Keywords: Laguerre functions basis, wavelets, Laplace deconvolution, DCE imaging
The high frequency Dynamical Contrast Enhanced (DCE) imaging techniques are used for various medical assessments such as brain flows, strokes or cancer angiogenesis.The DCE imaging experiments can be described by a collection of Laplace convolution equations based on noisy observations, one equation per unit volume (voxel). Previously, available data curves were pre-clustered and averaged, and the inverse problem was solved with these secondary data. In the present work, we do not use pre-clustering and just analyze all available data together by expanding the curves over the Laguerre functions basis in time domain and finitely supported wavelets in spatial domain.
The resulting solutions have good theoretical properties and show good precision in simulations. In addition, since for each voxel, the solution curve is represented via only few Laguerre coefficients, these curves can be clustered more efficiently than the original curves. We conducted simulation study to show that the estimation works well in finite simulations settings. Finally we carry out real data simulation which encourage the applicability of the method.