Image Sparse Reconstruction Based On Compressed Sensing

It’s well known that the traditional Nyquist sampling theory requests that sampling frequency has to be at least twice the highest frequency of the signal. However, under this theory, we are unable to fulfill the requirements of bandwith limitation. Recently, an emerging theory named compressed sensing (CS) has drawn great intention, showed that a signal can be accurately recovered using only a small fraction of the original signal. This theory has been applied into applications such as wireless communication, array signal processing, sensor netowork and biomedical imaging, etc. It’s considered as a breakthrough technology for signal compression, acquiring, transmitting, storing, and recovering, as well as an promising research area in future. The aim of this dissertation is to develop an image reconstruction algorithm, specifically focus on the reconstruction of biomedical images, based on the theory of compressed sensing. Two important problems are discussed in this dissertation, the development of sparse basis and the fast reconstruction algorithm on this special sparse basis. Moreover, a new sampling scheme was proposed in this dissertation. Firstly, we studied the characteristics of Optical Coherence Tomography (OCT) image, and designed a region differential representation model to sparsely represent OCT image; After that, a homotopic ι0minimization algorithm was proposed to solve the optimization problem, based on the specific sparse representation basis; Finally, according to the specific characteristic of energy distribution of OCT image, a new adaptive sparsely sampling scheme was proposed to reduce the sampling fraction. The main contribution of the thesis incudes:1. Sparsly representation of Optical Coherence Tomography imageThe basic prerequisite of using compressed sensing theory for sparsely sampling reconstruction is that the signal itself is sparse or can be sparsely represented by a specific basis. Wavelet and gradient have been widely applied on the sparse reconstruction of natural images and some biomedical images, such as Computer tomography (CT), Magnetic resonance imaging (MRI). By taken the structural similarity of OCT image, regional differential can sparsely represent the original image by using only a small number of coefficients. Experimental results showed that this novel regianl differential representation model is able to reduce the sampling fraction, and can achieve better reconstruction result under same sample fraction.2. CS optimization algorithm based on the regional differential represenataion modelAfter solving the problem of OCT image sparse representation, another important issue is to reconstruct the original image from only a small fraction of sampling. Orthogonal Matching Pursuit (OMP), Basic Pursuit (BP), ι1minimization and ι0minization algorithms have been deployed on solving the optimization problem. However, a disadvantage they all share is computationally expensive, which has restrict the application of compressed sensing in signal processing area. Based on the previous proposed sparse representation algorithm, we developed a non-local homotopic ι0minimization algorithm, which is able to decrease the computation complexity as well as achieve promising reconstruct results. Experimental results proved that at60%undersample fraction, two minites will be needed to reconstruct a whole OCT image.3. Adaptive sparse sampling algorithm based on energy distributionAccording to the further analysis of image energy distribution, an adaptive nonuniform sparse sampling scheme was proposed based on the previous research of uniform sparse sampling algorithm. It’s well known that the sampling number is direct relative to the sampling time, and most of the energy of OCT data is concentrated on a certain region. We choose to adaptively arrange more samples on high energy area, while sample less on low energy regions, which is able to reduce the sample number as well as keep all the important information. We have demonstrated the new energy-guided adaptively sampling algorithm is able to reduce the sample number while still able to produce a resonable reconstruction result.The research outputs related to this dissertation have been accepted as papers in IEEE journals and conferences.The research outputs related to this dissertation have been accepted as papers in IEEE journals and conferences.