This paper presents an algorithmic solution, the Adaptive Projected Subgradient Method, to the problem of asymptotically minimizing a certain sequence of nonnegative continuous convex functions over the fixed point set of strongly attracting nonexpansive mappings in a real Hilbert space. The proposed method provides with a strongly convergent, asymptotically optimal point sequence as well as with a characterization of the limiting point. As a side effect, the method allows the asymptotic minimization over the nonempty intersection of a finite number of closed convex sets. Thus, new directions for set theoretic adaptive filtering algorithms are revealed whenever the estimandum (system to be identified) is known to satisfy a number of convex constraints. This leads to a unification of a wide range of set theoretic adaptive filtering schemes such as NLMS, Projected or Constrained NLMS, APA, Adaptive Parallel Subgradient Projection Algorithm, Adaptive Parallel Min-Max Projection Algorithm as well as their embedded constraint versions. Numerical results demonstrate the effectiveness of the proposed method to the problem of stereophonic acoustic echo cancellation.
|ジャーナル||Conference Record - Asilomar Conference on Signals, Systems and Computers|
|出版ステータス||Published - 2004 12 1|
|イベント||Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers - Pacific Grove, CA, United States|
継続期間: 2004 11 7 → 2004 11 10
ASJC Scopus subject areas
- Signal Processing
- Computer Networks and Communications