Fast 2D Convolutions and Cross-Correlations Using Scalable Architectures.

The manuscript describes fast and scalable architectures and associated algorithms for computing convolutions and cross-correlations. The basic idea is to map 2D convolutions and cross-correlations to a collection of 1D convolutions and cross-correlations in the transform domain. This is accomplished through the use of the discrete periodic radon transform for general kernels and the use of singular value decomposition -LU decompositions for low-rank kernels.

Fast and Scalable Computation of the Forward and Inverse Discrete Periodic Radon Transform.

The discrete periodic radon transform (DPRT) has extensively been used in applications that involve image reconstructions from projections. Beyond classic applications, the DPRT can also be used to compute fast convolutions that avoids the use of floating-point arithmetic associated with the use of the fast Fourier transform. Unfortunately, the use of the DPRT has been limited by the need to compute a large number of additions and the need for a large number of memory accesses.