arXiv subjects

Eric Miller

Publications and source records attributed to Eric Miller.

At least 19 recordsLinked to original sources

arXiv2026

O VI Emission in Starbursting BCGs: An HST-COS Extension of "Reigniting the FUSE"

In this extension of our "Reigniting the FUSE" series, we have obtained new far-ultraviolet spectroscopy of 3 starbursting brightest cluster galaxies with the Cosmic Origins Spectrograph (COS) aboard HST. With these new data, in combination with archival COS data of 2 additional systems, we measure star formation rates (SFRs) from the young stellar continuum and cooling rates through $10^{5.5}$ K gas with the O VI $1032,1038\,\mathring{\rm A}$ doublet ($\dot{M}_{\rm O\,VI}$). We use these measurements to increase the size of the "Reigniting the FUSE" sample, which itself contains high resolution far UV spectroscopy for 29 nearby massive elliptical galaxies from FUSE, and extend it 1 dex upwards in SFR and cooling rate. Our derived SFRs agree well with photometric GALEX$+$WISE SFRs from the literature. The new data also reinforce the previously observed trend in cooling efficiency ($\dot{M}_{\rm O\,VI}/\dot{M}_{\rm max}$; where $\dot{M}_{\rm max}$ is the X-ray luminosity-based cooling rate) versus mass, with groups cooling more efficiently than clusters by a factor of $\sim$4-5. When we isolate a sample of the most star-forming central galaxies, we find that the star formation rates, X-ray spectroscopic cooling rates, and UV spectroscopic cooling rates are all consistent with one another, on average, while retaining substantial system-to-system scatter, reflecting time-depenent multiphase condensation and cold gas reservoir evolution. The remainder of the sample, in contrast, overwhelmingly shows ratios of ${\rm SFR}/\dot{M}_{\rm O\,VI} \sim {\rm SFR}/\dot{M}_{\rm X,spec} \sim 10\%$.

astro-ph.GA↗

arXiv2026

Reigniting the FUSE II: O VI Emission in Massive Elliptical Galaxies

This is the second paper in a series where we examine archival far-ultraviolet spectroscopy of 29 massive elliptical galaxies from the Far Ultraviolet Spectroscopic Explorer (FUSE) with modern methods. In the first paper, we performed SED modeling with aperture-matched photometry and analyzed the young and old stellar populations in these galaxies. In this paper, we report extinction-corrected O VI $λλ$1032,1038 $\mathring{\rm A}$ fluxes and upper limits for each galaxy, which we use to infer the rate at which gas is cooling through $10^{5.5}$ K via multiphase condensation of the galaxy's CGM ($\dot{M}_{\rm O\,VI}$) under the assumption of steady radiative cooling. By considering both Galactic and intrinsic extinction, we overwhelmingly find $\dot{M}_{\rm O\,VI}$ to be larger than values found previously in the literature by a median of $\sim 80\%$. Additionally, we quantify correlations between $\dot{M}_{\rm O\,VI}$ and star formation rates, classical luminosity-based X-ray cooling rates, and X-ray spectroscopic cooling rates. The results suggest that the efficiency of cooling from the $\gtrsim 10^7$ K circumgalactic medium evolves with host mass, being suppressed by a factor of $\sim 4$-$5$ more at the cluster scale than it is at the group and elliptical scales. In contrast, under the steady cooling assumption, cooling from $10^{5.5}$ K to the molecular phase appears to be suppressed by an order of magnitude, independent of mass, requiring turbulent mixing layers, thermal conduction, multiphase recycling, a bottom-heavy initial mass function, or some other additional physics to explain.

