Signal processing for microwave imaging systems with very sparse array

This dissertation investigates image reconstruction algorithms for near-field, two dimensional (2D) synthetic aperture radar (SAR) using compressed sensing (CS) based methods. In conventional SAR imaging systems, acquiring higher-quality images requires longer measuring time and/or more elements in an antenna array. Millimeter wave imaging systems using evenly-spaced antenna arrays also have spatial resolution constraints due to the large size of the antennas. This dissertation applies the CS principle to a bistatic antenna array that consists of separate transmitter and receiver subarrays very sparsely and non-uniformly distributed on a 2D plane. One pair of transmitter and receiver elements is turned on at a time, and different pairs are turned on in series to achieve synthetic aperture and controlled random measurements. This dissertation contributes to CS-hardware co-design by proposing several signal-processing methods, including monostatic approximation, re-gridding, adaptive interpolation, CS-based reconstruction, and image denoising. The proposed algorithms enable the successful implementation of CS-SAR hardware cameras, improve the resolution and image quality, and reduce hardware cost and experiment time. This dissertation also describes and analyzes the results for each independent method. The algorithms proposed in this dissertation break the limitations of hardware configuration. By using 16 x 16 transmit and receive elements with an average space of 16 mm, the sparse-array camera achieves the image resolution of 2 mm. This is equivalent to six percent of the λ/4 evenly-spaced array. The reconstructed images achieve similar quality as the fully-sampled array with the structure similarity (SSIM) larger than 0.8 and peak signal-to-noise ratio (PSNR) greater than 25 --Abstract, page iv

A novel approach to visibility-space modelling of interferometric gravitational lens observations at high angular resolution

We present a new gravitational lens modelling technique designed to model high-resolution interferometric observations with large numbers of visibilities without the need to pre-average the data in time or frequency. We demonstrate the accuracy of the method using validation tests on mock observations. Using small data sets with $\sim 10^3$ visibilities, we first compare our approach with the more traditional direct Fourier transform (DFT) implementation and direct linear solver. Our tests indicate that our source inversion is indistinguishable from that of the DFT. Our method also infers lens parameters to within 1 to 2 per cent of both the ground truth and DFT, given sufficiently high signal-to-noise ratio (SNR). When the SNR is as low as 5, both approaches lead to errors of several tens of per cent in the lens parameters and a severely disrupted source structure, indicating that this is an issue related to the data quality rather than the modelling technique of choice. We then analyze a large data set with $\sim 10^8$ visibilities and a SNR matching real global Very Long Baseline Interferometry observations of the gravitational lens system MG J0751+2716. The size of the data is such that it cannot be modelled with traditional implementations. Using our novel technique, we find that we can infer the lens parameters and the source brightness distribution, respectively, with an RMS error of 0.25 and 0.97 per cent relative to the ground truth.Comment: Submitted to MNRA

Improved 3D MR Image Acquisition and Processing in Congenital Heart Disease

Congenital heart disease (CHD) is the most common type of birth defect, affecting about 1% of the population. MRI is an essential tool in the assessment of CHD, including diagnosis, intervention planning and follow-up. Three-dimensional MRI can provide particularly rich visualization and information. However, it is often complicated by long scan times, cardiorespiratory motion, injection of contrast agents, and complex and time-consuming postprocessing. This thesis comprises four pieces of work that attempt to respond to some of these challenges. The first piece of work aims to enable fast acquisition of 3D time-resolved cardiac imaging during free breathing. Rapid imaging was achieved using an efficient spiral sequence and a sparse parallel imaging reconstruction. The feasibility of this approach was demonstrated on a population of 10 patients with CHD, and areas of improvement were identified. The second piece of work is an integrated software tool designed to simplify and accelerate the development of machine learning (ML) applications in MRI research. It also exploits the strengths of recently developed ML libraries for efficient MR image reconstruction and processing. The third piece of work aims to reduce contrast dose in contrast-enhanced MR angiography (MRA). This would reduce risks and costs associated with contrast agents. A deep learning-based contrast enhancement technique was developed and shown to improve image quality in real low-dose MRA in a population of 40 children and adults with CHD. The fourth and final piece of work aims to simplify the creation of computational models for hemodynamic assessment of the great arteries. A deep learning technique for 3D segmentation of the aorta and the pulmonary arteries was developed and shown to enable accurate calculation of clinically relevant biomarkers in a population of 10 patients with CHD

