NEW ALGORITHMS FOR COMPRESSED SENSING OF MRI: WTWTS, DWTS, WDWTS

Magnetic resonance imaging (MRI) is one of the most accurate imaging techniques that can be used to detect several diseases, where other imaging methodologies fail. MRI data takes a longer time to capture. This is a pain taking process for the patients to remain still while the data is being captured. This is also hard for the doctor as well because if the images are not captured correctly then it will lead to wrong diagnoses of illness that might put the patients lives in danger. Since long scanning time is one of most serious drawback of the MRI modality, reducing acquisition time for MRI acquisition is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory is an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse signals while projection on a low dimensional linear subspace. Further enhancements have extended the CS framework by performing Variable Density Sampling (VDS) or using wavelet domain as sparsity basis generator. Recent work in this approach considers parent-child relations in the wavelet levels. This paper further extends the prior approach by utilizing the entire wavelet tree structure as an argument for coefficient correlation and also considers the directionality of wavelet coefficients using Hybrid Directional Wavelets (HDW). Incorporating coefficient thresholding in both wavelet tree structure as well as directional wavelet tree structure, the experiments reveal higher Signal to Noise ratio (SNR), Peak Signal to Noise ratio (PSNR) and lower Mean Square Error (MSE) for the CS based image reconstruction approach. Exploiting the sparsity of wavelet tree using the above-mentioned techniques achieves further lessening for data needed for the reconstruction, while improving the reconstruction result. These techniques are applied on a variety of images including both MRI and non-MRI data. The results show the efficacy of our techniques

Accelerating MRI Data Acquisition Using Parallel Imaging and Compressed Sensing

Magnetic Resonance Imaging (MRI) scanners are one of important medical instruments, which can achieve more information of soft issues in human body than other medical instruments, such as Ultrasound, Computed Tomography (CT), Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET), etc. But MRI\u27s scanning is slow for patience of doctors and patients. In this dissertation, the author proposes some methods of parallel imaging and compressed sensing to accelerate MRI data acquisition. Firstly, a method is proposed to improve the conventional GRAPPA using cross-sampled auto-calibration data. This method use cross-sampled auto-calibration data instead of the conventional parallel-sampled auto-calibration data to estimate the linear kernel model of the conventional GRAPPA. The simulations and experiments show that the cross-sampled GRAPPA can decrease the quantity of ACS lines and reduce the aliasing artifacts comparing to the conventional GRAPPA under same reduction factors. Secondly, a Hybrid encoding method is proposed to accelerate the MRI data acquisition using compressed sensing. This method completely changes the conventional Fourier encoding into Hybrid encoding, which combines the benefits of Fourier and Circulant random encoding, under 2D and 3D situation, through the proposed special hybrid encoding pulse sequences. The simulations and experiments illustrate that the images can be reconstructed by the proposed Hybrid encoding method to reserve more details and resolutions than the conventional Fourier encoding method. Thirdly, a pseudo 2D random sampling method is proposed by dynamically swapping the gradients of x and y axes on pulse sequences, which can be implemented physically as the convention 1D random sampling method. The simulations show that the proposed method can reserve more details than the convention 1D random sampling method. These methods can recover images to achieve better qualities under same situations than the conventional methods. Using these methods, the MRI data acquisitions can be accelerated comparing to the conventional methods

APPLICATION OF SPARSE DICTIONARY LEARNING TO SEISMIC DATA RECONSTRUCTION

According to the principle of compressed sensing (CS), under-sampled seismic data can be interpolated when the data becomes sparse in a transform domain. To sparsify the data, dictionary learning presents a data-driven approach trained to be optimized for each target dataset. This study presents an interpolation method for seismic data in which dictionary learning is employed to improve the sparsity of data representation using improved Kth Singular Value Decomposition (K-SVD). In this way, the transformation will be highly compatible with the input data, and the data in the converted domain will be sparser. In addition, the sampling matrix is produced with the restricted isometry property (RIP). To reduce the sensitivity of the minimizer term to the outliers, we use the smooth L1 minimizer as a regularization term in the regularized orthogonal matching pursuit (ROMP). We apply the proposed method to both synthetic and real seismic data. The results show that it can successfully reconstruct the missing seismic traces

Robust and Efficient Inference of Scene and Object Motion in Multi-Camera Systems

