing ultrasound image quality involves balancing concurrent factors like contrast, resolution, and speckle preservation. Recently, there has been progress in both model-based and learning-based approaches addressing the problem of ultrasound image reconstruction. Bringing the best from both worlds, we propose a hybrid reconstruction method combining an ultrasound linear direct model with a learning-based prior coming from a generative Denoising Diffusion model. More specifically, we rely on the unsupervised fine-tuning of a pre-trained Denoising Diffusion Restoration Model (DDRM). Given the nature of multiplicative noise inherent to ultrasound, this paper proposes an empirical model to characterize the stochasticity of diffusion reconstruction of ultrasound images, and shows the interest of its variance as an echogenicity map estimator. We conduct experiments on synthetic, in-vitro, and in-vivo data, demonstrating the efficacy of our variance imaging approach in achieving high-quality image reconstructions from single plane-wave acquisitions and in comparison to state-of-the-art methods. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/DRUSvar, Comment: 5 pages; accepted by EUSIPCO 2024. arXiv admin note: text overlap with arXiv:2310.20618

We prove Burnett's conjecture in general relativity when the metrics satisfy a generalized wave coordinate condition, i.e., suppose $\{g_n\}_{n=1}^\infty$ is a sequence of Lorentzian metrics (in arbitrary dimensions $d \geq 3$) satisfying a generalized wave coordinate condition and such that $g_n\to g$ in a suitably weak and "high-frequency" manner, then the limit metric $g$ satisfies the Einstein--massless Vlasov system. Moreover, we show that the Vlasov field for the limiting metric can be taken to be a suitable microlocal defect measure corresponding to the convergence. The proof uses a compensation phenomenon based on the linear and nonlinear structure of the Einstein equations., Comment: 28 pages

Despite its wide use in medicine, ultrasound imaging faces several challenges related to its poor signal-to-noise ratio and several sources of noise and artefacts. Enhancing ultrasound image quality involves balancing concurrent factors like contrast, resolution, and speckle preservation. In recent years, there has been progress both in model-based and learning-based approaches to improve ultrasound image reconstruction. Bringing the best from both worlds, we propose a hybrid approach leveraging advances in diffusion models. To this end, we adapt Denoising Diffusion Restoration Models (DDRM) to incorporate ultrasound physics through a linear direct model and an unsupervised fine-tuning of the prior diffusion model. We conduct comprehensive experiments on simulated, in-vitro, and in-vivo data, demonstrating the efficacy of our approach in achieving high-quality image reconstructions from a single plane wave input and in comparison to state-of-the-art methods. Finally, given the stochastic nature of the method, we analyse in depth the statistical properties of single and multiple-sample reconstructions, experimentally show the informativeness of their variance, and provide an empirical model relating this behaviour to speckle noise. The code and data are available at: (upon acceptance)., Comment: This work has been submitted to the IEEE for possible publication. (10 pages)

Ultrasound image reconstruction can be approximately cast as a linear inverse problem that has traditionally been solved with penalized optimization using the $l_1$ or $l_2$ norm, or wavelet-based terms. However, such regularization functions often struggle to balance the sparsity and the smoothness. A promising alternative is using learned priors to make the prior knowledge closer to reality. In this paper, we rely on learned priors under the framework of Denoising Diffusion Restoration Models (DDRM), initially conceived for restoration tasks with natural images. We propose and test two adaptions of DDRM to ultrasound inverse problem models, DRUS and WDRUS. Our experiments on synthetic and PICMUS data show that from a single plane wave our method can achieve image quality comparable to or better than DAS and state-of-the-art methods. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/DRUS-v1., Comment: accepted for DGM4MICCAI 2023

In this paper we show the classical global stability of the flat Kaluza-Klein spacetime, which corresponds to Minkowski spacetime in $\m R^{1+4}$ with one direction compactified on a circle. We consider small perturbations which are allowed to vary in all directions including the compact direction. These perturbations lead to the creation of massless modes and Klein-Gordon modes. On the analytic side, this leads to a PDE system coupling wave equations to an infinite sequence of Klein-Gordon equations with different masses. The techniques we use are based purely in physical space using the vectorfield method., Comment: 80 pages

