First-order Reconstruction Research Articles

Reconstructing cosmological initial conditions from late-time structure with convolutional neural networks

ABSTRACT We present a method to reconstruct the initial linear-regime matter density field from the late-time non-linearly evolved density field in which we channel the output of standard first-order reconstruction to a convolutional neural network (CNN). Our method shows dramatic improvement over the reconstruction of either component alone. We show why CNNs are not well-suited for reconstructing the initial density directly from the late-time density: CNNs are local models, but the relationship between initial and late-time density is not local. Our method leverages standard reconstruction as a preprocessing step, which inverts bulk gravitational flows sourced over very large scales, transforming the residual reconstruction problem from long-range to local and making it ideally suited for a CNN. We develop additional techniques to account for redshift distortions, which warp the density fields measured by galaxy surveys. Our method improves the range of scales of high-fidelity reconstruction by a factor of 2 in wavenumber above standard reconstruction, corresponding to a factor of 8 increase in the number of well-reconstructed modes. In addition, our method almost completely eliminates the anisotropy caused by redshift distortions. As galaxy surveys continue to map the Universe in increasingly greater detail, our results demonstrate the opportunity offered by CNNs to untangle the non-linear clustering at intermediate scales more accurately than ever before.

Magnetic Field Reconstruction for a Realistic Multi-Point, Multi-Scale Spacecraft Observatory

Future in situ space plasma investigations will likely involve spatially distributed observatories comprised of multiple spacecraft, beyond the four and five spacecraft configurations currently in operation. Inferring the magnetic field structure across the observatory, and not simply at the observation points, is a necessary step towards characterizing fundamental plasma processes using these unique multi-point, multi-scale data sets. We propose improvements upon the classic first-order reconstruction method, as well as a second-order method, utilizing magnetometer measurements from a realistic nine-spacecraft observatory. The improved first-order method, which averages over select ensembles of four spacecraft, reconstructs the magnetic field associated with simple current sheets and numerical simulations of turbulence accurately over larger volumes compared to second-order methods or first-order methods using a single regular tetrahedron. Using this averaging method on data sets with fewer than nine measurement points, the volume of accurate reconstruction compared to a known magnetic vector field improves approximately linearly with the number of measurement points.

Reducing the Complexity of Model-Based MRI Reconstructions via Sparsification.

Model-based reconstruction methods have emerged as a powerful alternative to classical Fourier-based MRI techniques, largely because of their ability to explicitly model (and therefore, potentially overcome) moderate field inhomogeneities, streamline reconstruction from non-Cartesian sampling, and even allow for the use of custom designed non-Fourier encoding methods. Their application in such scenarios, however, often comes with a substantial increase in computational cost, owing to the fact that the corresponding forward model in such settings no longer possesses a direct Fourier Transform based implementation. This paper introduces an algorithmic framework designed to reduce the computational burden associated with model-based MRI reconstruction tasks. The key innovation is the strategic sparsification of the corresponding forward operators for these models, giving rise to approximations of the forward models (and their adjoints) that admit low computational complexity application. This enables overall a reduced computational complexity application of popular iterative first-order reconstruction methods for these reconstruction tasks. Computational results obtained on both synthetic and experimental data illustrate the viability and efficiency of the approach.

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Reconstructions for Forward-in-Time Schemes

Abstract The finite-volume transport scheme of Miura, for icosahedral–hexagonal meshes on the sphere, is extended by using higher-order reconstructions of the transported scalar within the formulation. The use of second- and fourth-order reconstructions, in contrast to the first-order reconstruction used in the original scheme, results in significantly more accurate solutions at a given mesh density, and better phase and amplitude error characteristics in standard transport tests. The schemes using the higher-order reconstructions also exhibit much less dependence of the solution error on the time step compared to the original formulation. The original scheme of Miura was only tested using a nondeformational time-independent flow. The deformational time-dependent flow test used to examine 2D planar transport in Blossey and Durran is adapted to the sphere, and the schemes are subjected to this test. The results largely confirm those generated using the simpler tests. The results also indicate that the scheme using the second-order reconstruction is most efficient and its use is recommended over the scheme using the first-order reconstruction. The second-order reconstruction uses the same computational stencil as the first-order reconstruction and thus does not create any additional parallelization issues.