astro-ph.GA↗

arXiv2026

Reigniting the FUSE I: Star Formation in Massive Elliptical Galaxies

In this inaugural paper of our "Reigniting the FUSE" series, we present the data collection & reduction, methodology, and preliminary results for a comprehensive and homogeneous reanalysis of all 30 massive elliptical galaxies that have archival far-ultraviolet (FUV) spectra with the Far Ultraviolet Spectroscopic Explorer (FUSE). We perform SED fitting to these spectra, with aperture-matched photometry from GALEX, SDSS, DES/DECaLS, 2MASS, and WISE, and construct a catalogue of high quality constraints on their stellar masses, star formation histories, stellar and gas-phase metallicities, and dust opacities. As a part of this analysis, we have also compiled a comprehensive modern set of stellar template libraries, with high resolution in the FUV, and broad coverage from $90\,\mathring{\rm A}$ - $1000\,{\rm μm}$ at lower resolution, which is made available through modified versions of FSPS and Python FSPS. We find strong evidence to suggest that the youngest stars in these systems do not form out of recycled gas from the old stellar populations, but instead are fueled either by gas cooling out of the hot circumgalactic/intracluster medium, or cool gas stripped from nearby or merging dwarf systems. Future papers in this series will reexamine the O VI $λλ$1032,1038 $\mathring{\rm A}$ emission in the context of the cooling flow problem.

astro-ph.GA↗

arXiv2026

Advancing X-Ray Camera Front-End Electronics Architecture through the AXIS-TAP Technology Platform

Advancing time-domain soft X-ray astronomy demands focal plane readout electronics capable of high-speed digitization with low noise while maintaining spectral fidelity across multiple detector channels. The Advanced X-ray Imaging Satellite (AXIS), a NASA Probe-class mission concept, provided the driving requirements and heritage for developing a generalized high-speed (>=5 fps) camera Front-End Electronics (FEE) architecture applicable to future soft X-ray missions. The FEE architecture defines a modular, dual-box redundant configuration to operate a focal plane of four 16-channel CCDs, with functional partitioning for power distribution, thermal management, mechanism control, and image data acquisition and transmission to the spacecraft. To validate the core signal chain architecture, particularly the analog-to-digital conversion, FPGA-based processing, and Ethernet data transmission, a dedicated technology demonstrator, AXIS-TAP (ADC Testing and Acquisition Platform), has been designed and is currently in fabrication. AXIS-TAP employs commercial equivalents of radiation-tolerant components (FPGA, ADCs, Ethernet PHY) and interfaces directly with the STA Archon benchtop readout system, enabling simultaneous image acquisition from both systems to validate that the flight-like architecture achieves equivalent or superior noise performance. This paper presents the FEE architectural framework, the AXIS-TAP demonstrator design, and the design principles that enable scalability to future soft X-ray missions with similar detector requirements. Performance validation results will be reported upon completion of AXIS-TAP system integration and testing.

astro-ph.IM↗

arXiv2026

Unveiling the Cosmic Chemistry II: "Direct" $T_e$-based metallicity of galaxies at 3 $< z <$ 10 with JWST/NIRSpec

We report the detection of the [O III] auroral line in 42 galaxies within the redshift range of $3 < z < 10$. These galaxies were selected from publicly available JWST data releases, including the JADES and PRIMALsurveys, and observed using both the low-resolution PRISM/CLEAR configuration and medium-resolution gratings. The measured electron temperatures in the high-ionization regions of these galaxies range from $T_e$([O III]) = 12,000 to 24,000 K, consistent with temperatures observed in local metal-poor galaxies and previous JWST studies. In 10 galaxies, we also detect the [O II] auroral line, allowing us to determine electron temperatures in the low-ionization regions, which range between $T_e$([O II]) = 10,830 and 20,000 K. The direct-$T_e$-based metallicities of our sample span from 12 + log(O/H) = 7.2 to 8.4, indicating these high-redshift galaxies are relatively metal-poor. By combining our sample with 25 galaxies from the literature, we expand the dataset to a total of 67 galaxies within $3 < z < 10$, effectively more than doubling the previous sample size for direct-$T_e$ based metallicity studies. This larger dataset allow us to derive empirical metallicity calibration relations based exclusively on high-redshift galaxies, using six key line ratios: R3, R2, R23, Ne3O2, O32, and O3N2. Notably, we derive a novel metallicity calibration relation for the first time using high-redshift $T_e$-based metallicities: $\hat{R}$ = 0.18log $R2$ + 0.98log $R3$. This new calibration significantly reduces the scatter in high-redshift galaxies compared to the $\hat{R}$ relation previously calibrated for low-redshift galaxies.

