Onur Afacan, Abstract Co-Author: Nothing to Disclose

Dana H. Brooks, Abstract Co-Author: Nothing to Disclose

Robert Vincent Mulkern PhD, Abstract Co-Author: Nothing to Disclose

Dimitris Mitsouras PhD, Presenter: Nothing to Disclose

To systematically compare 2D CS k-space sampling schemes and associated MRI reconstruction methods using precise SNR and RMS error metrics.

Linearly and quadratically decreasing, and piecewise-constant density 2D spiral trajectories were generated at 40 undersampling levels for nominal resolutions between 2.54 (none) to 1.82mm (max undersampling). Five reconstruction methods were applied to data acquired/simulated for each of the 160 trajectories: linear FFT/Pipe-Menon DC,F or L2-norm, and, CS L1-, Total Variation (TV)-, or combined L1/TV-norm. Results were obtained for a simulated phantom and a Magphan phantom at 1.5T. Experiments were repeated 100-fold for each trajectory. SNR was summarized by the average pixel SD in the FOV and over the 10% of the FOV exhibiting the highest SD. RMS error was similarly summarized. An “error probability map” was developed as the number of times a pixel’s value was in the top quartile of residuals.

This study summarized 16,000 acquisitions/reconstructions of a 2D image. SNR differed slightly between trajectories, following theoretical expectations. However, for CS compared to linear reconstruction, pixel SD was as much as 2- to 3.5-fold higher in the 10% of pixels with highest noise (Figure). With CS, high-uncertainty pixels mirrored the “inverse” of the CS transform functional (e.g., regions of high signal for L1-, or, image edges for TV-norm). Linear reconstructions had the highest RMSE (Figure), but traded aliasing error for high-resolution information more readily than CS reconstructions. For both SNR and RMSE, better FOV-average performance of CS reconstruction was directly related to image sparsity in the transform domain (the more sparse, the better the performance).

CS MRI reconstruction yields more accurate images than linear reconstruction on average, but this accuracy is accompanied by increased uncertainty from one scan to the next, driven by changes in sample noise.

CS MRI increases uncertainty as to whether an image contains a given feature (e.g., localized hypointensity) because of the particular instantiation of signal noise, or because it is truly present in the underlying spin density. The ability to determine with more precision whether a clinically significant variation of MRI signal occurs will likely depend on the choice of CS transform domain and its parameters.

Afacan, O, Brooks, D, Mulkern, R, Mitsouras, D, An Uncertainty Principle for “Compressed Sensing” (CS) MRI: Trajectory Choice and Reconstruction Algorithm Effects on Image Accuracy.  Radiological Society of North America 2014 Scientific Assembly and Annual Meeting, - ,Chicago IL. http://archive.rsna.org/2014/14011860.html