Adaptive filter theory (2nd ed.)
Adaptive filter theory (2nd ed.)
Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics
Online Kernel-Based Classification Using Adaptive Projection Algorithms
IEEE Transactions on Signal Processing - Part I
Adaptive constrained learning in reproducing Kernel Hilbert spaces: the robust beamforming case
IEEE Transactions on Signal Processing
A unified view of adaptive variable-metric projection algorithms
EURASIP Journal on Advances in Signal Processing
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The goal of this paper is to establish a novel signal processing paradigm that enables us to find a point meeting time-variable specifications in dual domain (e.g., time and frequency domains) Simultaneously. For this purpose. we define a new problem which we call adaptive split feasibility problem (ASFP). In the ASFP formulation, we have (i) a priori knowledge based convex constraints iii the Euclidean spaces RN and RM and (ii) data-dependent convex sets in RN and RM; the latter are obtained in a sequential fashion. Roughly speaking, the problem is to find a common point of all the sets defined on RN such that its image under a given linear transformation is a common point of all the sets defined on RM, if such a point exists. We prove that the adaptive projected subgradient method (APSM) deals with the ASFP by employing (i) a projected gradient operator with respect to (w.r.t.) a 'fixed' proximity function reflecting the convex constraints and (ii) a subgradient projection w.r.t. 'time-varying' objective functions reflecting the data-dependent sets. The resulting algorithm requires no unwanted operations such as matrix inversion, therefore it is suitable for real-time implementation. A convergence analysis is presented and verified by numerical examples.