压缩感知中结构化测量矩阵与编码算法的研究

发布时间：2018-04-26 02:20

本文选题：压缩感知 + 测量矩阵　；参考：《天津大学》2014年硕士论文

【摘要】：压缩感知中,传统的测量矩阵对图像进行单一采样率的压缩采样,在信号的获取和重构过程中起着重要的作用。传统的随机测量矩阵在采样率较高的情况下,能够获得比较好的重构效果,但因采样数目较多,故而资源耗费也较多。确定性测量矩阵自身存在一些限制因素,与随机测量矩阵相比,重构效果不够理想。为了解决上述问题,提出了两种结构随机矩阵和多层分块自适应编码算法。基于广义轮换矩阵,对其循环基础和循环构造过程中所生成的每一行向量的第一个元素进行改进,提出了两种结构随机矩阵:广义二进制轮换矩阵和伪随机广义二进制轮换矩阵。相对于传统的测量矩阵,新的测量矩阵在二维图像重建方面效果较好,所需重构时间相差不大,在较低的采样率下能够获得更加精确的重建。基于分块OSTM的自适应分块压缩感知算法,提出了多层分块自适应编码算法以及多层分块自适应压缩感知编解码方法。多层分块自适应压缩感知编解码方法基于多层分块自适应编码算法,能够根据图像局部结构进行不同层数和大小的分块,并自适应分配采样率。在同等重构性能的前提下,相比较于单一采样率下的压缩感知,新的编解码方法能够不同程度地降低重构图像所需的采样数目;相比于基于分块OSTM的自适应分块压缩感知算法,所提出的编解码方法突破了其对矩阵要求的限制,在处理具有较大面积平滑图像块的图像方面有着一定的优势。结构随机矩阵与自适应分块压缩感知算法在实际应用中有着广阔的前景,值得进一步深入研究。
[Abstract]:In compression sensing, the traditional measurement matrix performs compression sampling at a single sampling rate, which plays an important role in the process of signal acquisition and reconstruction. The traditional random measurement matrix can obtain better reconstruction effect under the condition of high sampling rate, but because of the large number of samples, the resources are consumed more. There are some limiting factors in deterministic measurement matrix. Compared with random measurement matrix, the reconstruction effect is not satisfactory. In order to solve the above problems, two kinds of structured random matrices and multi-layer block adaptive coding algorithms are proposed. Based on the generalized rotation matrix, the first element of each row vector generated in the cycle foundation and loop construction is improved. Two kinds of structured random matrices, generalized binary rotation matrix and pseudorandom generalized binary rotation matrix, are proposed. Compared with the traditional measurement matrix, the new measurement matrix has better effect in 2D image reconstruction, and the reconstruction time required is not different, so it can obtain more accurate reconstruction at lower sampling rate. An adaptive block compression sensing algorithm based on block OSTM is proposed in this paper. A multi-layer adaptive coding algorithm and a multi-layer block adaptive compression perceptual codec method are proposed. The multi-layer adaptive compression perceptual coding method is based on the multi-layer block adaptive coding algorithm. It can divide different layers and sizes according to the local structure of the image and allocate the sampling rate adaptively. On the premise of the same reconstruction performance, compared with the compression perception at a single sampling rate, the new coding and decoding method can reduce the number of samples needed for reconstructed image in varying degrees, compared with the adaptive block compression sensing algorithm based on block OSTM. The proposed coding and decoding method breaks through the limitation of matrix requirements and has some advantages in processing images with large area smooth image blocks. Structural random matrix and adaptive block compression sensing algorithm have a broad prospect in practical application, and deserve further research.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7

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