Improving the image quality in compressed sensing MRI by the exploitation of data properties

Abstract

Minimizing scan time without compromising image quality has been the main thrust of magnetic resonance imaging (MRI) since the establishment of the field. Tremendous effort has been put into MRI systems in pursuit of faster MR imaging techniques, which can substantially facilitate clinical diagnoses and improve the patient experience. Traditional MRI accelerated approaches mainly focused on hardware improvements to improve the speed of scanning. These methods are still governed by Nyquist-Shannon sampling rate. Hence, when the acceleration rate is pushed beyond the theoretical limit, aliasing artefacts are introduced which degrade the reconstructed image quality and are difficult to eliminate via current methods. Recently, it has been found that a newly developed signal processing theory, compressed sensing (CS), can be used to create high-resolution signal data sets from sparse samples, despite violating the classical Nyquist-Shannon sampling criteria. The application of CS to MRI opens up an appealing avenue to offer potentially significant scan time reductions. CS reconstructs MR images from incomplete k-space measurements. Taking advantage of the fact that MR images have sparse representations under certain mathematical transformations, CS overcomes the distortions resulting from the under-sampled k-space data. Significant progress has been made in the development of CS MRI. However, there are two major remaining challenges to its full adoption in clinical applications: (1) the small amount of under-sampled data (for example, less than 1/8 of the whole k-space data) will inherently introduce artefacts in the reconstructed image and compromise diagnosis accuracy for the reconstructed images; (2) owing to hardware limits, it is difficult to realise two-dimension random under-sampling, which is favoured by CS operation. Practically, the random phase-encode under-sampling pattern has been widely implemented. However, it introduces coherent aliasing artefacts that are hard to eliminate using the CS theory. In this thesis, several techniques are proposed that can improve the quality of images reconstructed by CS MRI. These techniques have the potential to facilitate faithful reconstruction of CS MRI in clinical applications. A novel two-stage reconstruction scheme is introduced in Chapter 3. In this method, the under-sampled k-space data is segmented into low-frequency and high-frequency parts. Then, in stage one, using dense measurements, the low-frequency region of k-space data is faithfully reconstructed. The fully reconstituted low-frequency k-space data from the first stage is then combined with the under-sampled high-frequency k-space data to complete the second stage reconstruction of the whole image. With this two-stage approach, each reconstruction inherently incorporates a lower data under-sampling rate than conventional approaches. Because the restricted isometric property is easier to satisfy than conventional CS method, the reconstruction consequently produces lower residual errors in each step. Results from different MR test cases demonstrate the remarkable improvement in the quality of reconstruction using the proposed approach. Chapter 4 then introduces a novel approach to reduce the aliasing artefacts induced by random phase-encode under-sampling. The proposed reconstruction process is separated into two steps in our new algorithm. In step one, we transfer the original two-dimensional (2D) image reconstruction into a parallel one-dimensional (1D) signal reconstruction procedure, which takes advantage of the superior incoherence property in the phase direction. In step two, using the new k-space data obtained from the 1D reconstructions, we then implement a follow-up 2D CS reconstruction to produce a better solution, which exploits the inherent correlations between the adjacent lines of 1D reconstructed signals. Validated by experiments, the proposed method achieves more accurate reconstruction results and effectively suppresses the coherent artefacts introduced by random phase-encode under-sampling. Chapter 5 introduces a novel non-Cartesian trajectory, a pseudo-polar (PP) trajectory, instead of random phase-encode under-sampling pattern in a Cartesian grid. As a compromise with the hardware limitations, a Cartesian trajectory is widely used in current CS MRI, even though it introduces coherent aliasing artefacts in the corresponding random phase-encode under-sampling pattern. Compared with the conventional Cartesian trajectory, the PP trajectory collects more data from the central k-space region and the radially sampled data are more incoherent. These properties are very suitable for CS based fast imaging. When reconstructing under-sampled PP data with CS, PP Fast Fourier Transform (FFT) is implemented to realize the fast and accurate transform between k-space and image domain. Based on the standard 1D FFT and the Fractional Fourier Transform (FRFT), PPFFT avoids the time-consuming interpolation process in the transform of other non-Cartesian trajectories. Investigated by simulations and in vivo experiments, the proposed scheme provides a practical and accurate CS-based rapid MR imaging method for clinical applications. This thesis presents a series of original research contributions as described above. The key novelty of these CS MRI methods relies upon the exploitation of the features of the MRI data. These methods have been tested with typical MR datasets, and the experimental results suggest that, these innovative methods are capable of producing high quality MRI images with reduced scan time (usually 4-8 times faster). These new CS MRI methods have the potential for both clinical and preclinical applications.