We propose, analyze, and illustrate several best basis search algorithms for dictionaries consisting of lapped orthogonal bases. We improve upon the best local cosine basis selection based on a dyadic tree , , by considering larger dictionaries of bases. We show that this can result in sparser representations and approximate shift-invariance. We also provide an algorithm which is strictly shift-invariant. Our experiments suggest that the new dictionaries can be advantageous for time-frequency analysis, compression, and noise removal. We provide accelerated versions of the basic algorithm which explore various trade-offs between computational efficiency and adaptability. We show that our algorithms are in fact applicable to any finite dictionary comprised of lapped orthogonal bases. We propose one such novel dictionary which constructs the best local cosine representation in the frequency domain, and show that the new dictionary is better suited for representing certain types of signals.
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