Convergence properties of wavelet estimators with multiple sampling rates
G. Kerkyacharian, D. Picard, Hall, P. · HAL (Le Centre pour la Communication Scientifique Directe) · 2004
Adaptive sampling schemes with multiple sampling rates have the poten- tial to significantly improve the efficiency and effectiveness of methods for signal analysis. For example, in the case of equipment which transmits data continuously, multi-rate methods can reduce the cost of transmission. For equipment which trans- mits data only periodically they can reduce the costs of both storage and transmis- sion. When multiple sampling rates are used in connection with wavelet estima- tors, the most natural algorithms for rate-switching are arguably those based on threshold-crossings by wavelet coefficients. In this paper we study the performance of such algorithms, and show that even simple threshold-crossing rules can achieve near-optimal convergence rates. A new mathematical model is suggested for as- sessing performance, combining the simplicity and familiarity of global approaches with an account of the local variation to which multi-rate sampling responds.