Reflective Imaging Solved by the Radon Transform

Rigaud, Gaël; Bellet, Jean-Baptiste; Berginc, Gérard; Berechet, Ion; Berechet, Stefan

doi:10.1109/lgrs.2016.2554662

Cited by 9 publications

(4 citation statements)

References 17 publications

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“…These values should be taken as a qualitative evaluation of the goodness of the proposed approach, as they represent the outcomes of a system composed of an atmosphere defined by only 256 × 256 pixels. This serves to simplify calculations and such an approximation is not uncommon in the scientific bibliography, but it prevents us from knowing the final quantitative scope of the improvement in a real situation (Rigaud et al 2016). A reference Strehl value was Fig.…”

Section: Discussionmentioning

confidence: 99%

Weighted nonnegative tensor factorization for atmospheric tomography reconstruction

Carmona-Ballester

Trujillo-Sevilla²,

Bonaque-González³

et al. 2018

A&A

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Context. Increasing the area on the sky over which atmospheric turbulences can be corrected is a matter of wide interest in astrophysics, especially when a new generation of extremely large telescopes (ELT) is to come in the near future. Aims. In this study we tested if a method for visual representation in three-dimensional displays, the weighted nonnegative tensor factorization (WNTF), is able to improve the quality of the atmospheric tomography (AT) reconstruction as compared to a more standardized method like a randomized Kaczmarz algorithm. Methods. A total of 1000 different atmospheres were simulated and recovered by both methods. Recovering was computed for two and three layers and for four different constellations of laser guiding stars (LGS). The goodness of both methods was tested by means of the radial average of the Strehl ratio across the field of view of a telescope of 8m diameter with a sky coverage of 97.8 arcsec. Results. The proposed method significantly outperformed the Kaczmarz in all tested cases (p ≤ 0.05). In WNTF, three-layers configuration provided better outcomes, but there was no clear relation between different LGS constellations and the quality of Strehl ratio maps. Conclusions. The WNTF method is a novel technique in astronomy and its use to recover atmospheric turbulence profiles was proposed and tested. It showed better quality of reconstruction than a conventional Kaczmarz algorithm independently of the number and height of recovered atmospheric layers and of the constellation of laser guide star used. The WNTF method was shown to be a useful tool in highly ill-posed AT problems, where the difficulty of classical algorithms produce high Strehl value maps.

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Section: Discussionmentioning

confidence: 99%

Weighted nonnegative tensor factorization for atmospheric tomography reconstruction

Carmona-Ballester

Trujillo-Sevilla²,

Bonaque-González³

et al. 2018

A&A

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“…Radon Transform is a transform which reorganizes an image or a distribution into line-projected phase [60]. A polygon or function in Cartesian coordinate (…”

Section: Restoration Of Detected Vessel Positionmentioning

confidence: 99%

Restoration of Authentic Position of Unidentified Vessels in SAR Imagery: A Deep Learning Based Approach

Song

Kim

et al. 2022

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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Enhancement of vessel detection performance in SAR images generated academic advancements related to amelioration of the algorithmic accuracy and training data procurement. For practical implementation of vessel detection algorithm to maritime surveillance however, presentation of authentic position of vessels was essential. Accordingly, this study aimed to propose an algorithm which demonstrated realistic and azimuth shift-corrected position of vessel, especially out of conventional vessel monitoring apparatus: AIS and VPASS information. Two different analyses regarding the vessel detection output utilization were therefore presented. Primary analysis demonstrated a vessel identification algorithm, comparing the vessel detection output with elaborately preprocessed AIS and VPASS information, which indicated the discrete position and velocity of vessel. The other presented a position restoration algorithm via (i) velocity estimator complementing the conventional FrFT velocity estimation analysis, while investigating the effect of range acceleration in deriving the azimuth velocity and (ii) measuring the vessel orientation angle from Radon Transform. Both algorithms were implemented to the vessel detection output in Cosmo-SkyMed SAR images, depicting an enhanced accuracy compared to the conventional algorithm both in velocity estimation and azimuth shift estimation; velocity offset reduced from 1.64 m/s to 1.29 m/s and average azimuth shift offset reduced from 70.75 m to 62.39 m. The presented algorithms would be decisive in terms of practicality if robustly attached to CNN-based vessel detection algorithms demonstrating ideal detection performances.

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“…The superposition principle is violated and so the optical projection cannot be modeled by the X-ray transform, and we come back to the question about the meaning. Moreover the occlusions introduce incompleteness in the data [13], whereas it is known in the field of transmission tomography that incompleteness introduces artifacts in the reconstruction [3]. Other questions arise, concerning the artifacts of reflective tomography, and especially concerning the artifacts due to the occlusions.…”

Section: Backprojection Outside the Range Of The Transformmentioning

confidence: 99%

Heuristic imaging from generic projections: backprojection outside the range of the Radon transform

Bellet¹,

Berginc²

2020

MathematicS in Action

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Reflective tomography is an efficient method for optical imaging in the visible and near infrared ranges. It computes empirical reconstructions based on algorithms from X-ray tomography. This subject introduces mathematical gaps to be filled, about the meaning of the reconstructions, and about their artifacts. To tackle these questions, we study more generally the filtered backprojection on projections outside the range of the Radon transform. We consider generic projections that can involve any kind of physical and geometric parameters. We claim that the backprojection contains partially the geometry of the original scene. More precisely, we compare the singularities of the backprojection with the singularities of a representation of the scene. This comparison of wavefront sets, inspired by studies of the artifacts in X-ray tomography, is based on microlocal analysis. It gives a precise meaning to the well-reconstructed geometry, describes the invisible parts, and the artifacts. We illustrate the heuristic and the analysis principle on canonical cases that belong to various fields: shape from silhouettes, constructible tomography, cloaking, reconstruction from cartoon images, imaging of occluded lambertian objects. Numerical results show the relevance of the heuristic and its analysis. In a word, this study provides a mathematical framework that covers the solver of reflective tomography, and exhibits an imaging method whose range of application is wide.

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Reflective Imaging Solved by the Radon Transform

Cited by 9 publications

References 17 publications

Weighted nonnegative tensor factorization for atmospheric tomography reconstruction

Weighted nonnegative tensor factorization for atmospheric tomography reconstruction

Restoration of Authentic Position of Unidentified Vessels in SAR Imagery: A Deep Learning Based Approach

Heuristic imaging from generic projections: backprojection outside the range of the Radon transform

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