Chaotic Compressed Sensing and Its Application to Magnetic Resonance Imaging

Fast image acquisition in magnetic resonance imaging (MRI) is important, due to the need to find ways that help relieve patient’s stress during MRI scans. Methods for fast MRI have been proposed, most notably among them are pMRI (parallel MRI), SWIFT (SWeep Imaging with Fourier Transformation), and compressed sensing (CS) based MRI. Although it promises to significantly reduce acquisition time, applying CS to MRI leads to difficulties with hardware design because of the randomness nature of the measurement matrix used by the conventional CS methods. In this paper, we propose a novel method that combines the above-mentioned three approaches for fast MRI by designing a compound measurement matrix from a series of single measurement matrices corresponding to pMRI, SWIFT, and CS. In our method, the CS measurement matrix is designed to be deterministic via chaotic systems. This chaotic compressed sensing (CCS) measurement matrix, while retaining most features of the random CS matrix, is simpler to realize in hardware. Several compound measurement matrices have been constructed and examined in this work, including CCS-MRI, CCS-pMRI, CCS-SWIFT, and CCS-pSWIFT. Simulation results showed that the proposed method allows an increase in the speed of the MRI acquisition process while not compromising the quality of the acquired MR images

Fractal Compressive Sensing

This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and one-dimensional (1D) trajectories derived from the discrete Radon transform (DRT). Unlike radial trajectories, DRT projections can be back-projected without interpolation. Thus, we also propose a novel reconstruction method based on the exact projections of the DRT called finite Fourier reconstruction (FFR). We term this combined p.frac and FFR strategy, finite compressive sensing (FCS), with image recovery demonstrated on experimental and simulated data; image quality comparisons are made with Cartesian random sampling in 1D and two-dimensional (2D), as well as radial under-sampling in a more constrained experiment. Our experiments indicate FCS enables 3-5dB gain in peak signal-to-noise ratio (PSNR) for 2-, 4- and 8-fold under-sampling compared to 1D Cartesian random sampling. This paper aims to: Review common sampling strategies for compressed sensing (CS)-magnetic resonance imaging (MRI) to inform the motivation of a projective and Cartesian sampling scheme. Compare the incoherence of these sampling strategies and the proposed p.frac. Compare reconstruction quality of the sampling schemes under various reconstruction strategies to determine the suitability of p.frac for CS-MRI. It is hypothesised that because p.frac is a highly incoherent sampling scheme, that reconstructions will be of high quality compared to 1D Cartesian phase-encode under-sampling.Comment: 12 pages, 10 figures, 1 tabl

Perturbed spiral real-time phase-contrast MR with compressive sensing reconstruction for assessment of flow in children

PURPOSE: we implemented a golden‐angle spiral phase contrast sequence. A commonly used uniform density spiral and a new ‘perturbed’ spiral that produces more incoherent aliases were assessed. The aim was to ascertain whether greater incoherence enabled more accurate Compressive Sensing reconstruction and superior measurement of flow and velocity. METHODS: A range of ‘perturbed’ spiral trajectories based on a uniform spiral trajectory were formulated. The trajectory that produced the most noise‐like aliases was selected for further testing. For in‐silico and in‐vivo experiments, data was reconstructed using total Variation L1 regularisation in the spatial and temporal domains. In‐silico, the reconstruction accuracy of the ‘perturbed’ golden spiral was compared to uniform density golden‐angle spiral. For the in‐vivo experiment, stroke volume and peak mean velocity were measured in 20 children using ‘perturbed’ and uniform density golden‐angle spiral sequences. These were compared to a reference standard gated Cartesian sequence. RESULTS: In‐silico, the perturbed spiral acquisition produced more accurate reconstructions with less temporal blurring (NRMSE ranging from 0.03 to 0.05) than the uniform density acquisition (NRMSE ranging from 0.06 to 0.12). This translated in more accurate results in‐vivo with no significant bias in the peak mean velocity (bias: −0.1, limits: −4.4 to 4.1 cm/s; P = 0.98) or stroke volume (bias: −1.8, limits: −9.4 to 5.8 ml, P = 0.19). CONCLUSION: We showed that a ‘perturbed’ golden‐angle spiral approach is better suited to Compressive Sensing reconstruction due to more incoherent aliases. This enabled accurate real‐time measurement of flow and peak velocity in children

Chaotic Sensing

We propose a sparse imaging methodology called Chaotic Sensing (ChaoS) that enables the use of limited yet deterministic linear measurements through fractal sampling. A novel fractal in the discrete Fourier transform is introduced that always results in the artefacts being turbulent in nature. These chaotic artefacts have characteristics that are image independent, facilitating their removal through dampening (via image denoising) and obtaining the maximum likelihood solution. In contrast with existing methods, such as compressed sensing, the fractal sampling is based on digital periodic lines that form the basis of discrete projected views of the image without requiring additional transform domains. This allows the creation of finite iterative reconstruction schemes in recovering an image from its fractal sampling that is also new to discrete tomography. As a result, ChaoS supports linear measurement and optimisation strategies, while remaining capable of recovering a theoretically exact representation of the image. We apply the method to simulated and experimental limited magnetic resonance (MR) imaging data, where restrictions imposed by MR physics typically favour linear measurements for reducing acquisition time

