Point spread function approximation of high rank Hessians with locally supported non-negative integral kernels

We present an efficient matrix-free point spread function (PSF) method for approximating operators that have locally supported non-negative integral kernels. The method computes impulse responses of the operator at scattered points, and interpolates these impulse responses to approximate integral kernel entries. Impulse responses are computed by applying the operator to Dirac comb batches of point sources, which are chosen by solving an ellipsoid packing problem. Evaluation of kernel entries allows us to construct a hierarchical matrix (H-matrix) approximation of the operator. Further matrix computations are performed with H-matrix methods. We use the method to build preconditioners for the Hessian operator in two inverse problems governed by partial differential equations (PDEs): inversion for the basal friction coefficient in an ice sheet flow problem and for the initial condition in an advective-diffusive transport problem. While for many ill-posed inverse problems the Hessian of the data misfit term exhibits a low rank structure, and hence a low rank approximation is suitable, for many problems of practical interest the numerical rank of the Hessian is still large. But Hessian impulse responses typically become more local as the numerical rank increases, which benefits the PSF method. Numerical results reveal that the PSF preconditioner clusters the spectrum of the preconditioned Hessian near one, yielding roughly 5x-10x reductions in the required number of PDE solves, as compared to regularization preconditioning and no preconditioning. We also present a numerical study for the influence of various parameters (that control the shape of the impulse responses) on the effectiveness of the advection-diffusion Hessian approximation. The results show that the PSF-based preconditioners are able to form good approximations of high-rank Hessians using a small number of operator applications

Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin

A very efficient RCS data compression and reconstruction technique, volume 4

A very efficient compression and reconstruction scheme for RCS measurement data was developed. The compression is done by isolating the scattering mechanisms on the target and recording their individual responses in the frequency and azimuth scans, respectively. The reconstruction, which is an inverse process of the compression, is granted by the sampling theorem. Two sets of data, the corner reflectors and the F-117 fighter model, were processed and the results were shown to be convincing. The compression ratio can be as large as several hundred, depending on the target's geometry and scattering characteristics

An evaluation of the performance of multi-static handheld ground penetrating radar using full wave inversion for landmine detection

This thesis presents an empirical study comparing the ability of multi-static and bi-static, handheld, ground penetrating radar (GPR) systems, using full wave inversion (FWI), to determine the properties of buried anti-personnel (AP) landmines. A major problem associated with humanitarian demining is the occurrence of many false positives during clearance operations. Therefore, a reduction of the false alarm rate (FAR) and/or increasing the probability of detection (POD) is a key research and technical objective. Sensor fusion has emerged as a technique that promises to significantly enhance landmine detection. This study considers a handheld, combined metal detector (MD) and GPR device, and quantifies the advantages of the use of antenna arrays. During demining operations with such systems, possible targets are detected using the MD and further categorised using the GPR, possibly excluding false positives. A system using FWI imaging techniques to estimate the subsurface parameters is considered in this work.A previous study of multi-static GPR FWI used simplistic, 2D far-field propagation models, despite the targets being 3D and within the near field. This novel study uses full 3D electromagnetic (EM) wave simulation of the antenna arrays and propagation through the air and ground. Full EM simulation allows the sensitivity of radio measurements to landmine characteristics to be determined. The number and configuration of antenna elements are very important and must be optimised, contrary to the 2D sensitivity studies in (Watson, Lionheart 2014, Watson 2016) which conclude that the degree (number of elements) of the multi-static system is not critical. A novel sensitivity analysis for tilted handheld GPR antennas is used to demonstrate the positive impact of tilted antenna orientation on detection performance. A time domain GPR and A-scan data, consistent with a commercial handheld system, the MINEHOUND, is used throughout the simulated experiments which are based on synthetic GPR measurements.Finally, this thesis introduces a novel method of optimising the FWI solution through feature extraction or estimation of the internal air void typically present in pressure activated mines, to distinguish mines from non-mine targets and reduce the incidence of false positives