astro-ph.GA↗

arXiv2025

From Words to Wisdom: Discourse Annotation and Baseline Models for Student Dialogue Understanding

Identifying discourse features in student conversations is quite important for educational researchers to recognize the curricular and pedagogical variables that cause students to engage in constructing knowledge rather than merely completing tasks. The manual analysis of student conversations to identify these discourse features is time-consuming and labor-intensive, which limits the scale and scope of studies. Leveraging natural language processing (NLP) techniques can facilitate the automatic detection of these discourse features, offering educational researchers scalable and data-driven insights. However, existing studies in NLP that focus on discourse in dialogue rarely address educational data. In this work, we address this gap by introducing an annotated educational dialogue dataset of student conversations featuring knowledge construction and task production discourse. We also establish baseline models for automatically predicting these discourse properties for each turn of talk within conversations, using pre-trained large language models GPT-3.5 and Llama-3.1. Experimental results indicate that these state-of-the-art models perform suboptimally on this task, indicating the potential for future research.

cs.CL↗

arXiv2025

Chandra Large Project Observations of the Supernova Remnant N132D: Measuring the Expansion of the Forward Shock

We present results from the Chandra X-ray Observatory Large Project (878 ks in 28 observations) of the Large Magellanic Cloud supernova remnant N132D. We measure the expansion of the forward shock in the bright southern rim to be $0.\!^{\prime\prime}10 \pm 0.\!^{\prime\prime}02$ over the $\sim14.5$ yr baseline, which corresponds to a velocity of $1620\pm400~\mathrm{km\,s^{-1}}$ after accounting for several instrumental effects. We measure an expansion of $0.\!^{\prime\prime}23 \pm 0.\!^{\prime\prime}02$ and a shock velocity of $3840\pm260~\mathrm{km\,s^{-1}}$ for two features in an apparent blowout region in the northeast. The emission-measure-weighted average temperature inferred from X-ray spectral fits to regions in the southern rim is $0.95\pm0.17$ keV, consistent with the electron temperature implied by the shock velocity after accounting for Coulomb equilibration and adiabatic expansion. In contrast, the emission-measure-weighted average temperature for the northeast region is $0.77\pm0.04$ keV, which is significantly lower than the value inferred from the shock velocity. We fit 1-D evolutionary models for the shock in the southern rim and northeast region, using the measured radius and propagation velocity into a constant density and power-law profile circumstellar medium. We find good agreement with the age of $\sim2500$ years derived from optical expansion measurements for explosion energies of $1.5-3.0 \times 10^{51}\,\mathrm{erg}$, ejecta masses of $2-6 \,\mathrm{M_{\odot}}$ and ambient medium densities of $\sim0.33-0.66$ $\mathrm{amu~cm}^{-3}$ in the south and $\sim0.01-0.02$ $\mathrm{amu~cm}^{-3}$ in the northeast assuming a constant density medium. These results are consistent with previous studies that suggested the progenitor of N132D was an energetic supernova that exploded into a pre-existing cavity.

astro-ph.HE↗

arXiv2025

XRISM observations of solar flare X-ray emission reflected in the Earth's atmosphere