Computational polarimetric microwave imaging

We propose a polarimetric microwave imaging technique that exploits recent advances in computational imaging. We utilize a frequency-diverse cavity-backed metasurface, allowing us to demonstrate high-resolution polarimetric imaging using a single transceiver and frequency sweep over the operational microwave bandwidth. The frequency-diverse metasurface imager greatly simplifies the system architecture compared with active arrays and other conventional microwave imaging approaches. We further develop the theoretical framework for computational polarimetric imaging and validate the approach experimentally using a multi-modal leaky cavity. The scalar approximation for the interaction between the radiated waves and the target---often applied in microwave computational imaging schemes---is thus extended to retrieve the susceptibility tensors, and hence providing additional information about the targets. Computational polarimetry has relevance for existing systems in the field that extract polarimetric imagery, and particular for ground observation. A growing number of short-range microwave imaging applications can also notably benefit from computational polarimetry, particularly for imaging objects that are difficult to reconstruct when assuming scalar estimations.Comment: 17 pages, 15 figure

Acceleration of Subtractive Non-contrast-enhanced Magnetic Resonance Angiography

Although contrast-enhanced magnetic resonance angiography (CE-MRA) is widely established as a clinical examination for the diagnosis of human vascular diseases, non-contrast-enhanced MRA (NCE-MRA) techniques have drawn increasing attention in recent years. NCE-MRA is based on the intrinsic physical properties of blood and does not require the injection of any exogenous contrast agents. Subtractive NCE-MRA is a class of techniques that acquires two image sets with different vascular signal intensity, which are later subtracted to generate angiograms. The long acquisition time is an important drawback of NCE-MRA techniques, which not only limits the clinical acceptance of these techniques but also renders them sensitive to artefacts from patient motion. Another problem for subtractive NCE-MRA is the unwanted residual background signal caused by different static background signal levels on the two raw image sets. This thesis aims at improving subtractive NCE-MRA techniques by addressing both these limitations, with a particular focus on three-dimensional (3D) femoral artery fresh blood imaging (FBI). The structure of the thesis is as follows: Chapter 1 describes the anatomy and physiology of the vascular system, including the characteristics of arteries and veins, and the MR properties and flow characteristics of blood. These characteristics are the foundation of NCE-MRA technique development. Chapter 2 introduces commonly used diagnostic angiographic methods, particularly CE-MRA and NCE-MRA. Current NCE-MRA techniques are reviewed and categorised into different types. Their principles, implementations and limitations are summarised. Chapter 3 describes imaging acceleration theories including compressed sensing (CS), parallel imaging (PI) and partial Fourier (PF). The Split Bregman algorithm is described as an efficient CS reconstruction method. The SPIRiT reconstruction for PI and homodyne detection for PF are also introduced and combined with Split Bregman to form the basis of the reconstruction strategy for undersampled MR datasets. Four image quality metrics are presented for evaluating the quality of reconstructed images. In Chapter 4, an intensity correction method is proposed to improve background suppression for subtractive NCE-MRA techniques. Residual signals of background tissues are removed by performing a weighted subtraction, in which the weighting factor is obtained by a robust regression method. Image sparsity can also be increased and thereby potentially benefit CS reconstruction in the following chapters. Chapter 5 investigates the optimal k-space sampling patterns for the 3D accelerated femoral artery FBI sequence. A variable density Poisson-disk with a fully sampled centre region and missing partial Fourier fractions is employed for k-space undersampling in the ky-kz plane. Several key parameters in sampling pattern design, such as partial Fourier sampling ratios, fully sampled centre region size and density decay factor, are evaluated and optimised. Chapter 6 introduces several reconstruction strategies for accelerated subtractive NCE-MRA. A new reconstruction method, k-space subtraction with phase and intensity correction (KSPIC), is developed. By performing subtraction in k-space, KSPIC can exploit the sparsity of subtracted angiogram data and potentially improve the reconstruction performance. A phase correction procedure is used to restore the polarity of negative signals caused by subtraction. The intensity correction method proposed in Chapter 4 is also incorporated in KSPIC as it improves background suppression and thereby sparsity. The highly accelerated technique can be used not only to reduce the acquisition time, but also to enable imaging with increased resolution with no time penalty. A time-efficient high-resolution FBI technique is proposed in Chapter 7. By employing KSPIC and modifying the flow-compensation/spoiled gradients, the image matrix size can be increased from 256×256 to up to 512×512 without prolonging the acquisition time. Chapter 8 summarises the overall achievements and limitations of this thesis, as well as outlines potential future research directions.Cambridge Trust China Scholarship Council Addenbrooke’s Charitable Trust National Institute of Health Research, Cambridge Biomedical Research Cente