基于梯度优化的CS重构算法研究

发布时间：2018-03-20 09:10

本文选题：压缩感知　切入点：重构算法　出处：《南京邮电大学》2017年硕士论文　论文类型：学位论文

【摘要】：压缩感知(CS)主要包括稀疏、观测和重构三个步骤,其中,重构算法的设计影响着信号重构的效果,基于l_0范数的贪婪算法是一类重要的重构算法。为了进一步提高重构的速度和精确度,本文结合梯度优化的理论和方法对CS重构算法进行研究,具体的工作内容如下:1.提出了基于PRP共轭梯度的SL_0算法。用双曲正切函数族近似逼近l_0范数,将最小化l_0范数问题转化为凸优化问题,通过PRP共轭梯度法对函数的极值进行求解。仿真结果表明,该算法的均方误差比其他基于l_0范数的重构算法更小,重构性能更好。2.提出了基于L-BFGS拟牛顿法的梯度追踪算法。将最优化方法中的L-BFGS拟牛顿法与梯度追踪算法相结合,通过L-BFGS拟牛顿法对梯度追踪法中的更新方向进行求解,形成基于L-BFGS拟牛顿法的梯度追踪算法(L-BFGS Method based Gradient Pursuit,LMGP)。仿真结果表明,该算法的重构时间相较于其他贪婪算法更少,重构效果更好。3.提出了基于PRP共轭梯度改进字典学习的LMGP算法。在稀疏阶段用基于PRP共轭梯度的SL0算法对稀疏系数矩阵进行计算,将原始信号进行稀疏表示,形成新的基于PRP共轭梯度法的字典学习方法。接着,用基于L-BFGS拟牛顿法的梯度追踪算法对视频帧进行重构。仿真结果表明,该算法在峰值信噪比方面优于其他算法,算法的性能更佳。
[Abstract]:Compression sensing (CSS) consists of three steps: sparse, observation and reconstruction, in which the design of reconstruction algorithm affects the effect of signal reconstruction. The greedy algorithm based on L _ 0 norm is an important class of reconstruction algorithms. In order to improve the speed and accuracy of reconstruction, this paper combines the theory and method of gradient optimization to study the CS reconstruction algorithm. The main work is as follows: 1. The SL_0 algorithm based on PRP conjugate gradient is proposed. By using hyperbolic tangent function family to approximate L _ 0 norm, the minimization of l _ 0 norm problem is transformed into a convex optimization problem. The PRP conjugate gradient method is used to solve the extremum of the function. The simulation results show that the mean square error of the algorithm is smaller than that of other reconstruction algorithms based on L _ 0 norm. 2. A gradient tracking algorithm based on L-BFGS quasi-Newton method is proposed. The L-BFGS quasi-Newton method is combined with the gradient tracking algorithm, and the updating direction of the gradient tracking method is solved by L-BFGS quasi-Newton method. A gradient tracking algorithm based on L-BFGS quasi Newton method is formed. The simulation results show that the reconstruction time of the algorithm is less than that of other greedy algorithms. 3. A LMGP algorithm based on PRP conjugate gradient is proposed to improve dictionary learning. In the sparse stage, the sparse coefficient matrix is calculated by SL0 algorithm based on PRP conjugate gradient, and the original signal is represented sparsely. A new dictionary learning method based on PRP conjugate gradient method is proposed. Secondly, the gradient tracking algorithm based on L-BFGS quasi-Newton method is used to reconstruct the video frame. The simulation results show that the proposed algorithm is superior to other algorithms in the aspect of peak signal-to-noise ratio (PSNR). The performance of the algorithm is better.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7

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