Magnetic resonance is an imaging modality that does not involve patient irradiation or significant side effects, while maintaining a high spatial resolution. However, the need for a strong and homogeneous magnetic field causes limitations of size, cost and availability, so that the benefits of MRI are not used to their full potential. Open-coil systems such as the NMR-MOUSE (Fig. 1) were developed as a means of non-destructive testing. Imaging with these systems is limited due to strong magnetic field inhomogeneity and low field strength, which result in very long acquisition times.

The objective of this project is to reduce the MOUSE’s acquisition time by atleast 50% without compromising image quality, using partial sampling of the k-space and non-linear reconstruction of the image.

Introduction

The NMR-MOUSE

Compressed Sensing (CS)

• Natural images have a well-documented susceptibility to compression with little or no visual loss of information (JPEG, MPEG…).

• According to the CS approach, it is possible to acquire the compressed information directly from a small number of samples ‘Undersampling’

• Undersampling violates the Nyquist criterion aliasing

• To avoid aliasing Lustig et al. (2007) proposed random undersampling incoherent artifacts that behave much like additive random noise.

• Random undersampling is performed by:1. Building a probability density function:

pdf = (1 – r)p s.t. pdf (center) = 12. Generating a sampling pattern using the logical expression:

random[0,1] < pdf (m,n)

Method #1

Incoherent artifacts afterrandom k-space undersampling

1

The pdf

Reconstruction

• Lustig et al. offered performing the CS image reconstruction using a nonlinear conjugate gradient method. This requires solving the following optimization problem: ψ – the sparsifying transform operator (wavelet, DCT…), m – the reconstructed image, Fu – the undersampled Fourier operator,

y – the measured k-space data

• The missing k-space data is not filled. Instead, the image is changed until an optimal solution is reached: mk+1 = mk + tΔm (t = step size)

Method #2

Promote image sparsity

Maintain data consistency

minimize ||ψm||1 s.t. ||Fum – y||2 < ε

Results

The probability density function (pdf) The sampling pattern

15%30%

RMS: 15.5 9.6 4.6

50%

Matlab simulationCS reconstruction atvarious undersamplingrates

30% undersampling

Matlab simulation 30% undersampling

Full samplingNon-random

undersamplingLow resolution

Randomundersampling

+ CS reconstruction

Future work involves applying a sampling scheme that exploits the fact that samples in every scan are averaged. The general concept is to fully sample the k-space in the first few scans, and then use these scans to determine the significant spatial frequencies of the image and thus optimize undersampling.

Fast imaging using an NMR device with a weak and non-homogeneous magnetic fieldMiri Belgart, Dr. Uri Nevo

Dept. of Biomedical Engineering, Tel-Aviv University

Randomundersampling

+ 2D IFFT