基于K-SVD 字典学习的岩心图像压缩感知重构

针对传统方法进行岩心图像压缩感知重构时，在低码率下容易产生细节丢失的问题，提出一种基于 K-SVD( K-Singular Value Decomposition) 超完备字典学习的压缩感知重构算法。首先根据分块压缩感知理论，将 岩心图像分块，采用高斯随机矩阵对相应层级的图像块进行观测，得到对应的观测值块，然后用MMSE ( Minimum Mean Squareerror Estimation) 方法获得初始解的估计并利用提示小波进行滤波，通过全局阈值的思想 得到自适应阈值，最后利用K-SVD 字典结合Landweber 迭代实现压缩与重构。实验结果表明，与传统方法相 比，在相同的采样率下获得的重构图像能较好地保留岩心图像的纹理信息，重构岩心图像的PSNR( Peak Signal to Noise Ratio) 值提高约0． 1 ～ 0． 8 dB。

Compressed Sensing Reconstruction of Core Image Based on K-SVD Dictionary Learning#br#

In order to solve the problem that the traditional compression sensing reconstruction methods of core image are prone to losing details at low bit rates，a block compression sensing reconstruction algorithm based on K-SVD( K-Singular Value Decomposition) dictionary learning is proposed． Firstly，according to the theory of block compression sensing，the core image is divided into multi-blocks，and the corresponding blocks are observed by Gaussian random matrix． Then，the initial solution is obtained by MMSE ( Minimum Mean Squareerror Estimation) estimation and the adaptive threshold is calculated by global threshold formula with the lifting wavelet decomposition． Finally，the sparse representation method of K-SVD dictionary learning combined with Landweber iteration is used to achieve compression and reconstruction． The experimental results show that the reconstructed image can retain the texture information of the core image better than the traditional methods at the same sampling rate，and the PSNR( Peak Signal to Noise Ratio) of the reconstructed core image is increased by about 0． 1 ～ 0． 8 dB．