Averages of best wavelet basis estimates for denoising

Donoho and Johnstone introduced an adaptive algorithm that extends nonlinear thresholding denoising in a fixed orthonormal basis to a multiple basis setting. In their work, a search for an optimal basis from a large collection of orthonormal bases – i.e., a library – is introduced. That technique gives the so-called best ortho-basis estimate. In this paper we study the situation when many such libraries are available. We propose an algorithm that exploits the availability of many best ortho-basis approximations. The algorithm uses a strengthening of the convexity of the L2 norm to produce an estimate which is an average of best ortho-basis estimates. Conditions under which the proposed algorithm offers improvements and corresponding numerical examples are also described.