The inverse scattering problem has numerous significant applications, including in geophysical explorations, medical imaging, and radar imaging. To achieve better performance of the imaging system, ...theoretical knowledge of the resolution of the algorithm is required for most of these applications. However, analytical investigations about the resolution presently feel inadequate. In order to estimate the achievable resolution, we address the point spread function (PSF) evaluation of the scattered field for a single frequency and the multi-view case both for the near and the far fields and the scalar case when the angular domain of the incident field and observation ranges is a round angle. Instead of the common free space condition, an inhomogeneous background medium, consisting of a homogeneous dielectric cylinder with a circular cross-section in free space, is assumed. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an analytical approximation of the resolution is also considered. For the sake of its comparison, the truncated singular value decomposition (TSVD) algorithm can be used to implement the exact PSF. We show how the behavior of the singular values and the resolution change by varying the permittivity of the background medium. The usefulness of the theoretical discussion is demonstrated in localizing point-like scatterers within a dielectric cylinder, so mimicking a scenario that may occur in breast cancer imaging. Numerical results are provided to validate the analytical investigations.
Existing data returned in >40 years of planetary missions to Mars provided a good basis to understand that an ocean never existed on the surface of the planet during its whole history. The presence ...of environmental indicators like unaltered jarosite and olivine deposited by the early volcanic activity can be seen as evidence that liquid water was never abundant nor widespread on the surface of Mars since the pre‐Noachian or Noachian at least. There is a dramatic mismatch with the water equivalent volume of the outflow channels sources with the volume needed to form an ocean. The ubiquitous presence of large volcanoes, with their huge lava fields exactly where liquid water was claimed to be abundant during the Noachian age, makes now very clear that lava and not water was involved in the formation of the outflow channels and the fluvial networks. As a consequence, cheaper robotic exploration might be favored with respect to the ambitious human exploration program planned for Mars. Unless enough water supplies will be brought to the equatorial regions from the poles through long pipelines, or from nearby asteroids through cargo ships, it will be very difficult to exploit the rich equatorial resources brought up from the mantle by the massive volcanism that characterized the early history of the planet. Digging deeply the equatorial regions searching for water would be too expensive, of uncertain reward, and thus unpractical.
Key Points
The lowlands of Mars likely never hosted an ocean of water
Liquid water never was available on the surface of Mars
Water needed for the exploration of Mars can be retrieved from nearby asteroids
In linear inverse scattering, the performance of the imaging system is sometimes evaluated in terms of its resolution, i.e., its capability to reconstruct a point-like scatterer. However, there is ...still a lack of analytical studies on the achievable resolution. To address this, we consider the point spread function (PSF) evaluation of the scattered near field for the single frequency and multi-view/multi-static case in homogeneous medium. Instead of numerically computing the PSF, we propose and discuss an approximate closed form under series expansions according to the angular ranges of both source and receiver location. In order to assess the effectiveness of the proposed approximation, we consider two cases including both full and limited view angles for the incident field and observation ranges. In addition, we provide a localization application to show the usefulness of the theoretical discussion. Numerical results confirmed the analytical investigations.
In the aftermath of trauma, little is known about why the unwanted and unbidden recollection of traumatic memories persists in some individuals but not others. We implemented neutral and inoffensive ...intrusive memories in the laboratory in a group of 102 individuals exposed to the 2015 Paris terrorist attacks and 73 nonexposed individuals, who were not in Paris during the attacks. While reexperiencing these intrusive memories, nonexposed individuals and exposed individuals without posttraumatic stress disorder (PTSD) could adaptively suppress memory activity, but exposed individuals with PTSD could not. These findings suggest that the capacity to suppress memory is central to positive posttraumatic adaptation. A generalized disruption of the memory control system could explain the maladaptive and unsuccessful suppression attempts often seen in PTSD, and this disruption should be targeted by specific treatments.
The solution to an ill-posed linear inverse problem requires the use of regularization methods to achieve a stable approximation solution. One powerful approach is the truncated singular value ...decomposition (TSVD), but it requires an appropriate choice of the truncation level. One suitable option is to take into account the number of degrees of freedom (NDF) of the scattered field, which is defined by the step-like behavior of the singular values of the relevant operator. Then, the NDF can be estimated as the number of singular values preceding the knee or the exponential decay. Therefore, an analytical estimation of the NDF is significant for obtaining a stable, regularized solution. This paper addresses the analytical estimation of the NDF of the field scattered by the surface of a cube geometry for a single frequency and the multi-view case in the far-zone. In addition, a method is proposed to find the minimum numbers of plane waves and their directions to achieve the total estimated NDF. The main results are that the NDF is related to the measure of the surface of the cube and can be achieved by only considering a limited number of impinging plane waves. The efficiency of the theoretical discussion is demonstrated through a reconstruction application for microwave tomography of a dielectric object. Numerical examples are provided to confirm the theoretical results.
