Best basis algorithm for signal enhancement

This paper appeared in the proceedings of ICASSP'95 bases can approximate it with only a few non-zero coefficients. It then becomes necessary to adaptively se-ABSTRACT lect an appropriate "best basis" which provides the best We propose a Best Basis Algorithm for Signal Enhance-signal estimate by discarding (thresholding) the noisy ment in white gaussian noise. We base our search of coefficients. This approach was first proposed by John-best basis on a criterion of minimal reconstruction er-stone and Donoho [3] who proceed to a best basis search ror of the underlying signal. We subsequently com-in families of orthonormal bases constructed with pare our simple error criterion to the Stein unbiased wavepackets or local cosine bases. risk estimator, and provide a subtantiating example to This paper focuses on a more precise estimate of the demonstrate its performance. mean-square error introduced by the thresholding algorithm , which leads to a new strategy of searching for