Low latency vs. non linear phase: A balanced approach for UNFOLD filter design in quantitative Real-Time MRI

G. Maclair, M. Ries, C. Moonen IMF CNRS / University of Bordeaux 2, Bordeaux, France Purpose/Introduction: The UNFOLD method can be used to accelerate dynamic MRI acquisitions [1] and to remove artifacts in parallel-imaging and partial-fourier imaging [2]. The essential basic reconstruction step of the UNFOLD method is a temporal low-pass filter. Recent filtering approaches can be coarsely classified into spectral-domain filter methods such as finite impulse-response filter (FIR) and time-domain filtering methods such as infinite impulse-response filter (IIR) [3]. FIR filters have two important advantages over IIR filters. First, they are guaranteed to be stable and second, they may easily constraint to have a (generalized) linear phase. On the other hand, FIR filters have a symmetric impulse response and can thus in general not been designed to have the short latencies of IIRs which allow for asymmetric impulse responses [3]. In addition, compared to IIR filters, their implementation adds to the multiplication with the filter-coefficients two additional FFTs. Consequently, for MRI-applications requiring real-time reconstruction of MR data with low latencies (interventional imaging) and for the off-line reconstruction of extensive data-sets, IIR filters are in general preferable. However, their non-linear phase (vs. Frequency), or delay distortion, limits their use when a quantitative analysis of the temporal evolution of the MR-signal is needed (MR-guided thermotherapy, the quantification of contrast agent passages and fMRI). Kellman's filter design [3] for interventional imaging, based on an elliptical-IIR, focused mainly on the aspect of low-latency of the filter. We propose an alternative design based on a Bessel-IIR, which maintains the low-latency aspect but reduces the phase-dispersion in the pass-band and is thus suitable for quantitative interventional applications such as MR-guided thermotherapy. In addition, for the off-line reconstruction of UNFOLD encoded data-sets, we extend the proposed filter concept by cascading an additional matched all-pass filter which sacrifices latency but achieves a virtually linear phase response, which is is comparable to FIR filter designs, while maintaining the computational advantages of IIR filters. In order to demonstrate the different filter characteristics, we applied three IIR filter designs to a dynamic MRI data-set of a bolus passage through the kidney.