Combined Reduced-Rank Transform
Anatoli Torokhti · Symmetry Integrability and Geometry Methods and Applications · 2006
We propose and justify a new approach to constructing optimal nonlinear transforms of random vectors.We show that the proposed transform improves such characteristics of rank-reduced transforms as compression ratio, accuracy of decompression and reduces required computational work.The proposed transform T p is presented in the form of a sum with p terms where each term is interpreted as a particular rank-reduced transform.Moreover, terms in T p are represented as a combination of three operations F k , Q k and ϕ k with k = 1, . . ., p.The prime idea is to determine F k separately, for each k = 1, . . ., p, from an associated rank-constrained minimization problem similar to that used in the Karhunen-Loève transform.The operations Q k and ϕ k are auxiliary for finding F k .The contribution of each term in T p improves the entire transform performance.A corresponding unconstrained nonlinear optimal transform is also considered.Such a transform is important in its own right because it is treated as an optimal filter without signal compression.A rigorous analysis of errors associated with the proposed transforms is given.