Polyharmonic wavelet are a new and exciting family of wavelets. Recently, our lab has proposed new flavors based on a more isotropic discretization of the Laplacian operator. The implementation of the corresponding wavelet transform requires the computation of the so-called autocorrelation sequence. For this, we have found a fast iterative and Fourier-based implementation. However, for some applications, an even faster implementation would be very valuable.
In this project, we propose to evaluate the several way available to optimize the calculation of the autocorrelation function. Two main approaches are possible: 1) Find the "important" orders/size of precomputed autocorrelation sequences to be tabulated; find the expected worst-case error when using these as a starting for the iterative approach. 2) Look for an analytical approximation formula of the autocorrelation sequence (based on its resembles to the Gaussian) and use this to compute an initial estimate; eventually, improve this estimate if required by the iterative approach.
As a prerequisite for this project, the student should be familiar with Java and Matlab programming.