深圳大学学报理工版

针对压缩感知中测量矩阵的优化问题,提出一种基于混沌因子和动量项的梯度下降法.在测量矩阵优化过程中,梯度下降法具有收敛速度慢,容易陷入局部最小的缺点. 为此,基于混沌运动的随机性和遍历性,在步长变化中引入混沌因子,避免因初始步长选择不当导致算法的不稳定且实现步长的自适应变化; 同时利用动量项,避免算法陷入局部最小值,提高算法的收敛速度,优化测量矩阵性能,降低测量矩阵与稀疏矩阵互相关性.仿真结果表明,该方法收敛速度快,互相关系数的分布更加集中在零附近,且重构图像的峰值信噪比大大提高.

A hybrid method is proposed for optimizing the measurement matrix in compressed sensing.A significantly improved gradient descent algorithm combining chaos motion and momentum term is presented to solve the problem of slow convergence speed and local minimum of gradient descent.Based on randomness and ergodicity of chaotic motion,a chaos factor is introduced to stepsize so that the stepsize is adaptive in the iteration process.Momentum term is added to avoid falling into local minimum and improve convergence speed.The simulation results have demonstrated that the speed of optimizing matrix is fast, and more mutual coherence coefficients are distributed around zero. The peak signal to noise ratio(PSNR)of reconstructed image through compressed sensing is improved with the optimized measurement matrix.

引言
1 压缩感知理论框架
2 测量矩阵优化设计
3 实验结果与分析
4 结语

表1 测量矩阵优化的混合方法步骤<br/>Table 1 The step of hybird method

表1 测量矩阵优化的混合方法步骤
Table 1 The step of hybird method

图1 J随η取值不同的变化曲线<br/>Fig.1 The variation of J with different η

图1 J随η取值不同的变化曲线
Fig.1 The variation of J with different η

图2 重构图像的PSNR随测量数目m的变化<br/>Fig.2 The variation of PSNR of reconstructed image with measurement number m

图2 重构图像的PSNR随测量数目m的变化
Fig.2 The variation of PSNR of reconstructed image with measurement number m

图3 测量矩阵为200×256的高斯随机矩阵重建图像<br/>Fig.3 The reconstructed images with Gaussian measurement matrix of 200×256

图3 测量矩阵为200×256的高斯随机矩阵重建图像
Fig.3 The reconstructed images with Gaussian measurement matrix of 200×256

图4 测量矩阵与稀疏矩阵的互相关系数分布<br/>Fig.4 The distribution of mutual coherence between measurement matrix and sparse matrix

图4 测量矩阵与稀疏矩阵的互相关系数分布
Fig.4 The distribution of mutual coherence between measurement matrix and sparse matrix

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备注

引言

1 压缩感知理论框架

2 测量矩阵优化设计

3 实验结果与分析

4 结语

期刊信息

备注

引言

1 压缩感知理论框架

2 测量矩阵优化设计

3 实验结果与分析

4 结 语

期刊信息

4 结语