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The binary-tree best base (BTBB) searching method developed by R. Coifman and M.V. Wickerhauser (1992) is well known and widely used in wavelet packet applications. However, the requirement that the base vectors be chosen from either a parent or its directly related children in the binary-tree structure is a limitation because it does not search all possible orthogonal bases and therefore may not provide an optimal result. We have recently found that the set of all possible orthogonal bases in a wavelet packet is much larger than the set searched by the BTBB method. Based on this observation, we have developed a tree-elimination based best orthogonal base (TBB) searching method, a new way to search the best base among a much larger set of orthogonal bases. We show that considerable improvements in signal compression, time-frequency analysis, and feature extraction may be achieved using the newly developed TBB method. Similar to the matching pursuit method (MP), TBB uses an aggressive searching method. However, its computation is faster than that of the orthogonal MP searching method.