Theory And Application On Multidimensional Compressed Imaging Based Tensor And Nonlinear Sparsity

As the foundation of data sampling, Nyquist sampling theory shoulders the irreplaceable mission in signal processing in the past half century. However, the demand for information is far more than the development of hardware and in many practical applications such as video, hyperspectral images, ultra-wideband signal processing, it is difficult to satisfy the traditional Nyquist sampling rate. The new developed Compressed Sensing theory in the last 10 years gives an effective answer. The key idea of CS is that signals can be accurately recovered by a a small amount of non-correlation measurements through optimization algorithm under the assumption compressibility.The development of sensor technology results in more high-dimensional signals to be processed while the researches focus on one or two dimensional signals and generally the processing method for multidimensional signals is vectorization. It is easy to destroy the structural information of the signal, requesting more prior knowledge to obtain an accurate restoration. It increases the complexity of the optimization algorithm and reduces signal recovery efficiency. Expressing high dimensional signals as tensor and operations in the form of tensor can maintain the structure of the data itself to some extent. Additionally, the sparse model is based on the assumption of linearity, while the actual physical scene is a complex, multi-factor, multilevel, with an open system architecture and dynamic obvious geographical differences, in which objects are usually observed with high dimensionality, variability and complexity. Therefore, it is difficult to obtain the desired sparsity via linear encoder, needing to expand to the nonlinear model to get better sparsity. Based on these considerations, this article is subject to spectral imaging to study the theory and application on Multidimensional Compressed Imaging Based Tensor and Nonlinear sparsity. The main work is as follows:Firstly, for multidimensional spectral information acquisition, we design a multiplexed compressed hyperspectral imaging method and spatial-spectral dictionary learning and signal recovery method based on tensor. According the research of hyperspectral imaging principle, we proposed a multiplexed compressed hyperspectral imaging methods, to complete the spatial and spectral domain imaging in one imaging process. We also design a tensor sparse model of hyperspectral images and a tensor dictionary learning method consult with methods in vector form to obtain the dictionaries on various dimensions simultaneously. Experiment results on three hyperspectral images show that compared to fixed dictionary, the multidimensional dictionary learning method can represent signals sparser and tensor-based recovery algorithm has better recovery results. When the sampling ratio is 6.25%, the average PSNR of the proposed method is 4 to 5 higher than the traditional Basis Pursuit and Orthogonal Matching Pursuit while time consuming is more than halved.Secondly, for the compressive acquisition and reconstruction of multidimensional information, we design a nonlinear compressed sensing model based on kernel function and tensor according to reproducing Hilbert space. We also develop a new Tensor-Nonlinear Compressed Sensing(Tensor-NCS) framework for an accurate and non-iterative recovery of hyperspectral images. In addition, a self-learning Tensor-NCS based CHI scheme is proposed when the training examples are not necessary. Experiment results on three hyperspectral images obtained by AVIRIS and HYDICE spectroscopy show that the reconstruct average PSNR of our Tensor-NCS method is 5 to 7 higher than the traditional Basis Pursuit and Orthogonal Matching Pursuit even when the sampling ratio is as low as 1%. This method gives an feasible option to obtain high spectral resolution and high spatial resolution simultaneously.Thirdly,for dictionary leaning in kernel space, we design a new non-negative dictionary learning method in the feature space. Dictionary atoms learned by non-negative methods can express signal more precisely and fit actual physical meaning. Due to the introduction of complicated nonlinear function, it is difficult to obtain a dictionary in the feature space so that all types of computing in the nonlinear space. Based on the study of non-negative dictionary leaning and non-negative sparse coding, we propose non-negative basis pursuit and non-negative orthogonal matching pursuit in the kernel space and the corresponding dictionary update methods. Experiment results on three hyperspectral images show that the reconstruct average PSNR of our non-negative dictionary method is 0.5 to 1 higher than the other dictionaries.