Optimal sampling for “Noquist” reduced‐data cine magnetic resonance imaging
Authors: Moratal David , Thomas Dixon W. , Ramamurthy Senthil , Lerakis Stamatios , James Parks W. , Brummer Marijn E. 
Published: December 2012

Purpose:To analyze and optimize the signal‐to‐noise ratio (SNR) for the “Noquist” method for acceleration of cine magnetic resonance imaging in the presence of partially static field of view, designing practical methods for selection of optimal or near‐optimal sample sets to allow reliable application of the method for variable image dimensions.Methods:To investigate the impact of the Noquist method and its experimental parameters on the SNR in the image reconstructed from reduced data, and to explore optimization of methods for highest SNR stability, three different optimization parameters have been selected: the condition of the forward matrix (Rcond) as it defines the propagation of noise into the reconstructed image, and the maximum (ΦmaxD) and the mean (ΦmeanD) linear noise amplification factor of the dynamic field‐of‐view (FOV) region. As SNR in a Noquist reconstruction is often not uniform across the FOV and since dynamic regions may contain the part of the image more clinically relevant, primarily these noise levels are targeted for optimization. Using these three optimization parameters, three experiments were conducted: characterization of Noquist SNR properties as a function of important image size parameters; for sufficiently small image dimensions, employment of exhaustive search using lexicographical algorithms to visit all possibilities under the cine imaging constraint that equal numbers of views are acquired at each time point of the sequence; and, departing from an hypothetically optimal pattern, generation and evaluation of SNR characteristics of a series of random variations to that optimal pattern.Results:The impact of favorable sparse data selection is illustrated, and SNR properties are characterized as a function of relevant acquisition parameters. Optimal data selection is investigated by exhaustive methods for small image sizes, and compared with algorithmic selection patterns. Observations from these experiments are confirmed by further studies on data selection for realistic image dimensions and an optimal selection algorithm is proposed. Sixty‐four cases of small image sizes were analyzed through exhaustive search with a total of 527 984 141 matrix inversions called in the process, evaluating several SNR parameters for each case. An algorithm, named “Stairwell,” that permits to design image dimensions with optimal SNR characteristics is presented, evaluated and compared with cases analyzed through exhaustive search. In 71.9% of the cases exhaustively studied, the Stairwell algorithm yielded optimal solutions. For no case did the deviation from optimum exceed 3.2% (Rcond), 1.0% (ΦmeanD), and 4.9% (ΦmaxD).Conclusions:We have demonstrated SNR‐optimality of the “Stairwell” selection algorithm for small image dimensions, and performed additional experiments which all support hypothesized optimality of the algorithm for any image dimensions that satisfy certain symmetry constraints for Noquist reduced‐data cine MR imaging. Furthermore, we have presented overall SNR characteristics associated with use of the Noquist method by this algorithm for practical clinical image dimensions. Additionally, observations from our optimization experiments allow us to formulate recommendations for dimensioning Noquist image acquisition parameters which guarantee stable inversion. Moreover, these results allow prediction of the anticipated SNR properties of the reconstruction for given image dimensions (S,D,T), relative to SNR in a conventional full‐grid acquisition.