An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]

This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. To make this possible, CS relies on two principles: sparsity, which pertains to the signals of interest, and incoherence, which pertains to the sensing modality. Our intent in this article is to overview the basic CS theory that emerged in the works [1]–[3], present the key mathematical ideas underlying this theory, and survey a couple of important results in the field. Our goal is to explain CS as plainly as possible, and so our article is mainly of a tutorial nature. One of the charms of this theory is that it draws from various subdisciplines within the applied mathematical sciences, most notably probability theory. In this review, we have decided to highlight this aspect and especially the fact that randomness can — perhaps surprisingly — lead to very effective sensing mechanisms. We will also discuss significant implications, explain why CS is a concrete protocol for sensing and compressing data simultaneously (thus the name), and conclude our tour by reviewing important applications

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