中文摘要：

压缩感知是一种充分利用信号稀疏性的全新的信号采样理论. 如何从采样得到的低维数据中高效地恢复出原始的高维数据是压缩感知理论的一个关键研究问题. 本文基于图像二维离散余弦变换（ Discrete Cosine Transform,DCT）系数的分布特性,研究图像DCT域非均匀压缩采样,并在子空间追踪（ Subspace Pursuit, SP ）算法的基础上,提出一种变步长SP算法,用以实现压缩感知图像的快速重构. 该算法自适应地设置图像DCT系数矩阵中不同列向量的采样率,将有限的采样值尽可能地分配给高幅值系数较集中的列向量. 在重建DCT系数列向量时,动态调整不同子空间内的原子搜索步长,在高幅值系数集中区域对应的原子子集中进行小步长密集搜索,而在其它原子子集中进行大步长快速搜索. 实验结果表明,与基于SP算法的DCT域均匀采样图像重构算法相比,本文提出的基于变步长SP算法的DCT域非均匀采样图像重构算法在图像重构精度与重构算法运行时间方面均具有明显优势.

英文摘要：

Compressive sensing is a novel sampling theory that takes full advantage of the signal′s sparsity. A key research subject in it is how to recover the original high-dimensional data from the low-dimensional compressed data. Non-uniform sampling is stud-ied in this paper, based on the distribution character of image Discrete Cosine Transform （ DCT） coefficients. Moreover, a new Subspace Pursuit （SP） algorithm with variable step-sizes in DCT domain is proposed, to reconstruct the compressed images fast and accurately. This algorithm sets the sampling rates of columns in DCT coefficient matrix adaptively, so that more samples are as-signed to the columns with more high-magnitude coefficients. When reconstructing the columns of DCT coefficients, this algorithm adjusts the support search step-sizes used in different subspaces dynamically. In the atom subsets which correspond to the coeffi-cients with high amplitudes, small step-sizes are preferred. On the contrary, large step-sizes are preferred. Simulation results show that the proposed algorithm prevails over the original DCT-domain SP algorithm both on image reconstruction accuracy and on the reconstruction runtime.