PIC-projection technique for decreasing of statistical error in signals reconstruction problems

As is well known, the problem of signal reconstruction may be reduced to estimation of coefficients of some signal decomposition. In the previous paper [1] we have shown that an optimal coordinate basis for this method must be formed from eigenfunctions of the Fisher information operator (so-called PIC-basis). However direct usage of the PIC-basis is not always convenient. Therefore we propose the combined technique, according to which any given basis (FFT, DCT, wavelet, filterbanks, etc.) is replaced by its projection on the subspace generated by the PIC-basis. Such projective basis, keeping all advantages of the initial representation, allows us to decrease the range of possible fluctuations of a signal estimate. The effectiveness of the proposed technique is illustrated by numerical examples from the area of nonlinear tomography of a medium.