Inversion formulas for the broken-ray Radon transform

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the filtered backprojection formula of the conventional Radon transform. The advantages of the broken ray transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium simultaneously and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is typically discarded.Comment: To be submitted to Inverse Problem

Convergence and Stability of the Inverse Scattering Series for Diffuse Waves

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the serie

Novel time-resolved camera based on compressed sensing

Time-resolved cameras with high temporal resolution (down to ps) enable a huge set of novel applications ranging from biomedicine and environmental science to material and device characterization. In this work, we propose, and experimentally validate, a novel detection scheme for time-resolved imaging based on a compressed sampling approach. The proposed scheme unifies into a single element all the required operations, i.e. space modulation, space integration and time-resolved detection, paving the way to dramatic cost reduction, performance improvement and ease of use

Controlling Light Through Optical Disordered Media : Transmission Matrix Approach

We experimentally measure the monochromatic transmission matrix (TM) of an optical multiple scattering medium using a spatial light modulator together with a phase-shifting interferometry measurement method. The TM contains all information needed to shape the scattered output field at will or to detect an image through the medium. We confront theory and experiment for these applications and we study the effect of noise on the reconstruction method. We also extracted from the TM informations about the statistical properties of the medium and the light transport whitin it. In particular, we are able to isolate the contributions of the Memory Effect (ME) and measure its attenuation length

Cassini observations of ion and electron beams at Saturn and their relationship to infrared auroral arcs

We present Cassini Visual and Infrared Mapping Spectrometer observations of infrared auroral emissions from the noon sector of Saturn's ionosphere revealing multiple intense auroral arcs separated by dark regions poleward of the main oval. The arcs are interpreted as the ionospheric signatures of bursts of reconnection occurring at the dayside magnetopause. The auroral arcs were associated with upward field-aligned currents, the magnetic signatures of which were detected by Cassini at high planetary latitudes. Magnetic field and particle observations in the adjacent downward current regions showed upward bursts of 100–360 keV light ions in addition to energetic (hundreds of keV) electrons, which may have been scattered from upward accelerated beams carrying the downward currents. Broadband, upward propagating whistler waves were detected simultaneously with the ion beams. The acceleration of the light ions from low altitudes is attributed to wave-particle interactions in the downward current regions. Energetic (600 keV) oxygen ions were also detected, suggesting the presence of ambient oxygen at altitudes within the acceleration region. These simultaneous in situ and remote observations reveal the highly energetic magnetospheric dynamics driving some of Saturn's unusual auroral features. This is the first in situ identification of transient reconnection events at regions magnetically conjugate to Saturn's magnetopause

Thermal electron periodicities at 20RS in Saturn’s magnetosphere

Cassini fields and particles observations show clear evidence of periodic phenomena in Saturn's magnetosphere. Periodicities have been observed in kilometric radio emissions, total electron density (in the inner magnetosphere), magnetic fields, and energetic particles (in the outer magnetosphere). In this letter the first analysis of periodicities in thermal electron densities in Saturn's outer magnetosphere are presented. Plasma sheet electron densities and temperatures at 20 ± 2 RS in Saturn's magnetosphere are studied and examined as a function of SLS3 longitude. Evidence for a density minimum at 170° is presented which is in excellent agreement with total electron density results in the 3–5 RS range. The density asymmetry is interpreted as the result of a periodic plasma sheet motion where the northward offset of the plasma sheet varies with longitude hence producing a density modulation in the equatorial plane. The effect of magnetospheric compressions on the dayside density asymmetry are discussed.Fil: Arridge, C. S.. University College London; Estados UnidosFil: Andre, N.. European Space Agency; Países BajosFil: Achilleos, N.. University College London; Estados UnidosFil: Khurana, K. K.. University of California; Estados UnidosFil: Bertucci, Cesar. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Gilbert, L. K.. University College London; Estados UnidosFil: Lewis, G. R.. University College London; Estados UnidosFil: Coates, A. J.. University College London; Estados UnidosFil: Dougherty, M. K.. Imperial College London; Reino Unid

Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain

In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of [41], obtained for the Schr\"odinger operator without magnetic potentials. In the case of a bounded domain in $R^n$, $n\ge 3$, extending the results of [2], we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of [31], we also obtain uniqueness results for the magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane

The evolution of solar wind strahl with heliospheric distance

Field-aligned beams of suprathermal electrons, known as strahl, are a frequently observed constituent of solar wind plasma. However, the formation and interplanetary evolution of the strahl electron populations has yet to be fully understood. As strahl electrons travel away from the Sun, they move into regions of decreasing magnetic field strength and thus are subject to adiabatic focusing. However, the widths of strahl pitch angle distributions observed at 1AU are significantly broader than expected. Previous investigations have found that the average observed strahl pitch angle width actually increases with heliocentric radial distance. This implies that strahl electrons must be subjected to some form of pitch angle scattering process or processes, details of which as of yet remain elusive. In this paper, we use Cassini electron measurements to examine strahl beams across a distance range of approximately 8 AU, from its Earth Flyby in 1999 until its insertion into orbit around Saturn in 2004. We find that, in general, there is a relatively constant rate of broadening of strahl pitch angle distributions with distance between similar to 1 and 5.5 AU. Our results from beyond this distance indicate that the strahl population is likely to be completely scattered, presumably to form part of the halo. We find multiple energy dependences at different radial distances implying that there are multiple strahl scattering mechanisms in operation

Breast lesion classification based on absorption and composition parameters: a look at SOLUS first outcomes

A machine learning classification algorithm is applied to the SOLUS database to discriminate benign and malignant breast lesions, based on absorption and composition properties retrieved through diffuse optical tomography. The Mann-Whitney test indicates oxy-hemoglobin (p-value = 0.0007) and lipids (0.0387) as the most significant constituents for lesion classification, but work is in progress for further analysis. Together with sensitivity (91%), specificity (75%) and the Area Under the ROC Curve (0.83), special metrics for imbalanced datasets (27% of malignant lesions) are applied to the machine learning outcome: balanced accuracy (83%) and Matthews Correlation Coefficient (0.65). The initial results underline the promising informative content of optical data