Proceedings PaperEfficient adaptive signal and signal dimension estimation using piecewise libraries
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Previously, methods to estimate the number of jumps in a piecewise constant signal were presented in the framework of projection libraries. In this paper, these concepts are extended to general piecewise projection libraries appropriate for modeling, for example, piecewise polynomial and piecewise stationary signals. A general piecewise best basis algorithm is also presented that offers an efficient alternative to standard methods. Particularly, an algorithm for best piecewise wavelet basis is shown to reduce the entropy over wavelet packets. While a dynamic programming algorithm can still be employed to efficiently calculate optical estimates for these new piecewise projection libraries, additional modifications are often needed to reduce the computational requirements for practical implementation. An alternative approach, termed subspace pursuit, is presented that is applicable to all projection libraries and is especially suited for signal dimension estimation. The method is an order-recursive least square implementation of matched pursuit that requires roughly twice the computation but has the advantage that at each iteration the coefficients are optimal, that is, are obtained by a projection onto the subspace spanned by signals in the dictionary. Additionally, for the signal dimension estimation problem, an interesting paradox is presented where estimates are shown to be worse with increased signal-to-noise ratio (SNR) past a certain threshold and to converge to a level less than this optimum performance for infinite SNR.