Multi-camera systems have the ability to overcome some of the fundamental limitations of single camera based systems. Having multiple view points of a scene goes a long way in limiting the influence of field of view, occlusion, blur and poor resolution of an individual camera. This dissertation addresses robust and efficient inference of object motion and scene in multi-camera and multi-sensor systems. The first part of the dissertation discusses the role of constraints introduced by projective imaging towards robust inference of multi-camera/sensor based object motion. We discuss the role of the homography and epipolar constraints for fusing object motion perceived by individual cameras. For planar scenes, the homography constraints provide a natural mechanism for data association. For scenes that are not planar, the epipolar constraint provides a weaker multi-view relationship. We use the epipolar constraint for tracking in multi-camera and multi-sensor networks. In particular, we show that the epipolar constraint reduces the dimensionality of the state space of the problem by introducing a ``shared'' state space for the joint tracking problem. This allows for robust tracking even when one of the sensors fail due to poor SNR or occlusion. The second part of the dissertation deals with challenges in the computational aspects of tracking algorithms that are common to such systems. Much of the inference in the multi-camera and multi-sensor networks deal with complex non-linear models corrupted with non-Gaussian noise. Particle filters provide approximate Bayesian inference in such settings. We analyze the computational drawbacks of traditional particle filtering algorithms, and present a method for implementing the particle filter using the Independent Metropolis Hastings sampler, that is highly amenable to pipelined implementations and parallelization. We analyze the implementations of the proposed algorithm, and in particular concentrate on implementations that have minimum processing times. The last part of the dissertation deals with the efficient sensing paradigm of compressing sensing (CS) applied to signals in imaging, such as natural images and reflectance fields. We propose a hybrid signal model on the assumption that most real-world signals exhibit subspace compressibility as well as sparse representations. We show that several real-world visual signals such as images, reflectance fields, videos etc., are better approximated by this hybrid of two models. We derive optimal hybrid linear projections of the signal and show that theoretical guarantees and algorithms designed for CS can be easily extended to hybrid subspace-compressive sensing. Such methods reduce the amount of information sensed by a camera, and help in reducing the so called data deluge problem in large multi-camera systems

Model-Based Acquisition for Compressive Sensing & Imaging

Compressive sensing (CS) is a novel imaging technology based on the inherent redundancy of natural scenes. The minimum number of required measurements which defines the maximum image compression rate is lower-bounded by the sparsity of the image but is dependent on the type of acquisition patterns employed. Increased measurements by the Rice single pixel camera (SPC) slows down the acquisition process, which may cause the image recovery to be more susceptible to background noise and thus limit CS's application in imaging, detection, or classifying moving targets. In this study, two methods (hybrid-subspace sparse sampling (HSS) for imaging and secant projection on a manifold for classification are applied to solving this problem. For the HSS method, new image pattern are designed via robust principle component analysis (rPCA) on prior knowledge from a library of images to sense a common structure. After measuring coarse scale commonalities, the residual image becomes sparser, and then fewer measurements are needed. For the secant projection case, patterns that can preserve the pairwise distance between data points based on manifold learning are designed via semi-definite programming. These secant patterns turn out to be better in object classification over those learned from PCA. Both methods considerably decrease the number of required measurements for each task when compared with the purely random patterns of a more universal CS imaging system

Side Information in Coded Aperture Compressive Spectral Imaging

Coded aperture compressive spectral imagers sense a three-dimensional cube by using two-dimensional projections of the coded and spectrally dispersed source. These imagers systems often rely on FPA detectors, SLMs, micromirror devices (DMDs), and dispersive elements. The use of the DMDs to implement the coded apertures facilitates the capture of multiple projections, each admitting a different coded aperture pattern. The DMD allows not only to collect the sufficient number of measurements for spectrally rich scenes or very detailed spatial scenes but to design the spatial structure of the coded apertures to maximize the information content on the compressive measurements. Although sparsity is the only signal characteristic usually assumed for reconstruction in compressing sensing, other forms of prior information such as side information have been included as a way to improve the quality of the reconstructions. This paper presents the coded aperture design in a compressive spectral imager with side information in the form of RGB images of the scene. The use of RGB images as side information of the compressive sensing architecture has two main advantages: the RGB is not only used to improve the reconstruction quality but to optimally design the coded apertures for the sensing process. The coded aperture design is based on the RGB scene and thus the coded aperture structure exploits key features such as scene edges. Real reconstructions of noisy compressed measurements demonstrate the benefit of the designed coded apertures in addition to the improvement in the reconstruction quality obtained by the use of side information

Compressed sensing in fluorescence microscopy.

Compressed sensing (CS) is a signal processing approach that solves ill-posed inverse problems, from under-sampled data with respect to the Nyquist criterium. CS exploits sparsity constraints based on the knowledge of prior information, relative to the structure of the object in the spatial or other domains. It is commonly used in image and video compression as well as in scientific and medical applications, including computed tomography and magnetic resonance imaging. In the field of fluorescence microscopy, it has been demonstrated to be valuable for fast and high-resolution imaging, from single-molecule localization, super-resolution to light-sheet microscopy. Furthermore, CS has found remarkable applications in the field of mesoscopic imaging, facilitating the study of small animals' organs and entire organisms. This review article illustrates the working principles of CS, its implementations in optical imaging and discusses several relevant uses of CS in the field of fluorescence imaging from super-resolution microscopy to mesoscopy