A computationally efficient algorithm for the 2D covariance method

The estimated covariance matrix is a building block for many algorithms, including signal and image processing. The Covariance Method is an estimator for the covariance matrix, favored both as an estimator and in view of the convenient properties of the matrix that it produces. However, the considerable computational requirements limit its use. We present a novel computation algorithm for the covariance method, which dramatically reduces the computational complexity (both ALU operations and memory access) relative to previous algorithms. It has a small memory footprint, is highly parallelizable and requires no synchronization among compute threads. On a 40-core X86 system, we achieve 1200X speedup relative to a straightforward single-core implementation; even on a single core, 35X speedup is achieved.