Sparse nonlinear optimization for signal processing and communications

This dissertation proposes three classes of new sparse nonlinear optimization algorithms for network echo cancellation (NEC), 3-D synthetic aperture radar (SAR) image reconstruction, and adaptive turbo equalization in multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications, respectively. For NEC, the proposed two proportionate affine projection sign algorithms (APSAs) utilize the sparse nature of the network impulse response (NIR). Benefiting from the characteristics of l₁-norm optimization, affine projection, and proportionate matrix, the new algorithms are more robust to impulsive interferences and colored input than the conventional adaptive algorithms. For 3-D SAR image reconstruction, the proposed two compressed sensing (CS) approaches exploit the sparse nature of the SAR holographic image. Combining CS with the range migration algorithms (RMAs), these approaches can decrease the load of data acquisition while recovering satisfactory 3-D SAR image through l₁-norm optimization. For MIMO UWA communications, a robust iterative channel estimation based minimum mean-square-error (MMSE) turbo equalizer is proposed for large MIMO detection. The MIMO channel estimation is performed jointly with the MMSE equalizer and the maximum a posteriori probability (MAP) decoder. The proposed MIMO detection scheme has been tested by experimental data and proved to be robust against tough MIMO channels. --Abstract, page iv

Magnetic Resonance Imaging of Short-T2 Tissues with Applications for Quantifying Cortical Bone Water and Myelin

The human body contains a variety of tissue species with short T2 ranging from a few microseconds to hundreds of microseconds. Detection and quantification of these short-T2 species is of considerable clinical and scientific interest. Cortical bone water and myelin are two of the most important tissue constituents. Quantification of cortical bone water concentration allows for indirect estimation of bone pore volume and noninvasive assessment of bone quality. Myelin is essential for the proper functioning of the central nervous system (CNS). Direct assessment of myelin would reveal CNS abnormalities and enhance our understanding of neurological diseases. However, conventional MRI with echo times of several milliseconds or longer is unable to detect these short-lived MR signals. Recent advances in MRI technology and hardware have enabled development of a number of short-T2 imaging techniques, key among which are ultra-short echo time (UTE) imaging, zero echo time (ZTE) imaging, and sweep imaging with Fourier transform (SWIFT). While these pulse sequences are able to detect short-T2 species, they still suffer from signal interference between different T2 tissue constituents, image artifacts and excessive scan time. These are primary technical hurdles for application to whole-body clinical scanners. In this thesis research, new MRI techniques for improving short-T2 tissue imaging have been developed to address these challenges with a focus on direct detection and quantification of cortical bone water and myelin on a clinical MRI scanner. The first focus of this research was to optimize long-T2 suppression in UTE imaging. Saturation and adiabatic RF pulses were designed to achieve maximum long-T2 suppression while maximizing the signal from short-T2 species. The imaging protocols were optimized by Bloch equation simulations and were validated using phantom and in vivo experiments. The results show excellent short-T2 contrast with these optimized pulse sequences. The problem of blurring artifacts resulting from the inhomogeneous excitation profile of the rectangular pulses in ZTE imaging was addressed. The proposed approach involves quadratic phase-modulated RF excitation and iterative solution of an inverse problem formulated from the signal model of ZTE imaging and is shown to effectively remove the image artifacts. Subsequently image acquisition efficiency was improved in order to attain clinically-feasible scan times. To accelerate the acquisition speed in UTE and ZTE imaging, compressed sensing was applied with a hybrid 3D UTE sequence. Further, the pulse sequence and reconstruction procedure were modified to enable anisotropic field-of-view shape conforming to the geometry of the elongated imaged object. These enhanced acquisition techniques were applied to the detection and quantification of cortical bone water. A new biomarker, the suppression ratio (a ratio image derived from two UTE images, one without and the other with long-T2 suppression), was conceived as a surrogate measure of cortical bone porosity. Experimental data suggest the suppression ratio may be a more direct measure of porosity than previously measured total bone water concentration. Lastly, the feasibility of directly detecting and quantifying spatially-resolved myelin concentration with a clinical imager was explored, both theoretically and experimentally. Bloch equation simulations were conducted to investigate the intrinsic image resolution and the fraction of detectable myelin signal under current scanner hardware constraints. The feasibility of quantitative ZTE imaging of myelin extract and lamb spinal cord at 3T was demonstrated. The technological advances achieved in this dissertation research may facilitate translation of short-T2 MRI methods from the laboratory to the clinic

