An interior point iterative maximum-likelihood reconstruction algorithm incorporating upper and lower bounds with application to SPECT transmission imaging

The algorithm we consider here is a block-iterative (or ordered subset) ver sion of the interior point algorithm for transmission reconstruction. Our a lgorithm is an interior point method because each vector of the iterative s equence (x(k)), k = 0, 1, 2,... satisfies the constraints a(j) < x(j)(k) < b(j),j = 1,..., J. Because it is a block-iterative algorithm that reconstru cts the transmission attenuation map and places constraints above and below the pixel values of the reconstructed image, we call it the BITAB method. Computer simulations using the three-dimensional mathematical cardiac and t orso phantom, reveal that the BITAB algorithm in conjunction with reasonabl y selected prior upper and lower bounds has the potential to improve the ac curacy of the reconstructed attenuation coefficients from truncated fan bea m transmission projections. By suitably selecting the bounds, it is possibl e to restrict the over estimation of coefficients outside the fully sampled region, that results from reconstructing truncated fan beam projections wi th iterative transmission algorithms such as the maximum-likelihood gradien t type algorithm.