1. 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 at least 50% without compromising image quality, using partial sampling of the k-space and non-linear reconstruction of the image. 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 at least 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) = 1 2. Generating a sampling pattern using the logical expression: random[0,1] < pdf (m,n) 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) = 1 2. Generating a sampling pattern using the logical expression: random[0,1] < pdf (m,n) Method #1 Incoherent artifacts after random 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, F u – 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: m k+1 = m k + tΔm ( t = step size) 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, F u – 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: m k+1 = m k + tΔm ( t = step size) Method #2 Promote image sparsity Maintain data consistency minimize ||ψm|| 1 s.t. ||F u m – y|| 2 < ε Results The probability density function (pdf)The sampling pattern 15% 30% RMS: 15.5 9.6 4.6 50% Matlab simulation CS reconstruction at various undersampling rates 30% undersampling Matlab simulation 30% undersampling Full sampling Non-random undersampling Low resolution Random undersampling + 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 field Miri Belgart, Dr. Uri Nevo Dept. of Biomedical Engineering, Tel-Aviv University Random undersampling + 2D IFFT