Basic study of random sampling for compressed sensing using MRI simulator

Magnetic resonance imaging (MRI) is a tomography technology that enables the depiction of anatomical structures with information about various features. Compressed sensing (CS) technology has recently been used for magnetic resonance image reconstruction from sparse information. Random sampling methods based on the various probability density function (PDF) are being developed to allow the efficient application of CS technology. Accurate numerical simulation is obviously important for the evaluation of the sampling method that are developed. In this study, the simulation method with MRI simulator and actual MRI scanner was carried out. Moreover, the difference between the result acquired from our simulation and basic one was revealed.

We first examined a basic method using a 2D Shepp-Logan phantom. This method was only conducted with k-space data obtained from the 2D Fourier transform of the original image. Our method of numerical simulation was applied with the MRI simulator (Bloch Solver, MRI simulations Inc.), an actual MRI system (Vantage Titan 3T, Canon Medical Systems) and a phantom (CAGN-3.0T phantom, Kato Medience). The real and imaginary part of the k-space were acquired with the MRI simulator using a phase map that was imaged by the actual MRI scanner. Random sampling was performed with two types of PDF and image reconstruction was processed by projection onto convex sets (POCS). Hermitian symmetry is a point-symmetry respect to origin and each point located on the opposite side maintains a relation of complex conjugate. Thus, there is no need to acquire data that formed in point-symmetry with the data that had already been acquired. We used the gaussian random sampling method (GA) and a method that considered Hermitian symmetry (GH). The image quality was evaluated using the normalized root mean squared error (NRMSE).

In the basic simulation, the average and standard deviation of NRMSE from GH was better than that from GA because consideration of the Hermitian symmetry enables the efficient acquisition of data. However, in our method of numerical simulation, the average and standard deviation of the NRMSE from GH was worse than that from GA. In this simulation method, the phase error was included in the real and imaginary part of the k-space; thus, the Hermitian symmetry cannot hold and the calculation error of reconstruction images from GH stood out.

The method of numerical simulation with the MRI simulator using a phase map was close to the actual conditions and was considered to be useful for the validation of new sampling methods. The random sampling method using GH is expected to be useful for the highly efficient acquisition of data under ideal conditions; however, more accurate phase correction is necessary to apply the actual measurement data.