The X-ray Imaging and Spectroscopy Mission (XRISM), launched into low-Earth orbit in 2023, observes the reflection of solar flare X-rays in the Earth's atmosphere as a by-product of celestial observations. Using a $\sim$one-year data set covering from October 2023 to November 2024, we report on our first results of the measurement of the metal abundance pattern and high-resolution Fe-K spectroscopy. The abundances of Mg, Si, S, Ar, Ca, and Fe measured with the CCD detector Xtend during M- and X-class flares show the inverse-first-ionization-potential (inverse-FIP) effect, which is consistent with the results of Katsuda et al., ApJ, 2020 using the Suzaku satellite. The abundances of Si, S, and Ar are found to decrease with increasing flare magnitude, which is consistent with the theoretical model by Laming (Laming, ApJ, 2021), whereas Ca exhibits an opposite trend. The large effective area and field of view of Xtend allow us to trace the evolution of the abundances in several X-class flare loops on a timescale of a few 100 s, finding an enrichment of low-FIP elements before flare peaks. The high-resolution Fe-K spectrum obtained with the microcalorimeter Resolve successfully separates the Rayleigh- and Compton-scattered Fe XXIV/XXV lines and neutral or low-ionized Fe-K$α$ lines. The neutral/low-ionized Fe-K$α$ equivalent width shows an anti-correlation with hard X-ray flux with the best-fit power-law slope of $-0.14 \pm 0.09$, suggesting that hard X-rays from flare loops are stimulating the Fe K$α$ fluorescence. This work demonstrates that XRISM can be a powerful tool in the field of solar physics, offering valuable high-statistic CCD data and high-resolution microcalorimeter spectra in the energy range extending to the Fe-K band.

astro-ph.SR↗

arXiv2025

XRISM/Resolve View of Abell 2319: Turbulence, Sloshing, and ICM Dynamics

We present results from XRISM/Resolve observations of the core of the galaxy cluster Abell 2319, focusing on its kinematic properties. The intracluster medium (ICM) exhibits temperatures of approximately 8 keV across the core, with a prominent cold front and a high-temperature region ($\sim$11 keV) in the northwest. The average gas velocity in the 3 arcmin $\times$ 4 arcmin region around the brightest cluster galaxy (BCG) covered by two Resolve pointings is consistent with that of the BCG to within 40 km s$^{-1}$ and we found modest average velocity dispersion of 230-250 km s$^{-1}$. On the other hand, spatially-resolved spectroscopy reveals interesting variations. A blueshift of up to $\sim$230 km s$^{-1}$ is observed around the east edge of the cold front, where the gas with the lowest specific entropy is found. The region further south inside the cold front shows only a small velocity difference from the BCG; however, its velocity dispersion is enhanced to 400 km s$^{-1}$, implying the development of turbulence. These characteristics indicate that we are observing sloshing motion with some inclination angle following BCG and that gas phases with different specific entropy participate in sloshing with their own velocities, as expected from simulations. No significant evidence for a high-redshift ICM component associated with the subcluster Abell 2319B was found in the region covered by the current Resolve pointings. These results highlight the importance of sloshing and turbulence in shaping the internal structure of Abell 2319. Further deep observations are necessary to better understand the mixing and turbulent processes within the cluster.

astro-ph.HE↗

arXiv2025

XRISM Reveals Complex Multi-Temperature Structures in the Abell 2029 Galaxy Cluster

