基于广义轮换矩阵的伪随机广义二进制轮换矩阵设计

Design of Pseudo-Random Generalized Binary Rotation Matrix Based on Generalized Rotation Matrix

压缩感知中,测量矩阵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,但在低采样率下的重构效果不够理想。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,重构效果有所降低。基于广义轮换矩阵(GR),提出了两种结构随机矩阵:广义二进制轮换矩阵(GBR)和伪随机广义二进制轮换矩阵(PGBR)。仿真结果表明,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。

In compressed sensing, measurement matrix plays an important role in signal acquisition and reconstruction. The traditional random measurement matrices can achieve good performance on the condition that the sampling rate is high enough, whereas the reconstructions are not satisfactory at low sampling rates. Compared with these random measurement matrices, the deterministic measurement matrices possess their own constraints, which lead to worse performance. Based on the generalized rotation （GR） matrix, two kinds of structured random matrices are proposed as the generalized binary rotation （GBR） matrix and the pseudorandom generalized binary rotation （PGBR） matrix. Simulation results for two dimensional signals show that the two series of new matrices perform better than the traditional measurement matrices. The amount of time required by the traditional and the new approaches is about the same. Moreover, they can obtain more accurate reconstructions at low sampling rates.