Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

First operation and performance of a 200 lt double phase LAr LEM-TPC with a 40x76 cm^2 readout

In this paper we describe the design, construction, and operation of a first large area double-phase liquid argon Large Electron Multiplier Time Projection Chamber (LAr LEM-TPC). The detector has a maximum drift length of 60 cm and the readout consists of a $40\times 76$ cm$^2$ LEM and 2D projective anode to multiply and collect drifting charges. Scintillation light is detected by means of cryogenic PMTs positioned below the cathode. To record both charge and light signals, we have developed a compact acquisition system, which is scalable up to ton-scale detectors with thousands of charge readout channels. The acquisition system, as well as the design and the performance of custom-made charge sensitive preamplifiers, are described. The complete experimental setup has been operated for a first time during a period of four weeks at CERN in the cryostat of the ArDM experiment, which was equipped with liquid and gas argon purification systems. The detector, exposed to cosmic rays, recorded events with a single-channel signal-to-noise ratio in excess of 30 for minimum ionising particles. Cosmic muon tracks and their $\delta$-rays were used to assess the performance of the detector, and to estimate the liquid argon purity and the gain at different amplification fields.Comment: 23 pages, 21 figure

On the injectivity of the circular Radon transform arising in thermoacoustic tomography

The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation theory to integral geometry, to inverse problems for PDEs, and recently to newly developing types of tomography. The article discusses known and provides new results that one can obtain by methods that essentially involve only the finite speed of propagation and domain dependence for the wave equation.Comment: To appear in Inverse Problem

Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography

The paper contains a simple approach to reconstruction in Thermoacoustic and Photoacoustic Tomography. The technique works for any geometry of point detectors placement and for variable sound speed satisfying a non-trapping condition. A uniqueness of reconstruction result is also obtained

Towards a liquid Argon TPC without evacuation: filling of a 6 m^3 vessel with argon gas from air to ppm impurities concentration through flushing

In this paper we present a successful experimental test of filling a volume of 6 m$^3$ with argon gas, starting from normal ambient air and reducing the impurities content down to few parts per million (ppm) oxygen equivalent. This level of contamination was directly monitored measuring the slow component of the scintillation light of the Ar gas, which is sensitive to {\it all} sources of impurities affecting directly the argon scintillation.Comment: 9 pages, 6 figures, to appear in Proc. 1st International Workshop towards the Giant Liquid Argon Charge Imaging Experiment (GLA2010), Tsukuba, March 201

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

Preasymptotic Convergence of Randomized Kaczmarz Method

Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the inverse solution is smooth (e.g., sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.Comment: 20 page

Fermiology via the electron momentum distribution

Investigations of the Fermi surface via the electron momentum distribution reconstructed from either angular correlation of annihilation radiation (or Compton scattering) experimental spectra are presented. The basis of these experiments and mathematical methods applied in reconstructing three-dimensional densities from line (or plane) projections measured in these experiments are described. The review of papers where such techniques have been applied to study the Fermi surface of metallic materials with showing their main results is also done.Comment: 22 pages, 9 Figures, 4 Table

Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors

We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$ which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The data consists of $n$ i.i.d. observations from a probability density equal to the Radon transform of the Wigner function. We construct an estimator for the Wigner function, and prove that it is minimax efficient for the pointwise risk over a class of infinitely differentiable functions. A similar result was previously derived by Cavalier in the context of positron emission tomography. Our work extends this result to the space of smooth Wigner functions, which is the relevant parameter space for quantum homodyne tomography.Comment: 15 page

ArDM: first results from underground commissioning

The Argon Dark Matter experiment is a ton-scale double phase argon Time Projection Chamber designed for direct Dark Matter searches. It combines the detection of scintillation light together with the ionisation charge in order to discriminate the background (electron recoils) from the WIMP signals (nuclear recoils). After a successful operation on surface at CERN, the detector was recently installed in the underground Laboratorio Subterr\'aneo de Canfranc, and the commissioning phase is ongoing. We describe the status of the installation and present first results from data collected underground with the detector filled with gas argon at room temperature.Comment: 6 pages, 3 figures, Light Detection In Noble Elements (LIDINE 2013