General entropy criteria for inverse problems, with applications to data compression, pattern classification, and cluster analysis

Minimum distance approaches are considered for the reconstruction of a real function from finitely many linear functional values. An optimal class of distances satisfying an orthogonality condition analogous to that enjoyed by linear projections in Hilbert space is derived. These optimal distances are related to measures of distances between probability distributions recently introduced by C.R. Rao and T.K. Nayak (1985) and possess the geometric properties of cross entropy useful in speech and image compression, pattern classification, and cluster analysis. Several examples from spectrum estimation and image processing are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>