Limited Angle Tomography of Sparse Images from Noisy Data using TLS MUSIC Algorithm

The limited angle tomography problem is to reconstruct an image from a set of its projections (Radon transform) over a limited range of angles. It has applications in medical imaging and synthetic aperture radar. From the Radon projectionslice theorem, this problem is equivalent to image reconstruction from partial Fourier data. This paper presents an algorithm for solving this problem for sparse images. The fraction of nonzero pixels must be one-fourth the fraction of Fourier data available or less; their locations are unknown; and there is no support constraint. The problem requires only solution of two Toeplitz-mosaic-Toeplitz (TMT) linear systems of equations and a 2D FFT. For noisy data, the minimum singular vector of a TMT matrix is required; this can be computed using inverse power method (TLS). Numerical examples illustrate the new algorithms. Keywords— Sparse reconstruction; Tomography Phone: 734-763-9810. Fax: 734-763-1503. Email: [email protected]. EDICS: 2-REST.