Abstract: 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．

Key words: core image, compressed sensing, sparse dictionary learning, adaptive threshold