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We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.

Hard x-ray spectra (10–100 keV) created in high contrast, 400 fs, laser pulse interaction with solid targets, have been studied for laser intensities in the 1017–1019 W/cm2 range. The target atomic numbers (Z) extended from Z=13 to Z=73. The measured conversion efficiency at Ag Kα emission line was 10−3% at 5×1018 W/cm2. It has been confirmed that the hot electron temperature increased as (Iλ2)1/3 and the fraction of laser energy in hot electrons follows scaling law of (Iλ2)3/4.

For high-noise simulated SPECT data, HOTV-PAPA outperforms TV-PAPA, GPF-EM, and TV-OSL in terms of hot lesion detectability, noise suppression, MSE, and computational efficiency. Unlike TV-PAPA and TV-OSL, HOTV-PAPA does not create sizable staircase artifacts. Moreover, HOTV-PAPA effectively suppresses noise, with only limited loss of local spatial resolution. Of the four methods, HOTV-PAPA shows the best lesion detectability, thanks to its superior noise suppression. HOTV-PAPA shows promise for clinically useful reconstructions of low-dose SPECT data.

Interaction of intense Ti:sapphire laser with solid targets has been studied experimentally by measuring hard x-ray and hot electron generation. Hard x-ray ͑8 -100 keV͒ emission spectrum and K␣ x-ray conversion efficiency ͑ K ͒ from plasma have been studied as a function of laser intensity ͑10 17 -10 19 W/cm 2 ͒, pulse duration ͑70-400͒fs, and laser pulse fluence. For intensity I Ͼ 1 ϫ 10 17 W/cm 2 , the Ag K increases to reach a maximum value of 2 ϫ 10 −5 at an intensity I =4 ϫ 10 18 W/cm 2 . Hot electron temperature ͑KT h ͒ and K scaling laws have been studied as a function of the laser parameters. A stronger dependence of KT h and K as a function of the laser fluence than on pulse duration or laser intensity has been observed. The contribution of another nonlinear mechanism, besides resonance absorption, to hard x-ray enhancement has been demonstrated via hot electron angular distribution and particle-in-cell simulations.

A maximum-likelihood (ML) expectation-maximization (EM) algorithm (called EM-IntraSPECT) is presented for simultaneously estimating single photon emission computed tomography (SPECT) emission and attenuation parameters from emission data alone. The algorithm uses the activity within the patient as transmission tomography sources, with which attenuation coefficients can be estimated. For this initial study, EM-IntraSPECT was tested on computer-simulated attenuation and emission maps representing a simplified human thorax as well as on SPECT data obtained from a physical phantom. Two evaluations were performed. First, to corroborate the idea of reconstructing attenuation parameters from emission data, attenuation parameters (mu) were estimated with the emission intensities (lambda) fixed at their true values. Accurate reconstructions of attenuation parameters were obtained. Second, emission parameters lambda and attenuation parameters mu were simultaneously estimated from the emission data alone. In this case there was crosstalk between estimates of lambda and mu and final estimates of lambda and mu depended on initial values. Estimates degraded significantly as the support extended out farther from the body, and an explanation for this is proposed. In the EM-IntraSPECT reconstructed attenuation images, the lungs, spine, and soft tissue were readily distinguished and had approximately correct shapes and sizes. As compared with standard EM reconstruction assuming a fix uniform attenuation map, EM-IntraSPECT provided more uniform estimates of cardiac activity in the physical phantom study and in the simulation study with tight support, but less uniform estimates with a broad support. The new EM algorithm derived here has additional applications, including reconstructing emission and transmission projection data under a unified statistical model.

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