Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Adaptive Projected Subgradient Method (APSM) serves as a unified guiding principle of various set-theoretic adaptive filtering algorithms including NLMS/APA. APSM asymptotically minimizes a sequence of non-negative convex functions in a real-Hilbert space. On the other hand, the exponentially ighted stepsize projection (ESP) algorithm has been reported to converge faster than APA in the acoustic echo cancellation (AEC) problem. ,  first clarify that ESP is derived by APSM in a real Hilbert space with a special inner product. This gives us an interesting interpretation that ESP is based on iterative projections onto the same convex sets as APA with a special metric.  can thus expect that a proper choice of metric will lead to improvement of convergence speed.  then propose an efficient adaptive algorithm named adaptive quadratic-metric parallel subgradient projection (AQ-PSP). Numerical examples demonstrate that AQ-PSP with a very simple metric achieves even better echo canceling ability than ESP, proportionate NLMS, and Euclidean-metric version of AQ-PSP, while keeping low computational complexity.
['Masahiro Yukawa', 'Isao Yamada']
I am writing a research paper on a idea Adaptive quadratic-metric parallel subgradient projection algorithm and its application to acoustic echo cancellation
[{"from": "human", "value": "I am writing a research paper on a idea Adaptive quadratic-metric parallel subgradient projection algorithm and its application to acoustic echo cancellation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Adaptive Projected Subgradient Method (APSM) serves as a unified guiding principle of various set-theoretic adaptive filtering algorithms including NLMS/APA. APSM asymptotically minimizes a sequence of non-negative convex functions in a real-Hilbert space. On the other hand, the exponentially ighted stepsize projection (ESP) algorithm has been reported to converge faster than APA in the acoustic echo cancellation (AEC) problem. ,  first clarify that ESP is derived by APSM in a real Hilbert space with a special inner product. This gives us an interesting interpretation that ESP is based on iterative projections onto the same convex sets as APA with a special metric.  can thus expect that a proper choice of metric will lead to improvement of convergence speed.  then propose an efficient adaptive algorithm named adaptive quadratic-metric parallel subgradient projection (AQ-PSP). Numerical examples demonstrate that AQ-PSP with a very simple metric achieves even better echo canceling ability than ESP, proportionate NLMS, and Euclidean-metric version of AQ-PSP, while keeping low computational complexity."}]