1,125 research outputs found
TV-min and Greedy Pursuit for Constrained Joint Sparsity and Application to Inverse Scattering
This paper proposes a general framework for compressed sensing of constrained
joint sparsity (CJS) which includes total variation minimization (TV-min) as an
example. TV- and 2-norm error bounds, independent of the ambient dimension, are
derived for the CJS version of Basis Pursuit and Orthogonal Matching Pursuit.
As an application the results extend Cand`es, Romberg and Tao's proof of exact
recovery of piecewise constant objects with noiseless incomplete Fourier data
to the case of noisy data.Comment: Mathematics and Mechanics of Complex Systems (2013
Phase Retrieval with Application to Optical Imaging
This review article provides a contemporary overview of phase retrieval in
optical imaging, linking the relevant optical physics to the information
processing methods and algorithms. Its purpose is to describe the current state
of the art in this area, identify challenges, and suggest vision and areas
where signal processing methods can have a large impact on optical imaging and
on the world of imaging at large, with applications in a variety of fields
ranging from biology and chemistry to physics and engineering
Iterative CT reconstruction from few projections for the nondestructive post irradiation examination of nuclear fuel assemblies
The core components (e.g. fuel assemblies, spacer grids, control rods) of the nuclear reactors encounter harsh environment due to high temperature, physical stress, and a tremendous level of radiation. The integrity of these elements is crucial for safe operation of the nuclear power plants. The Post Irradiation Examination (PIE) can reveal information about the integrity of the elements during normal operations and off‐normal events. Computed tomography (CT) is a tool for evaluating the structural integrity of elements non-destructively. CT requires many projections to be acquired from different view angles after which a mathematical algorithm is adopted for reconstruction. Obtaining many projections is laborious and expensive in nuclear industries. Reconstructions from a small number of projections are explored to achieve faster and cost-efficient PIE. Classical reconstruction algorithms (e.g. filtered back projection) cannot offer stable reconstructions from few projections and create severe streaking artifacts. In this thesis, conventional algorithms are reviewed, and new algorithms are developed for reconstructions of the nuclear fuel assemblies using few projections. CT reconstruction from few projections falls into two categories: the sparse-view CT and the limited-angle CT or tomosynthesis. Iterative reconstruction algorithms are developed for both cases in the field of compressed sensing (CS). The performance of the algorithms is assessed using simulated projections and validated through real projections. The thesis also describes the systematic strategy towards establishing the conditions of reconstructions and finds the optimal imaging parameters for reconstructions of the fuel assemblies from few projections. --Abstract, page iii
A Sparse Bayesian Estimation Framework for Conditioning Prior Geologic Models to Nonlinear Flow Measurements
We present a Bayesian framework for reconstruction of subsurface hydraulic
properties from nonlinear dynamic flow data by imposing sparsity on the
distribution of the solution coefficients in a compression transform domain
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Elevation and Deformation Extraction from TomoSAR
3D SAR tomography (TomoSAR) and 4D SAR differential tomography (Diff-TomoSAR) exploit multi-baseline SAR data stacks to provide an essential innovation of SAR Interferometry for many applications, sensing complex scenes with multiple scatterers mapped into the same SAR pixel cell. However, these are still influenced by DEM uncertainty, temporal decorrelation, orbital, tropospheric and ionospheric phase distortion and height blurring. In this thesis, these techniques are explored. As part of this exploration, the systematic procedures for DEM generation, DEM quality assessment, DEM quality improvement and DEM applications are first studied. Besides, this thesis focuses on the whole cycle of systematic methods for 3D & 4D TomoSAR imaging for height and deformation retrieval, from the problem formation phase, through the development of methods to testing on real SAR data. After DEM generation introduction from spaceborne bistatic InSAR (TanDEM-X) and airborne photogrammetry (Bluesky), a new DEM co-registration method with line feature validation (river network line, ridgeline, valley line, crater boundary feature and so on) is developed and demonstrated to assist the study of a wide area DEM data quality. This DEM co-registration method aligns two DEMs irrespective of the linear distortion model, which improves the quality of DEM vertical comparison accuracy significantly and is suitable and helpful for DEM quality assessment. A systematic TomoSAR algorithm and method have been established, tested, analysed and demonstrated for various applications (urban buildings, bridges, dams) to achieve better 3D & 4D tomographic SAR imaging results. These include applying Cosmo-Skymed X band single-polarisation data over the Zipingpu dam, Dujiangyan, Sichuan, China, to map topography; and using ALOS L band data in the San Francisco Bay region to map urban building and bridge. A new ionospheric correction method based on the tile method employing IGS TEC data, a split-spectrum and an ionospheric model via least squares are developed to correct ionospheric distortion to improve the accuracy of 3D & 4D tomographic SAR imaging. Meanwhile, a pixel by pixel orbit baseline estimation method is developed to address the research gaps of baseline estimation for 3D & 4D spaceborne SAR tomography imaging. Moreover, a SAR tomography imaging algorithm and a differential tomography four-dimensional SAR imaging algorithm based on compressive sensing, SAR interferometry phase (InSAR) calibration reference to DEM with DEM error correction, a new phase error calibration and compensation algorithm, based on PS, SVD, PGA, weighted least squares and minimum entropy, are developed to obtain accurate 3D & 4D tomographic SAR imaging results. The new baseline estimation method and consequent TomoSAR processing results showed that an accurate baseline estimation is essential to build up the TomoSAR model. After baseline estimation, phase calibration experiments (via FFT and Capon method) indicate that a phase calibration step is indispensable for TomoSAR imaging, which eventually influences the inversion results. A super-resolution reconstruction CS based study demonstrates X band data with the CS method does not fit for forest reconstruction but works for reconstruction of large civil engineering structures such as dams and urban buildings. Meanwhile, the L band data with FFT, Capon and the CS method are shown to work for the reconstruction of large manmade structures (such as bridges) and urban buildings
Compressed sensing of monostatic and multistatic SAR
In this paper we study the impact of sparse aperture data collection of a SAR sensor on reconstruction quality of a scene of interest. Different mono and multi-static SAR measurement configurations produce different Fourier sampling patterns. These patterns reflect different spectral and spatial diversity trade-offs that must be made during task planning. Compressed sensing theory argues that the mutual coherence of the measurement probes is related to the reconstruction performance of sparse domains. With this motivation we compare the mutual coherence and corresponding reconstruction behavior of various mono-static and ultra-narrow band multi-static configurations, which trade-off frequency for geometric diversity. We investigate if such simple metrics are related to SAR reconstruction quality in an obvious way
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