Inverse scattering problems stand at the center of many important imaging applications, such as geophysical explorations, radar imaging, and synthetic-aperture radar (SAR). Several methods have been ...proposed to solve them when the full data are available, usually providing satisfactory reconstructions. However, it is impossible to acquire the full data in many practical circumstances, such as target detection and ground penetrating radar (GPR); consequently, only limited data are available. Thus, this paper focuses on the mathematical analysis and some numerical simulations to estimate the achievable resolution in reconstructing an object from the knowledge of the scattered far-field when only limited data are available, with multi-view excitations at a single frequency. We focus on 2D full rectangular geometry as the investigation domain (ID). We also examine the number of degrees of freedom (NDF) and evaluate the point spread function (PSF). In particular, the NDF of the considered geometry can be estimated analytically. An approximated closed-form evaluation of the PSF is recalled, discussed, and compared with the exact one. Moreover, receiving, transmission, and angle sensing modes are considered to apply the analysis to more realistic scenarios to highlight the difference between the corresponding NDF and the resulting resolution performances. Finally, interesting numerical applications of the resolution analysis for the localization of a collection of point-like scatterers are presented to illustrate how it matches the expectations.
In microwave imaging, it is often of interest to inspect electrically large spatial regions. In these cases, data must be collected over a great deal of measurement points which entails long ...measurement time and/or costly, and often unfeasible, measurement configurations. In order to counteract such drawbacks, we have recently introduced a microwave imaging algorithm that looks for the scattering targets in terms of equivalent surface currents supported over a given reference plane. While this method is suited to detect shallowly buried targets, it allows one to independently process all frequency data, and hence the source and the receivers do not need to be synchronized. Moreover, spatial data can be reduced to a large extent, without any aliasing artifacts, by properly combining single-frequency reconstructions. In this paper, we validate such an approach by experimental measurements. In particular, the experimental test site consists of a sand box in open air where metallic plate targets are shallowly buried a (few cm) under the air/soil interface. The investigated region is illuminated by a fixed transmitting horn antenna, whereas the scattered field is collected over a planar measurement aperture at a fixed height from the air-sand interface. The transmitter and the receiver share only the working frequency information. Experimental results confirm the feasibility of the method.
Evidence of hot and cold igneous processes has been reported in small satellites and dwarf planets of the Solar System. Olivine and pyroxenes were detected in the spectral bands of both small ...satellites and dwarf planets. The aqueously altered form of olivine and serpentine has been detected in the spectrums of Ceres and Miranda hinting at possible hydrothermal processes in their interiors. Once more, the ubiquitous distribution of 26Al in the planetary nebula, then evolving in the protoplanetary disk, contributed to the primordial widespread heating. Volcanism, or cryovolcanism, then developed only in those bodies where long-lived radiogenic elements, and/or tidal processes, were available.
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Earth sciences; Physics; Space sciences
Background Treatment of vitiligo with narrowband ultraviolet B light (NBUVB) is an important component of the current standard of care. However, there are no consistent guidelines regarding the ...dosing and administration of NBUVB in vitiligo, reflected by varied treatment practices around the world. Objective To create phototherapy recommendations to facilitate clinical management and identify areas requiring future research. Methods The Vitiligo Working Group (VWG) Phototherapy Committee addressed 19 questions regarding the administration of phototherapy over 3 conference calls. Members of the Photomedicine Society and a group of phototherapy experts were surveyed regarding their phototherapy practices. Results Based on comparison and analysis of survey results, expert opinion, and discussion held during conference calls, expert recommendations for the administration of NBUVB phototherapy in vitiligo were created. Limitations There were several areas that required further research before final recommendations could be made. In addition, no standardized methodology was used during literature review and to assess the strength of evidence during the development of these recommendations. Conclusion This set of expert recommendations by the VWG is based on the prescribing practices of phototherapy experts from around the world to create a unified, broadly applicable set of recommendations on the use of NBUVB in vitiligo.
Aberrant predictions of future threat lead to maladaptive avoidance in individuals with post-traumatic stress disorder (PTSD). How this disruption in prediction influences the control of memory ...states orchestrated by the dorsolateral prefrontal cortex is unknown. We combined computational modeling and brain connectivity analyses to reveal how individuals exposed and nonexposed to the 2015 Paris terrorist attacks formed and controlled beliefs about future intrusive re-experiencing implemented in the laboratory during a memory suppression task. Exposed individuals with PTSD used beliefs excessively to control hippocampal activity during the task. When this predictive control failed, the prediction-error associated with unwanted intrusions was poorly downregulated by reactive mechanisms. This imbalance was linked to higher severity of avoidance symptoms, but not to general disturbances such as anxiety or negative affect. Conversely, trauma-exposed participants without PTSD and nonexposed individuals were able to optimally balance predictive and reactive control during the memory suppression task. These findings highlight a potential pathological mechanism occurring in individuals with PTSD rooted in the relationship between the brain's predictive and control mechanisms.
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