Many image processing operations can be abstracted into matrix operations. With the help of matrix analysis, we can understand the inherent properties of the operations and thus design better algorithms. In this paper, we propose a matrix decomposition method referred to as identity-plus-row decomposition. The decomposition is particularly useful in design of parallel projection algorithms on mesh-connected computers. Projection is a frequently used process in image processing and visualization. In volume graphics, projection is used to render the essential content of a three-dimensional volume onto a two-dimensional image plane. For Radon transform, projection is used to transform the image space into a parameter space. By applying the identity-plus-row matrix decomposition method, we solve the data redistribution problem due to the irregular data access patterns present in those applications on single instruction stream, multiple data stream (SIMD) meshconnected computers, developing fast algorithms for volume rendering and Radon transform on SIMD mesh-connected computers.
"Identity-plus-row matrix decomposition and its application in design of parallel projection algorithms," Journal of Electronic Imaging 10(3), (1 July 2001). https://doi.org/10.1117/1.1382611