Sampling and processing for multiple scattering in inline compressive holography

Inline holography is approached from a computational perspective by incorporating a nonlinear forward model based on the iterative Born approximation (IBA). Sampling and its effects on multiple scattering computations are discussed.Published versio

Deconvolving Instrumental and Intrinsic Broadening in Excited State X-ray Spectroscopies

Intrinsic and experimental mechanisms frequently lead to broadening of spectral features in excited-state spectroscopies. For example, intrinsic broadening occurs in x-ray absorption spectroscopy (XAS) measurements of heavy elements where the core-hole lifetime is very short. On the other hand, nonresonant x-ray Raman scattering (XRS) and other energy loss measurements are more limited by instrumental resolution. Here, we demonstrate that the Richardson-Lucy (RL) iterative algorithm provides a robust method for deconvolving instrumental and intrinsic resolutions from typical XAS and XRS data. For the K-edge XAS of Ag, we find nearly complete removal of ~9.3 eV FWHM broadening from the combined effects of the short core-hole lifetime and instrumental resolution. We are also able to remove nearly all instrumental broadening in an XRS measurement of diamond, with the resulting improved spectrum comparing favorably with prior soft x-ray XAS measurements. We present a practical methodology for implementing the RL algorithm to these problems, emphasizing the importance of testing for stability of the deconvolution process against noise amplification, perturbations in the initial spectra, and uncertainties in the core-hole lifetime.Comment: 35 pages, 13 figure

Target Detection Using Fractal Geometry

The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background

Sparsity driven ultrasound imaging

An image formation framework for ultrasound imaging from synthetic transducer arrays based on sparsity-driven regularization functionals using single-frequency Fourier domain data is proposed. The framework involves the use of a physics-based forward model of the ultrasound observation process, the formulation of image formation as the solution of an associated optimization problem, and the solution of that problem through efficient numerical algorithms. The sparsity-driven, model-based approach estimates a complex-valued reflectivity field and preserves physical features in the scene while suppressing spurious artifacts. It also provides robust reconstructions in the case of sparse and reduced observation apertures. The effectiveness of the proposed imaging strategy is demonstrated using experimental data