Purpose: To investigate the modulation transfer function (MTF) behavior of compressed sensing (CS) MR spectroscopic imaging (MRSI) with regard to CS reconstruction weights and the acquired peak signal-to-noise ratio (SNR); which may have an effect on MTF due to the nonlinear nature of the CS reconstruction process.
Methods: A specially designed phantom consisting of wedges arranged in a fan pattern was used to calculate the MTF of the MRSI scans. Arc profiles of the phantom yield a square wave with a spatial frequency inversely proportional to the radius of the profile. The MTF was derived by considering the amplitude ratio of the fundamental frequency between the ideal square wave and the reconstructed output. As compressed sensing relies on nonlinear reconstruction and a minimization algorithm that requires the definition of reconstruction weights, the behavior of the MTF with respect to the choice of reconstruction weights and peak SNR is not intuitive. As such, simulations were used to investigate the response of the MTF to CS reconstruction weights at varying peak SNRs. The resulting optimized reconstruction weight was used to reconstruct an experimental CS-MRSI scan of the phantom and compare the corresponding MTF to those of a fully sampled dataset, and a time-equivalent Nyquist-sampled low-resolution dataset.
Results: Simulations showed that MTFs of CS-MRSI datasets varied widely with different reconstruction weights. Moreover, the response of the MTF to peak SNR was not consistent across the range of reconstruction weights. An optimized reconstruction weight was derived from the simulations and used in reconstructing the experimental dataset. The MTF of the experimental CS-MRSI dataset showed improvement over the equivalent Nyquist sampled dataset at the resolution limit of 0.1 MTF, while it suffered from reduced response at low resolutions between 0.4 and 0.8 lp/cm.
Conclusions: The authors have shown that in certain cases small variations in the reconstruction weights yield a measureable effect on the CS reconstructed images, particularly with regard to MTF. Furthermore, it was found that peak SNR affects CS-MRSI MTF especially at higher wavelet reconstruction weights. Accordingly, prior knowledge of the expected peak SNR is essential to optimize the CS reconstruction process. Their phantom-MTF technique provides a quantitative performance measure of MRSI sequences, through which they were able to quantify a loss of 32.4% in spatial resolution for CS-MRSI at 0.1 MTF compared to a loss of 48.6% for the time-equivalent Nyquist-sampled low-resolution scans. They also showed that CS-MRSI suffered decreased low-resolution response as opposed to the equivalent low-resolution datasets.