摘要：Image reconstruction from nonuniformly sampled spatial frequency
domain data is an important problem that arises in computed
imaging. Current reconstruction techniques suffer from limitations
in their model and implementation. In this paper, we present a new
reconstruction method that is based on solving a system of linear
equations using an efficient iterative approach. Image pixel
intensities are related to the measured frequency domain data
through a set of linear equations. Although the system matrix is
too dense and large to solve by direct inversion in practice, a
simple orthogonal transformation to the rows of this matrix is
applied to convert the matrix into a sparse one up to a certain
chosen level of energy preservation. The transformed system is
subsequently solved using the conjugate gradient method. This
method is applied to reconstruct images of a numerical phantom as
well as magnetic resonance images from experimental spiral imaging
data. The results support the theory and demonstrate that the
computational load of this method is similar to that of standard
gridding, illustrating its practical utility.
