English

运筹学学报 ›› 2015, Vol. 19 ›› Issue (4): 59-71.doi: 10.15960/j.cnki.issn.1007-6093.2015.04.006

• 运筹学 • 上一篇    下一篇

基于部分三角函数变换矩阵的块压缩感知测量方法

陈建1, 苏凯雄1,*, 彭拯2, 苏立超3   

  1. 1.福州大学物理与信息工程学院, 福州 350116;2.福州大学数学与计算机科学学院, 福州 350116; 3.厦门大学信息科学与技术学院, 厦门 361005
  • 收稿日期:2015-01-04 出版日期:2015-12-15 发布日期:2015-12-15
  • 通讯作者: 苏凯雄 skx@fzu.edu.cn
  • 基金资助:

    1.国家自然科学基金(Nos. 61471124, 61571129);

    2.福建省自然科学基金(Nos.~2013J01234,2014J01234, 2015J01251)

Measurement method of block compressed sensing based  on partial trigonometric function transform matrices

 CHEN Jian1, SU Kaixiong1,*, PENG Zheng2, SU Lichao3   

  1. 1.College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China; 2.College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China; 3.School of Information Science and Engineering, Xiamen University, Xiamen 361005, Fujian,  China
  • Received:2015-01-04 Online:2015-12-15 Published:2015-12-15

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摘要：

为了提高块压缩感知的测量效率和重构性能,根据离散余弦变换和离散正弦变换具有汇聚信号能量的特性,提出了基于重复块对角结构的部分离散余弦变换partial discrete cosine transform in repeated block diagonal structure,简称PDCT-RBDS和部分离散正弦变换partial discrete sine transform in repeated block diagonal structure简称PDST-RBDS的两种压缩感知测量方法.所采用的测量矩阵是一种低复杂度的结构化确定性矩阵, 满足受限等距性质.并得到一个与采样能量有关的受限等距常数和精确重构的测量数下限.通过与采用重复块对角结构的部分随机高斯矩阵和部分贝努利矩阵的图像压缩感知对比,结果表明PDCT-RBDS和PDST-RBDS重构的PSNR大约提高1---5dBSSIM提高约0.05, 所需的重构时间和测量矩阵的存储空间大大减少.该方法特别适合大规模图像压缩及实时视频数据处理场合.

关键词: 块压缩感知, 结构化随机矩阵, 离散余弦变换, 离散正弦变换

Abstract:

To improve the measurement efficiency and reconstruction performance of the block compressed sensing (BCS), two measurement methods of compressed
sensing, based on partial discrete cosine transform in repeated block diagonal structure (abbreviated as PDCT-RBDS), and respectively, partial discrete sine transform in repeated block diagonal structure (abbreviated as PDST-RBDS), are proposed because of that the DCT (discrete cosine transform) and DST (discrete sine transform) have the property of collecting energy. The measurement matrices adopted are a structural deterministic matrix under the low complexity, and satisfy with the restricted isometry property (RIP). Moreover, by relating with sampling energy, the restricted isometry constant (RIC) and the lower bound of measurements for exact recovery are deduced. The experimental results, which compared with the partially random Gaussian matrices in repeated block diagonal structure (abbreviated as PRGS-RBDS) and partially Bernoulli matrices in repeated block diagonal structure (abbreviated as
PBNL-RBDS), indicate that, about 1---5 dB gain in the PSNR and 0.05 gain in the SSIM are observed, and the recovery time and storage space for measurement matrices are greatly reduced. The method is particularly suitable for the applications of image compressing in large scale and video data processing in real time.

Key words: Block Compressed Sensing, Structurally Random Matrices, Discrete Cosine Transform, Discrete Sine Transform