On the design of filters for Fourier and oSVD-based deconvolution in bolus tracking perfusion MRI

Bolus tracking perfusion evaluation relies on the deconvolution of a tracers concentration time-courses in an arterial and a tissue voxel following the tracer kinetic model. The object of this work is to propose a method to design a data-driven Tikhonov regularization filter in the Fourier domain and to compare it to the singular value decomposition (SVD)-based approaches using the mathematical equivalence of Fourier and circular SVD (oSVD).

The adaptive filter is designed using Tikhonov regularization that depends on only one parameter. Using a simulation, such an optimal parameter that minimizes the sum of statistical and systematic error is determined as a function of the first moment difference between the tissue and the arterial curve and the contrast to noise ratios of the input data (CNR( a ) in arteries and CNR( t ) in tissue). The performance of the method is evaluated and compared to oSVD in simulations and measured data.

The proposed method yields a smaller flow underestimation especially for high flows when compared to the oSVD approach with constant threshold. However, this improvement comes to the price of an increased uncertainty of the flow values. The translation of the Tikhonov regularization parameter to an adaptive oSVD-threshold is in good agreement with the literature.

The proposed method is a comprehensive approach for the design of data-driven filters that can be easily adapted to specific needs.