We present $\sim$500 ks XRISM observations covering the central and two northern regions of the Abell 2029 galaxy cluster. Resolve enables us to distinguish multiple emission lines from hydrogen-like and helium-like iron (Fe) ions. This study focuses on the multi-temperature structure of Abell 2029 using line-ratio diagnostics. Using a single-temperature collisionally ionized equilibrium model, we measure average plasma temperatures of 6.73 keV, 7.61 keV, and 8.14 keV in the central, inner northern, and outer northern regions, respectively, spanning a radial range up to 700 kpc. To further investigate thermal structure, we derive excitation and ionization temperatures by comparing observed emission-line flux ratios with atomic database predictions. Significant deviations from the single-temperature CIE model in the central and inner northern regions indicate the presence of multi-phase gas. The excitation and ionization temperatures range from 2.85 keV to 8.5 keV in the central region, 4.3 keV to 9.8 keV in the inner northern region, and 8.3 keV to 10.4 keV in the outer northern region. These temperature distributions are largely consistent with the previously observed temperature gradient of A2029. However, Resolve detects two notably cooler components--3.42 keV in the central region and $\sim$4.3 keV in the inner northern region--likely associated with displaced cool gas due to gas sloshing. Additionally, we thermally resolve a 2.85 keV gas component at the core of A2029--potentially a significant development in our understanding of gas cooling. We propose that this cooler gas is a direct product of ongoing cooling processes in A2029, having already cooled to its present temperature. If this temperature structure is stable and no heating mechanism is present, this reservoir is likely to cool to even lower temperatures and form stars.

astro-ph.HE↗

arXiv2025

Discovering group dynamics in coordinated time series via hierarchical recurrent switching-state models

We seek a computationally efficient model for a collection of time series arising from multiple interacting entities (a.k.a. "agents"). Recent models of temporal patterns across individuals fail to incorporate explicit system-level collective behavior that can influence the trajectories of individual entities. To address this gap in the literature, we present a new hierarchical switching-state model that can be trained in an unsupervised fashion to simultaneously learn both system-level and individual-level dynamics. We employ a latent system-level discrete state Markov chain that provides top-down influence on latent entity-level chains which in turn govern the emission of each observed time series. Recurrent feedback from the observations to the latent chains at both entity and system levels allows recent situational context to inform how dynamics unfold at all levels in bottom-up fashion. We hypothesize that including both top-down and bottom-up influences on group dynamics will improve interpretability of the learned dynamics and reduce error when forecasting. Our hierarchical switching recurrent dynamical model can be learned via closed-form variational coordinate ascent updates to all latent chains that scale linearly in the number of entities. This is asymptotically no more costly than fitting a separate model for each entity. Analysis of both synthetic data and real basketball team movements suggests our lean parametric model can achieve competitive forecasts compared to larger neural network models that require far more computational resources. Further experiments on soldier data as well as a synthetic task with 64 cooperating entities show how our approach can yield interpretable insights about team dynamics over time.

stat.ML↗

arXiv2025

Constraining gas motion and non-thermal pressure beyond the core of the Abell 2029 galaxy cluster with XRISM

We report a detailed spectroscopic study of the gas dynamics and hydrostatic mass bias of the galaxy cluster Abell 2029, utilizing high-resolution observations from XRISM Resolve. Abell 2029, known for its cool core and relaxed X-ray morphology, provides an excellent opportunity to investigate the influence of gas motions beyond the central region. Expanding upon prior studies that revealed low turbulence and bulk motions within the core, our analysis covers regions out to the scale radius $R_{2500}$ (670~kpc) based on three radial pointings extending from the cluster center toward the northern side. We obtain accurate measurements of bulk and turbulent velocities along the line of sight. The results indicate that non-thermal pressure accounts for no more than 2% of the total pressure at all radii, with a gradual decrease outward. The observed radial trend differs from many numerical simulations, which often predict an increase in non-thermal pressure fraction at larger radii. These findings suggest that deviations from hydrostatic equilibrium are small, leading to a hydrostatic mass bias of around 2% across the observed area.

astro-ph.CO↗

arXiv2024

Unveiling the Cosmic Chemistry: Revisiting the Mass-Metallicity Relation with JWST/NIRSpec at 4 < z < 10

