Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm

Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and 3-D) because frequently the region of interest cannot be completely surrounded by the detectors, as it happens, for example, in breast imaging. We present an efficient numerical algorithm for solving this problem in 2-D (similar methods are applicable in the 3-D case). Our method is based on the numerical approximation of plane waves by certain single layer potentials related to the acquisition geometry. After the densities of these potentials have been precomputed, each subsequent image reconstruction has the complexity of the regular filtration backprojection algorithm for the classical Radon transform. The peformance of the method is demonstrated in several numerical examples: one can see that the algorithm produces very accurate reconstructions if the data are accurate and sufficiently well sampled, on the other hand, it is sufficiently stable with respect to noise in the data

Analytic inversion of a Radon transform on double circular arcs with applications in Compton Scattering Tomography

In this work we introduce a new Radon transform which arises from a new modality of Compton Scattering Tomography (CST). This new system is made of a single detector rotating around a fixed source. Unlike some previous CST, no collimator is used at the detector. Such a system allows us to collect scattered photons coming from two opposite sides of the source-detector segment, hence the manifold of the associated Radon transform is a family of double circular arcs. As first main theoretical result, an analytic inversion formula is established for this new Radon transform. This is achieved through the formulation of the transform in terms of circular harmonic expansion satisfying the consistency conditions in Cormack's sense. Moreover, a fast and efficient numerical implementation via an alternative formulation based on Hilbert transform is carried out. Simulation results illustrate the theoretical feasibility of the new system. From a practical point of view, an uncollimated detector system considerably increases the amount of collected data, which is particularly significant in a scatter imaging system.Comment: 14 pages, 5 figure

Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates

The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct implementation by summation of traces with different moveouts is computationally expensive for large data sets. In this paper we present a new method for fast computation of the hyperbolic Radon transforms. It is based on using a log-polar sampling with which the main computational parts reduce to computing convolutions. This allows for fast implementations by means of FFT. In addition to the FFT operations, interpolation procedures are required for switching between coordinates in the time-offset; Radon; and log-polar domains. Graphical Processor Units (GPUs) are suitable to use as a computational platform for this purpose, due to the hardware supported interpolation routines as well as optimized routines for FFT. Performance tests show large speed-ups of the proposed algorithm. Hence, it is suitable to use in iterative methods, and we provide examples for data interpolation and multiple removal using this approach.Comment: 21 pages, 10 figures, 2 table

Detection of Ship Wakes in SAR Imagery Using Cauchy Regularisation

Ship wake detection is of great importance in the characterisation of synthetic aperture radar (SAR) images of the ocean surface since wakes usually carry essential information about vessels. Most detection methods exploit the linear characteristics of the ship wakes and transform the lines in the spatial domain into bright or dark points in a transform domain, such as the Radon or Hough transforms. This paper proposes an innovative ship wake detection method based on sparse regularisation to obtain the Radon transform of the SAR image, in which the linear features are enhanced. The corresponding cost function utilizes the Cauchy prior, and on this basis, the Cauchy proximal operator is proposed. A Bayesian method, the Moreau-Yoshida unadjusted Langevin algorithm (MYULA), which is computationally efficient and robust is used to estimate the image in the transform domain by minimizing the negative log-posterior distribution. The detection accuracy of the Cauchy prior based approach is 86.7%, which is demonstrated by experiments over six COSMO-SkyMed images.Comment: 9 pages, 2 Figures and 2 Table