The authors propose a method for reconstructing partial data slices using the theory of projections onto convex sets (POCS). The problem involves the reconstruction of a complex function, which consists of the desired magnitude image and an undesired phase. For that purpose the authors introduce, among other features, a convex constraint set based on a priori information about the phase. The authors show selected results of an extensive experimental study, using head images, taken from an actual MRI session. It is concluded that it is possible to obtain fair quality reconstructions using the proposed procedure, even from a relatively small amount of data.>

The problem of reconstructing a two-dimensional function from a set of spiral samples is addressed. This problem is of practical interest in magnetic resonance imaging (MRI). A theorem that enables exact interpolation from linear spiral samples to a Cartesian lattice is presented, dealing with nonlinear, expanding spirals. These kinds of spirals have a potential advantage in a situation for which the data collection time is limited. In general, there is no exact reconstruction procedure from nonlinear spiral samples. Two practical methods are furnished to reconstruct an image from a set of spiral samples of its Fourier transform and examples are shown of reconstructions obtained through both methods.>

The pinned sine transform (PST) coder described is a practical approximation to the pinned KLT coder. The image is partitioned into two fields: a boundary field, which depends only on the coded block boundaries, and a pinned field, which vanishes at the boundaries and is subsequently sine transformed and compressed. The reconstructed image is continuous across the block boundaries and "blocking effects" are hardly visible. Simulation results are given for fixed and adaptive compression schemes with fair image quality at low bit rates down to 0.3 bits/pel.