Ordered and partially ordered processing of multidimensional images
J.L. Aravena, W. Porter · IEEE Transactions on Acoustics Speech and Signal Processing · 1985
Multidimensional images are often converted by scanning to a raster format. For real-time processing a causal property relative to the scan order is important. In other examples the multidimensional image is processed without scanning. In such cases a partially ordered causality property is of interest. The present paper gives a definitive study of the interrelationship between the several causality properties. We establish also a new operator factorization. This factorization can be seen as an extension and refinement of triangular factorization, Shur-Coleski factotization, Gohberg-Krein factorization, and partially ordered factorizations of DeSantis-Porter. An application of the new results to optimal signal extraction and control is summarized.