Coupled Dictionary Learning for Multi-contrast MRI Reconstruction

Magnetic resonance (MR) imaging tasks often involve multiple contrasts, such as T1-weighted, T2-weighted and Fluid-attenuated inversion recovery (FLAIR) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities in either structure level or gray level. In this paper, we propose a Coupled Dictionary Learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage the dependency correlation between different contrasts for guided or joint reconstruction from their under-sampled k-space data. Our approach iterates between three stages: coupled dictionary learning, coupled sparse denoising, and enforcing k-space consistency. The first stage learns a set of dictionaries that not only are adaptive to the contrasts, but also capture correlations among multiple contrasts in a sparse transform domain. By capitalizing on the learned dictionaries, the second stage performs coupled sparse coding to remove the aliasing and noise in the corrupted contrasts. The third stage enforces consistency between the denoised contrasts and the measurements in the k-space domain. Numerical experiments, consisting of retrospective under-sampling of various MRI contrasts with a variety of sampling schemes, demonstrate that CDLMRI is capable of capturing structural dependencies between different contrasts. The learned priors indicate notable advantages in multi-contrast MR imaging and promising applications in quantitative MR imaging such as MR fingerprinting

Advancing Magnetic Resonance Spectroscopy and Endoscopy with Prior Knowledge

Reconstruction is key to the generation of anatomic, functional and biochemical information in the field of Magnetic Resonance (MR) in medicine. Here, prior knowledge based on various conditions is utilized through reconstruction to accelerate current MR techniques and reduce artifacts. First, prior knowledge from Magnetic Resonance Imaging (MRI) is exploited to accelerate spatial localization in Magnetic Resonance Spectroscopy (MRS). The MRS information is contained in one extra chemical shift dimension, beyond the three spatial dimensions of MRI, and can provide valuable in vivo metabolic information for the study of numerous diseases. However, its research and clinical applications are often compromised by long scan times. Here, a new method of localized Spectroscopy with Linear Algebraic Modeling (SLAM) is proposed for accelerating MRS scans. The method assumes pre-conditions that the MRS scan is preceded by a scout MRI scan and that a compartment-averaged MRS measurement will suffice for the assessment of metabolic status. SLAM builds a priori MRI-based segmentation information into the standard Fourier-encoded MRS model of chemical shift imaging (CSI), to directly reconstruct compartmental spectra. Second, SLAM is extended to higher dimensions and to incorporate parallel imaging techniques that deploy pre-acquired sensitivity information based on the use of separate multiple receive-coil elements, to further accelerate scan speed. In addition, eddy current-induced phase effects are incorporated into the SLAM model, and a modified reconstruction algorithm provides improved suppression of signal leakage due to heterogeneity in the MRS signal, especially when employing sensitivity encoding. Third, prior information from MRI is also used to reduce the problem of lipid artifacts in 1H brain CSI. CSI is routinely used for human brain MRS studies, and low spatial resolution in CSI causes partial volume error and signal ‘bleed’ that is especially deleterious to voxels near the scalp. A standard solution is to apply spatial apodization, which adversely affects spatial resolution. Here, a novel automated strategy for partial volume correction that employs grid shifting (‘PANGS’) is presented, which minimizes lipid signal bleed without compromising spatial resolution. PANGS shifts the reconstruction coordinate in a designated region of image space—the scalp, identified by MRI—to match the tissue center of mass instead of the geometric center of each voxel. Last, prior knowledge of the spatially sparse nature of endoscopic MRI images acquired with tiny internal MRI antennae, and that of the null signal location of the endoscopic probe, are used to accelerate MR endoscopy and reduce motion artifacts. High-resolution endoscopic MRI is susceptible to degradation from physiological motion, which can necessitate time-consuming cardiac gating techniques. Here, we develop acceleration techniques based on the compressed sensing theory, and un-gated motion compensation strategies using projection shifting, to effectively produce faster motion-suppressed MRI endoscopy