We present star formation rates (SFR), the mass-metallicity relation (MZR), and the SFR-dependent MZR across redshifts 4 to 10 using 81 star-forming galaxies observed by the JWST NIRSpec employing both low-resolution PRISM and medium-resolution gratings, including galaxies from the JADES GOODS-N and GOODS-S fields, the JWST-PRIMAL Legacy Survey, and additional galaxies from the literature in Abell 2744, SMACS-0723, RXJ2129, BDF, COSMOS, and MACS1149 fields. These galaxies span a 3 dex stellar mass range of $10^7 < M_{\ast}/M_{\odot} < 10^{10}$, with an average SFR of $7.2 \pm 1.2 M_{\odot} {\rm yr}^{-1}$ and an average metallicity of $12+{\rm log(O/H)} = 7.91 \pm 0.08$. Our findings align with previous observations up to $z=8$ for the MZR and indicate no deviation from local universe FMR up to this redshift. Beyond $z=8$, we observe a significant deviation $\sim 0.27$ dex) in FMR, consistent with recent JWST findings. We also integrate CEERS (135 galaxies) and JADES (47 galaxies) samples with our data to study metallicity evolution with redshift in a combined sample of 263 galaxies, revealing a decreasing metallicity trend with a slope of $0.067 \pm 0.013$, consistent with IllustrisTNG and EAGLE, but contradicts with FIRE simulations. We introduce an empirical mass-metallicity-redshift (MZ-$z$ relation): $12+{\rm log(O/H)}=6.29 + 0.237 \times{\rm log}(M_{\ast}/M_{\odot}) - 0.06 \times (1+z)$, which accurately reproduces the observed trends in metallicity with both redshift and stellar mass. This trend underscores the ``Grand Challenge'' in understanding the factors driving high-redshift galactic metallicity trends, such as inflow, outflow, and AGN/stellar feedback -- and emphasizes the need for further investigations with larger samples and enhanced simulations.

astro-ph.GA↗

arXiv2024

Tensor BM-Decomposition for Compression and Analysis of Video Data

Given tensors $\boldsymbol{\mathscr{A}}, \boldsymbol{\mathscr{B}}, \boldsymbol{\mathscr{C}}$ of size $m \times 1 \times n$, $m \times p \times 1$, and $1\times p \times n$, respectively, their Bhattacharya-Mesner (BM) product will result in a third-order tensor of dimension $m \times p \times n$ and BM-rank of 1 (Mesner and Bhattacharya, 1990). Thus, if an arbitrary $m \times p \times n$ third-order tensor can be written as a sum of a small number, relative to $m,p,n$, of such BM-rank 1 terms, this BM-decomposition (BMD) offers an implicitly compressed representation of the tensor. In this paper, we first show that grayscale surveillance video can be accurately captured by a low BM-rank decomposition and give methods for efficiently computing this decomposition. To this end, we first give results that connect rank-revealing matrix factorizations to the BMD. Next, we present a generative model that illustrates that spatio-temporal video data can be expected to have low BM-rank. We combine these observations to derive a regularized alternating least squares (ALS) algorithm to compute an approximate BMD of the video tensor. The algorithm itself is highly parallelizable since the bulk of the computations break down into relatively small regularized least squares problems that can be solved independently. Extensive numerical results compared against the state-of-the-art matrix-based DMD for surveillance video separation show our algorithms can consistently produce results with superior compression properties while simultaneously providing better separation of stationary and non-stationary features in the data. We then introduce a new type of BM-product suitable for color video and provide an algorithm that shows an impressive ability to extract important temporal information from color video while simultaneously compressing the data.

math.NA↗

arXiv2024

Continued developments in X-ray speed reading: fast, low noise readout for next-generation wide-field imagers

