Research On 2-D Image Restruction Algorithms Based On Compressive Sensing

As soon as it was developed, Compressed Sensing theory has received the wide attention.The reason is that it breaks the limitation of the traditional Nyquist sampling theorem, resulting in the pressure alleviation on the cost of signal transmission, and the improvement on the transmission efficiency, therefore, it quickly became a hot topics in the field of signal processing. Compressed sensing is exploited to perform sparse representation and image reconstruction on natural images. Besides, research and improvement on reconstruction algorithm with the local smooth and nonlocal self-similarity of natural images are also presented. The major contributions and research content are as follows:1. In the process of compressed sensing image reconstruction, discrete wavelet transform can only represent the singularity of image point while it fails to get the curve singularity characteristic of images. To solve this problem, the advantages of the second generation wavelet-contourlet transform, i.e., multi-scale, multi-direction, are utilized to effectively represent the curve singularity characteristic of images. In order to eliminate the phenomenon of spectrum aliasing, a controlled tower structure is adopted. Additionally, a two-dimension SLO algorithm is introduced. By integrating these points together, our work is able to greatly reduce the complexity of the algorithm and obviously improve the quality of image reconstruction.2. Natural images have gradient sparse characteristics, namely local smoothness, with which total variation (TV) compressed sensing reconstruction model may lose some edge and texture information in images. To overcome this problem, a fractional-order TV is introduced to combine with compressed sensing theory, which can efficiently strengthen the performance on catching the details (e.g., edges and contours) with its nonlocal correlation. In addition, the combination of fractional-order TV with Contourlet transform will effectively improve the sparsity degree and direction of representation of the signals. Besides, the weight l1 -norm is adopted to further enhance the sparsity degree in transformation domain. Two-dimensional observation model and gradient projection algorithm are utilized for image construction,leading to a better quality of reconstruction image with a relatively low computational complexity. Considering the noise in image reconstruction process, the minimum mean squared error filter is used to suppress noise, increasing the robustness.3. By combining local smoothness and nonlocal self-similarity, a two-dimensional joint sparse regularization model (2D-JSRM) is proposed, in which local smoothness is used for keeping local consistency to restrain noise and nonlocal self-similarity is used for maintaining nonlocal consistency to obtain more edges and details. A two-dimensional compressed sensing observation model and Split Bregman Iteration (SBI) algorithm are adopted to convert unconstrained problem into a constrained minimization problem. The experimental results have demonstrated that 2D-JSRM can not only successfully catch much more image details but also get higher peak-signal-to-noise ratio and structure similarity (SSIM) indexes in image reconstruction process, having a higher reconstruction quality.