Gaël Rigaud

Novel numerical inversions of two circular-arc radon transforms in Compton scattering tomography

Compton scattering tomography (CST) is an alternative imaging process which reconstructs, in a two-dimensional slice, the electron density of an object by collecting radiation emitted from an external source and scattered throughout this object. The collected data at specific scattering energies appears essentially as the integral of the electron density on definite families of arcs of circles. Reconstruction of the unknown electron density is achieved by the inversion of the corresponding circular-arcs Radon transforms (CART). We review two existing CST modalities, their corresponding CART and establish their numerical inversion algorithms in the formalism of the so-called circular harmonic decomposition (CHD) for a function. The quality of the reconstructed images is illustrated by numerical simulations on test phantoms. Comparison with standard tomography performances demonstrates the efficiency and interest of this inversion method via CHD in imaging science such as biomedical imaging and non-destructive industrial testing.

Modeling and simulation results on a new Compton scattering tomography modality

Conventional tomography (X-ray scanner, Single Photon Emission Computed Tomography, Positron Emission Tomography, etc.) is widely used in numerous fields such as biomedical imaging, non-destructive industrial testing and environmental survey, etc. In these tomographies, a detector rotates in space to collect primary radiation emitted or transmitted by an object under investigation. In this case Compton scattered radiation behaves as noise hindering image quality and consequently correction to scatter should be required. However recently an interesting new imaging concept, which uses precisely scattered radiation as imaging agent, has been advocated. The camera records now images labeled by scattered photon energy or equivalently by scattering angle. In the present paper we propose a new modality of Compton scattering tomography (CST), akin to the X-ray scanning tomography, in the sense that it works in transmission modality but uses Compton scattered radiation to recover the electron density of the studied medium. The new image formation modeling is based on a new class of Radon transforms on circular arcs (CART). Through numerical simulation results we show the feasibility and the relevance of this new imaging process.

A Novel Technological Imaging Process Using Ionizing Radiation Properties

Diverse imaging technologies have been invented during the last decades to uncover the hidden parts of objects of interest for diagnostic, evaluation, accident prevention, etc. The key issue is to produce a faithful image of details buried in the bulk of matter. In this work we describe a new way to achieve this goal by cleverly exploiting the propagation property of gamma radiation in material medium. The proposed scanning device is simple and can rapidly collect measurements necessary to reconstruct the sought image. The relevance and reliability of this procedure is demonstrated by efficient algorithms and numerical simulations.

A New Circular‐Arc Radon Transform and the Numerical Method for its Inversion

Until recently the known invertible classes of Radon transforms on circles of R2 are those defined on circles with their centers on a line or on another circle and those defined on circles that go through a fixed point. In this work we discuss a new class of Radon transforms which are defined on a family of circles which have a common chord of fixed length rotating around its middle point. An analytic inverse formula is derived leading the way to the reconstruction of L1(R2)‐functions with compact support. We implement this inversion using a numerical approach to illustrate function reconstruction. This transform has also its application in the modeling of a new modality in Compton scatter Tomography, which is in particular relevant for medical imaging and non‐destructive evaluation.

Series Expansions of the Reconstruction Kernel of the Radon Transform over a Cormack-Type Family of Curves with Applications in Tomography ∗

This paper is concerned with the Radon transform over a family of Cormack-type curves and provides an exact inversion formula. The studied family of curves, called

New bimodal scattered radiation tomographic imaging with attenuation and electron density correction algorithm

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Combined Modalities of Compton Scattering Tomography

, appeared in previous works as a suitable manifold for modeling imaging concepts in conventional and Compton scattering tomography (CST). More specifically, the straight line, integral support of the classical Radon transform used in computed tomography (CT) belongs to

Compton Scattering Tomography: Feature Reconstruction and Rotation-Free Modality

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Approximate Image Reconstruction in Landscape Reflection Imaging

. In conventional tomography, many reconstruction techniques compute the derivative of the data with the aim of reducing the order of singularity of the reconstruction kernel associated here to the Radon transform in two dimensions. However, differentiating data requires a regularization step (for instance, convolution with a smooth function) which reduces the resolution of reconstructed images. Here, the proposed analytical inversion formula recovers the circular harmonic components of the sought object without differentiation of the data, which leads to an improvemen...

Novel ultrasonic imaging modality based on circular integral data

Bimodal medical imaging, which combines two non-invasive techniques to explore two different aspects (e.g. function and morphology) of an organ, has emerged as a major clinical imaging modality nowadays. The gained information as compared to single modality imaging is overwhelmingly useful for diagnostics and therapy planning. Up to now all bimodal techniques make use exclusively of primary radiation. In this work, we describe a new bimodal imaging concept based solely on the exploitation of scattered radiation. Following a presentation of its theoretical basis, we discuss the modellings of measurements and inversion formulae used for image reconstruction. Thus an attenuation and electron density correction algorithm inspired of the Iterative Pre-Correction algorithm (IPC) is proposed. Simulation results demonstrate convincingly the feasibility and efficiency of this new bimodal imaging modality.