Future strategic X-ray astronomy missions will require unprecedentedly sensitive wide-field imagers providing high frame rates, low readout noise and excellent soft energy response. To meet these needs, our team is employing a multi-pronged approach to advance several key areas of technology. Our first focus is on advanced readout electronics, specifically integrated electronics, where we are collaborating on the VERITAS readout chip for the Athena Wide Field Imager, and have developed the Multi-Channel Readout Chip (MCRC), which enables fast readout and high frame rates for MIT-LL JFET (junction field effect transistor) CCDs. Second, we are contributing to novel detector development, specifically the SiSeRO (Single electron Sensitive Read Out) devices fabricated at MIT Lincoln Laboratory, and their advanced readout, to achieve sub-electron noise performance. Hardware components set the stage for performance, but their efficient utilization relies on software and algorithms for signal and event processing. Our group is developing digital waveform filtering and AI methods to augment detector performance, including enhanced particle background screening and improved event characterization. All of these efforts make use of an efficient, new X-ray beamline facility at Stanford, where components and concepts can be tested and characterized.

astro-ph.IM↗

arXiv2024

Demonstrating sub-electron noise performance in Single electron Sensitive Readout (SiSeRO) devices

Single electron Sensitive Read Out (SiSeRO) is a novel on-chip charge detection technology that can, in principle, provide significantly greater responsivity and improved noise performance than traditional charge coupled device (CCD) readout circuitry. The SiSeRO, developed by MIT Lincoln Laboratory, uses a p-MOSFET transistor with a depleted back-gate region under the transistor channel; as charge is transferred into the back gate region, the transistor current is modulated. With our first generation SiSeRO devices, we previously achieved a responsivity of around 800 pA per electron, an equivalent noise charge (ENC) of 4.5 electrons root mean square (RMS), and a full width at half maximum (FWHM) spectral resolution of 130 eV at 5.9 keV, at a readout speed of 625 Kpixel/s and for a detector temperature of 250 K. Importantly, since the charge signal remains unaffected by the SiSeRO readout process, we have also been able to implement Repetitive Non-Destructive Readout (RNDR), achieving an improved ENC performance. In this paper, we demonstrate sub-electron noise sensitivity with these devices, utilizing an enhanced test setup optimized for RNDR measurements, with excellent temperature control, improved readout circuitry, and advanced digital filtering techniques. We are currently fabricating new SiSeRO detectors with more sensitive and RNDR-optimized amplifier designs, which will help mature the SiSeRO technology in the future and eventually lead to the pathway to develop active pixel sensor (APS) arrays using sensitive SiSeRO amplifiers on each pixel. Active pixel devices with sub-electron sensitivity and fast readout present an exciting option for next generation, large area astronomical X-ray telescopes requiring fast, low-noise megapixel imagers.

astro-ph.IM↗

arXiv2024

Tensor Completion with BMD Factor Nuclear Norm Minimization

This paper is concerned with the problem of recovering third-order tensor data from limited samples. A recently proposed tensor decomposition (BMD) method has been shown to efficiently compress third-order spatiotemporal data. Using the BMD, we formulate a slicewise nuclear norm penalized algorithm to recover a third-order tensor from limited observed samples. We develop an efficient alternating direction method of multipliers (ADMM) scheme to solve the resulting minimization problem. Experimental results on real data show our method to give reconstruction comparable to those of HaLRTC (Liu et al., IEEE Trans Ptrn Anal Mchn Int, 2012), a well-known tensor completion method, in about the same number of iterations. However, our method has the advantage of smaller subproblems and higher parallelizability per iteration.

math.NA↗

arXiv2024

Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution involves a unique PaLS formulation utilizing a single level-set function to restore scenes containing multi-contrast piecewise-constant objects without requiring knowledge of the number of objects or their contrasts. Unlike standard PaLS methods employing radial basis functions (RBFs), our model integrates anisotropic basis functions (ABFs), thereby expanding its capacity to represent a wider class of shapes. Furthermore, PaLEnTIR improves the conditioning of the Jacobian matrix, required as part of the parameter identification process, and consequently accelerates optimization methods. We validate PaLEnTIR's efficacy through diverse experiments encompassing sparse and limited angle of view X-ray computed tomography (2D and 3D), nonlinear diffuse optical tomography (DOT), denoising, and deconvolution tasks using both real and simulated data sets.

math.NA↗