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Basis pursuit has been shown to be an effective method of solving inverse problems with a small amount of data when the system to be determined has a sparse representation. Adaptive filters fall under this general category of problems. Here, we use the echo cancellation context to introduce a method of solving the basis pursuit problem with an iterative method based on the proportionate normalized...
This paper indicates that an appropriate design of metric leads to significant improvements in the adaptive projected subgradient method (APSM), which unifies a wide range of projection-based algorithms [including normalized least mean square (NLMS) and affine projection algorithm (APA)]. The key is to incorporate a priori (or a posteriori) information on characteristics of an estimandum, a system...
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