Journal: SIAM Journal on Imaging Sciences

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SIAM

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1936-4954

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2015 - 201992020 - 20235
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Publications 1 - 10 of 14
  • Video Compressive Sensing for Spatial Multiplexing Cameras using Motion-Flow Models
    Item type: Journal Article
    Sankaranarayanan, Aswin C.; Xu, Lina; Studer, Christoph; et al. (2015)
    SIAM Journal on Imaging Sciences
    Spatial multiplexing cameras (SMCs) acquire a (typically static) scene through a series of coded projections using a spatial light modulator (e.g., a digital micro-mirror device) and a few optical sensors. This approach finds use in imaging applications where full-frame sensors are either too expensive (e.g., for short-wave infrared wavelengths) or unavailable. Existing SMC systems reconstruct static scenes using techniques from compressive sensing (CS). For videos, however, existing acquisition and recovery methods deliver poor quality. In this paper, we propose the CS multi-scale video (CS-MUVI) sensing and recovery framework for high-quality video acquisition and recovery using SMCs. Our framework features novel sensing matrices that enable the efficient computation of a low-resolution video preview, while enabling high-resolution video recovery using convex optimization. To further improve the quality of the reconstructed videos, we extract optical-flow estimates from the low-resolution previews and impose them as constraints in the recovery procedure. We demonstrate the efficacy of our CS-MUVI framework for a host of synthetic and real measured SMC video data, and we show that high-quality videos can be recovered at roughly 60x compression.
  • Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Data
    Item type: Journal Article
    Ammari, Habib; Ruiz, Matias; Yu, Sanghyeon; et al. (2018)
    SIAM Journal on Imaging Sciences
  • Multi-scale Classification for Electrosensing
    Item type: Journal Article
    Baldassari, Lorenzo; Scapin, Andrea (2021)
    SIAM Journal on Imaging Sciences
    This paper introduces a premier and innovative (real-time) multi-scale method for target classification in electrosensing. The intent is that of mimicking the behavior of the weakly electric fish, which is able to retrieve much more information about the target by approaching it. The method is based on a family of transform-invariant shape descriptors computed from generalized polarization tensors (GPTs) reconstructed at multiple scales. The evidence provided by the different descriptors at each scale is fused using Dempster--Shafer theory. Numerical simulations show that the recognition algorithm we propose performs undoubtedly well and yields a robust classification. © 2021, Society for Industrial and Applied Mathematics
  • Mathematical Framework for Abdominal Electrical Impedance Tomography to Assess Fatness
    Item type: Journal Article
    Ammari, Habib; Kwon, Hyeuknam; Lee, Seungri; et al. (2017)
    SIAM Journal on Imaging Sciences
  • The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
    Item type: Journal Article
    Alberti, Giovanni S.; Ammari, Habib; Jin, Bangti; et al. (2016)
    SIAM Journal on Imaging Sciences
  • Asymptotic Links between Signal Processing, Acoustic Metamaterials, and Biology
    Item type: Journal Article
    Ammari, Habib; Davies, Bryn (2023)
    SIAM Journal on Imaging Sciences
    Biomimicry is a powerful science that takes inspiration from nature's innovative solutions to challenging problems. In this work, we use asymptotic methods to develop the mathematical foundations for the exchange of design inspiration and features between biological hearing systems, signal processing algorithms, and acoustic metamaterials. Our starting point is a concise asymptotic analysis of high-contrast acoustic metamaterials. We are able to fine tune this graded structure to mimic the biomechanical properties of the cochlea, at the same scale. We then turn our attention to developing a biomimetic signal processing algorithm. We use the response of the cochlea-like metamaterial as an initial filtering layer and then add additional biomimetic processing stages, designed to mimic the human auditory system's ability to recognize the global properties of natural sounds. This demonstrates the three-way exchange of ideas that, thanks to our analysis, is possible between signal processing, metamaterials and biology.
  • Dynamic Spike Superresolution and Applications to Ultrafast Ultrasound Imaging
    Item type: Journal Article
    Alberti, Giovanni S.; Ammari, Habib; Romero, Francisco; et al. (2019)
    SIAM Journal on Imaging Sciences
  • An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities
    Item type: Journal Article
    Liu, Ping; Ammari, Habib (2023)
    SIAM Journal on Imaging Sciences
    By introducing a new operator theory, we provide a unified mathematical theory for general source resolution in the multi-illumination imaging problem. Our main idea is to transform multi-illumination imaging into single-snapshot imaging with a new imaging kernel that depends on both the illumination patterns and the point spread function of the imaging system. We therefore prove that the resolution of multi-illumination imaging is approximately determined by the essential cutoff frequency of the new imaging kernel, which is roughly limited by the sum of the cutoff frequency of the point spread function and the maximum essential frequency in the illumination patterns. Our theory provides a unified way to estimate the resolution of various existing super-resolution modalities and results in the same estimates as those obtained in experiments. In addition, based on the reformulation of the multi-illumination imaging problem, we also estimate the resolution limits for resolving both complex and positive sources by sparsity-based approaches. We show that the resolution of multi-illumination imaging is approximately determined by the new imaging kernel from our operator theory and better resolution can be realized by sparsity-promoting techniques in practice but only for resolving very sparse sources. This explains experimentally observed phenomena in some sparsity-based super-resolution modalities.
  • Superresolution in Recovering Embedded Electromagnetic Sources in High Contrast Media
    Item type: Journal Article
    Ammari, Habib; Li, Bowen; Zou, Jun (2020)
    SIAM Journal on Imaging Sciences
    The purpose of this work is to provide a rigorous mathematical analysis of the expected superresolution phenomenon in the time-reversal imaging of electromagnetic (EM) radiating sources embedded in a high contrast medium. It is known that the resolution limit is essentially determined by the sharpness of the imaginary part of the EM Green's tensor for the associated background. We first establish the close connection between the resolution and the material parameters and the resolvent of the electric integral operator, via the Lippmann--Schwinger representation formula. We then present an insightful characterization of the spectral structure of the integral operator for a general bounded domain and derive the pole-pencil decomposition of its resolvent in the high contrast regime. For the special case of a spherical domain, we provide some quantitative asymptotic behavior of the eigenvalues and eigenfunctions. These mathematical findings shall enable us to provide a concise and rigorous illustration of the superresolution in the EM source reconstruction in high contrast media. Some numerical examples are also presented to verify our main theoretical results. © 2020 Society for Industrial and Applied Mathematics.
  • Reconstruction of Domains with Algebraic Boundaries from Generalized Polarization Tensors
    Item type: Journal Article
    Ammari, Habib; Putinar, Mihai; Steenkamp, Andries; et al. (2019)
    SIAM Journal on Imaging Sciences
    This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari, M. Putinar, A. Steenkamp, and F. Triki, Math. Ann., 375 (2019), pp. 1337-1354], where it is proved that the minimal polynomial with real coefficients vanishing on the boundary can be identified as the generator of a one-dimensional kernel of a matrix whose entries are obtained from a finite number of generalized polarization tensors. The recovery procedure is implemented without any assumption on the regularity of the domain to be reconstructed, and its performance and limitations are illustrated. © 2019 Society for Industrial and Applied Mathematics.
Publications 1 - 10 of 14