Abstract: The ever increasing volume of terrain data require efficient strategies in storage and transmission. In this paper, a new DEM compressive sampling and reconstruction based on sparsity adaptive method is proposed. The detailed step and flow chart of the method are shown. In the method, the curvelet transform can be utilized to make DEM sparse firstly, and then the random Gaussian matrix after approximate orthogonal-matrix and Right-matrix（QR） decomposition can be employed to complete the low-dimension measurement and finish compress the DEM. Furthermore, the modified CoSaMP algorithm, inverse curvelet transform and so on can be used to achieve the final reconstruction. In this paper, on the condition of the same reconstruction precision, the modified CoSaMP algorithm conducts blind recovery without priori information of sparsity and the convergence speed is enhanced compared with the original CoSaMP algorithm. Experimental results indicate that compared with the JPEG2000 the proposed method obtains high compression ratio and high reconstruction accuracy.

Key words: modified CoSaMP algorithm, Digital Elevation Model（DEM）, compressed sensing, wavelet transform

摘要： 地形数据量的日益增长迫切地需要高效的存储和传输策略。提出了一种基于稀疏度自适应化的DEM压缩采样与重构方法，并给出了方法具体的实现及详细流程。该方法首先利用小波变换对原始DEM进行稀疏处理，然后利用QR分解后的随机高斯矩阵对稀疏处理结果进行降维观测，实现DEM的压缩。最后针对CoSaMP算法必须提供稀疏度和重构时间长的缺点提出一种稀疏度自适应化的改进算法，利用改进的CoSaMP算法进行重构和小波反变换等步骤获得DEM的重构结果。在保证相似重构精度的前提下，提出的改进的CoSaMP算法与传统的CoSaMP算法相比，在实现稀疏度自适应化的同时有效地提高了收敛速度。仿真实验结果表明与JPEG2000方法相比，提出的方法实现了更高压缩比的数据压缩和高峰值信噪比的数据重构。

关键词: 改进的CoSaMP算法, 数字高程模型（DEM）, 压缩感知, 小波变换