Cyclic multiaxial loadings of soft materials are usually studied throughout experiments involving machines that prescribe a combination of uniaxial tension and torsion. Due to the large strain framework, classical kinematic analyses of strain in uniaxial tension-torsion are usually very complex. Based on this observation, the present papers proposes a method to both analyze and visualize a strain measure during a duty cycle of uniaxial tension-torsion in large strain: based on the mathematical properties of the Hencky strain tensor $\mathbf{h}$, the method consists in projecting $\mathbf{h}$ onto a well-chosen tensorial basis, whose constituting elements are described in terms of physical meaning. Thanks to this decomposition, the history of $\mathbf{h}$ reduces to the time evolution of a 3-components vector $\alpha(t)$. This vector history can then be visualized as a path in the 3D space, rendering very visual the complex kinematic phenomenon. As a second result, an original definition of the mean and the amplitude of a strain path, based on the theory of the Minimum Circumscribed Spheres, is proposed. This definition could be useful for fatigue studies, for instance., Comment: 14 pages, 7 figures

The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the conformal method to reduce the constraint equations to a system of elliptic equation and work in the near CMC (constant mean curvature) regime. The main new feature of our paper is the introduction of new weighted Sobolev spaces, adapted to the inversion of the Laplacian on product manifolds.

We consider a system of quasilinear wave equations on the product space $\mathbb{R}^{1+3}\times \mathbb{S}^1$, which we want to see as a toy model for Einstein equations with additional compact dimensions. We show global existence for small and regular initial data with polynomial decay at infinity. The method combines energy estimates on hyperboloids inside the light cone and weighted energy estimates outside the light cone.

The Ra EDM experiment uses a pair of high voltage electrodes to search for the atomic electric dipole moment of $^{225}$Ra. We use identical, plane-parallel electrodes with a primary high gradient surface of 200 mm$^2$ to generate reversible DC electric fields. Our statistical sensitivity is linearly proportional to the electric field strength in the electrode gap. We adapted surface decontamination and processing techniques from accelerator physics literature to chemical polish and clean a suite of newly fabricated large-grain niobium and grade-2 titanium electrodes. Three pairs of niobium electrodes and one pair of titanium electrodes were discharge-conditioned with a custom high voltage test station at electric field strengths as high as $+52.5$ kV/mm and $-51.5$ kV/mm over electrode gap sizes ranging from 0.4 mm to 2.5 mm. One pair of large-grain niobium electrodes was discharge-conditioned and validated to operate at $\pm 20$ kV/mm with steady-state leakage current $\leq 25$ pA ($1\sigma$) and a polarity-averaged $98 \pm 19$ discharges per hour. These electrodes were installed in the Ra EDM experimental apparatus, replacing a copper electrode pair, and were revalidated to $\pm 20$ kV/mm. The niobium electrodes perform at an electric field strength 3.1 times larger than the legacy copper electrodes and are ultimately limited by the maximum output of our 30 kV bipolar power supply., Comment: 16 pages, 11 figures

Consider a sequence of $C^4$ Lorentzian metrics $\{h_n\}_{n=1}^{+\infty}$ on a manifold $\mathcal M$ satisfying the Einstein vacuum equation $\mathrm{Ric}(h_n)=0$. Suppose there exists a smooth Lorentzian metric $h_0$ on $\mathcal M$ such that $h_n\to h_0$ uniformly on compact sets. Assume also that on any compact set $K\subset \mathcal M$, there is a decreasing sequence of positive numbers $\lambda_n \to 0$ such that $$\|\partial^{\alpha} (h_n - h_0)\|_{L^{\infty}(K)} \lesssim \lambda_n^{1-|\alpha|},\quad |\alpha|\geq 4.$$ It is well-known that $h_0$, which represents a "high-frequency limit", is not necessarily a solution to the Einstein vacuum equation. Nevertheless, Burnett conjectured that $h_0$ must be isometric to a solution to the Einstein-massless Vlasov system. In this paper, we prove Burnett's conjecture assuming that $\{h_n\}_{n=1}^{+\infty}$ and $h_0$ in addition admit a $\mathbb U(1)$ symmetry and obey an elliptic gauge condition. The proof uses microlocal defect measures - we identify an appropriately defined microlocal defect measure to be the Vlasov measure of the limit spacetime. In order to show that this measure indeed obeys the Vlasov equation, we need some special cancellations which rely on the precise structure of the Einstein equations. These cancellations are related to a new "trilinear compensated compactness" phenomenon for solutions to (semilinear) elliptic and (quasilinear) hyperbolic equations., Comment: 63 pages; minor revisions