North American Ice Sheet build-up during the last glacial cycle, 115–21 kyr

The last glacial maximum (LGM) outline and subsequent retreat pattern (21–7 kyr) of North American ice sheets are reasonably well established. However, the evolution of the ice sheets during their build-up phase towards the LGM between 115 and 21 kyr has remained elusive, making it difficult to verify numerical ice sheet models for this important time interval. In this paper we outline the pre-LGM ice sheet evolution of the Laurentide and Cordilleran ice sheets by using glacial geological and geomorphological records to make a first-order reconstruction of ice sheet extent and flow pattern. We mapped the entire area covered by the Laurentide and Cordilleran ice sheets in Landsat MSS images and approximately 40% of this area in higher resolution Landsat ETM+ images. Mapping in aerial photographs added further detail primarily in Quebec-Labrador, the Cordilleran region, and on Baffin Island. Our analysis includes the recognition of approximately 500 relative-age relationships from crosscutting lineations. Together with previously published striae and till fabric data, these are used as the basis for relative-age assignments of regional flow patterns. For the reconstruction of the most probable ice sheet evolution sequence we employ a stepwise inversion scheme with a clearly defined strategy for delineating coherent landforms swarms (reflecting flow direction and configuration), and linking these to previously published constraints on relative and absolute chronology. Our results reveal that ice-dispersal centres in Keewatin and Quebec were dynamically independent for most of pre-LGM time and that a massive Quebec dispersal centre, rivalling the LGM in extent, existed at times when the SW sector of the ice sheet had not yet developed. The oldest flow system in eastern Quebec-Labrador (Atlantic swarm had an ice divide closer to the Labrador coast than later configurations). A northern Keewatin-Central Arctic Ice Sheet existed prior to the LGM, but is poorly chronologically constrained. There is also evidence for older and more easterly Cordilleran Ice Sheet divide locations than those that prevailed during the Late Wisconsinan. In terms of ice sheet build-up dynamics, it appears that “residual” ice caps after warming phases may have played an important role. In particular, the location and size of remnant ice masses at the end of major interstadials, i.e. OIS 5c and 5a, must have been critical for subsequent build-up patterns, because such remnant “uplands” may have fostered much more rapid ice sheet growth than what would have occurred on a fully deglaciated terrain. The ice-sheet configuration during stadials would also be governed largely by the additional topography that such “residual” ice constitutes because of inherent mass balance–topography feedbacks.

Ambient Noise Measurements for Preliminary Site-Effects Characterization in the Urban Area of Florence, Italy

Abstract Environmental noise measurements and borehole data were used for a preliminary seismic characterization of the Plio-Quaternary sedimentary basin underlying the city of Florence (Italy). An extensive survey of ambient vibrations was conducted by using the seismic noise horizontal-to-vertical (H/V) spectral ratio technique (HVSR) to map the fundamental resonance frequency of the sedimentary cover. In order to use this information to infer main features of the basin subsurface geometry, an estimate of the S -wave velocity profile in the sediment layer was obtained from array noise recordings along with information on resonance frequency and direct measurements of the sediment thickness available at 23 borehole sites. A first-order reconstruction of the seismic bedrock topography in the area was provided, which shows a good consistency with available geological/log data. From these pieces of information, a preliminary soil classification of the whole area was attempted in order to identify situations where possible seismic amplification effects are expected during future earthquakes and where more accurate investigations are needed to parameterize the local seismic response.

Basal ice temperatures during late Weichselian deglaciation: comparison of landform assemblages in west-central Sweden

AbstractThe mountainous area of west-central Sweden has a varied glacial morphology and three unique landform assemblages appear to mark areas of different basal thermal conditions during the decay of late Weichselian ice. A glacial geomorphological map was constructed through interpretation of aerial photographs at a scale 1:60 000. The relative abundance of landforms interpreted to indicate a frozen bed, a thawed bed, and late-frozen to thawed-bed conditions were used for a first-order reconstruction of the basal temperature pattern of the decaying ice sheet. The features used to outline areas with different temperature regimes during deglaciation are glacial scouring, flutings, eskers, meltwater channels, boulder blankets, Rogen moraines, relict surfaces and thermoerosion features.In the northern part of the area, as well as along most of the water divide to the Atlantic Ocean, the ice was warm-based during deglaciation. Glacially scoured bedrock, fluting/ drumlinization, subglacial eskers and extensive glacial lake sediments characterize the area. In the high mountain area, lateral meltwater channels are short and curve downslope to form chutes or eskers. The basal ice conditions changed from frozen- to thawedbed in a late stage of the late Weichselian cycle in most of the southern part of the area, shown by the Rogen moraines on both sides of the ice divide. However, substantial areas in the eastern and southern low mountains had frozen-bed conditions during the complete late Weichselian. In the high mountains in the north, only the summits were frozen.

A simplified first-order reconstruction algorithm for microwave tomography

ABSTRACT A first-order reconstruction algorithm for microwave tomographic imaging has been developed considering the wave nature of the probing signal. The algorithm has been simplified by neglecting mutual interaction terms. The traditional ray theory which is successfully applied in X-ray and ultrasound tomography, is totally inadequate to explain different electromagnetic phenomena, for example, scattering, diffraction and boundary reflections. A beam concept has been introduced in developing the algorithm. The results of applying the algorithm on a small biological model containing bone, muscle and muscle-like materials have been extremely encouraging indicating the possibility of development of a microwave imaging scheme. The image, however, at present is not as perfect as it should have been from clinical point of view, most probably due to the simplifying assumptions made in developing the algorithm.

Limitations of Imaging with First-Order Diffraction Tomography

In this paper, the results of computer simulations used to determine the domains of applicability of the first-order Born and Rytov approximations in diffraction tomography for cross-sectional (or three-dimensional) imaging of biosystems are shown. These computer simulations were conducted on single cylinders, since in this case analytical expressions are available for the exact scattered fields. The simulations establish the first-order Born approximation to be valid for objects where the product of the relative refractive index and the diameter of the cylinder is less than 0.35 lambda. The first-order Rytov approximation is valid with essentially no constraint on the size of the cylinders; however, the relative refractive index must be less than a few percent. We have also reviewed the assumptions made in the first-order Born and Rytov approximations for diffraction tomography. Further, we have reviewed the derivation of the Fourier Diffraction projection Theorem, which forms the basis of the first-order reconstruction algorithms. We then show how this derivation points to new FFT-based implementations for the higher order diffraction tomography algorithms that are currently being developed.