Document Type

Conference Proceeding


Review of Progress in Quantitative Nondestructive Evaluation

Publication Date



San Diego, CA


We apply expectation‐conditional maximization either (ECME) hard thresholding algorithms to X‐ray computed tomography (CT) reconstruction, where we implement the sampling operator using the nonuniform fast Fourier transform (NUFFT). The measurements follow an underdetermined linear model, where the regression‐coefficient vector is a sum of an unknown deterministic sparse signal component and a zero‐mean white Gaussian component with an unknown variance. Our ECME schemes aim at maximizing this model’s likelihood function with respect to the sparse signal and variance of the random signal component. These schemes exploit signal sparsity in the discrete wavelet transform (DWT) domain and yield better reconstructions than the traditional filtered backprojection (FBP) approach, which is demonstrated via numerical examples. In contrast with FBP, our methods achieve artifact‐free reconstructions in undersampled and limited‐angle projection examples. We also compare the ECME schemes with a state‐of‐the‐art convex sparse signal reconstruction approach in terms of the reconstruction speed.


Copyright 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

This article appeared in AIP Conference Proceedings 1335 (2011): 469–476 and may be found at

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American Institute of Physics




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