基于行列式随机循环的压缩感知测量矩阵研究

压缩感知理论,从信号的自身特性出发,通过变换作用域和线性投影实现对信号的采样和压缩。测量矩阵是该理论中获得最优测量,实现精确重构的关键。本文在介绍常用测量矩阵的基础上,重点研究了结构化测量矩阵。鉴于测量矩阵设计的最重要的原则是降低矩阵元素间的相干性,本文借鉴循环矩阵和广义轮换矩阵的优点,提出了采用均匀随机数对结构化测量矩阵进行随机循环的构造方法。仿真实验表明新矩阵在信号重建上具有更好的性能。     

基于超素数的托普利兹观测矩阵构造方法

观测矩阵在信号压缩感知中十分重要,直接决定信号的重构质量。为保证信号的重构精度,要求观测矩阵具有很强的随机性,但随机矩阵硬件实现非常困难;确定性观测矩阵易于实现,但其重构精度不足。针对观测矩阵对随机性与确定性的双重要求,提出利用超素数产生超长周期的伪随机序列,解决确定性观测矩阵对随机性的要求;结合托普利兹观测矩阵的确定性结构特征,得到一种改进的托普利兹观测矩阵。实验仿真表明:改进的托普利兹观测矩阵与高斯随机观测矩阵和常用托普利兹观测矩阵相比,其信号重构精度得到了很好的改善,且易于硬件实现。     

A new version of Kovarik’s approximate orthogonalization algorithm without matrix inversion

In 1970 Kovarik proposed approximate orthogonalization algorithms. One of them (algorithm B) has quadratic convergence but requires at each iteration the inversion of a matrix of similar dimension to the initial one. An attempt to overcome this difficulty was made by replacing the inverse with a finite Neumann series expansion involving the original matrix and its adjoint. Unfortunately, this new algorithm loses the quadratic convergence and requires a large number of terms in the Neumann series which results in a dramatic increase in the computational effort per iteration. In this paper we propose a much simpler algorithm which, by using only the first two terms in a different series expansion, gives us the desired result with linear convergence. Systematic numerical experiments for collocation and Toeplitz matrices are also described.     

一类新的Cartesian认证码

运用矩阵的标准型理论设计了一类新的Cartesian认证码,引入自然数的有序分拆计算了该认证码的全部参数。在密钥均匀分布的条件下,分析了该类认证方案被敌手成功攻击的两种概率。     

固定阵列长度两发多收MIMO系统功率偏移分析

高信噪比情况下,功率偏移是信噪比-容量曲线中信噪比轴的截距,优化功率偏移参数有助于提高系统容量。该文采用固定阵列长度的均匀直线阵,通过拟合三对角特普利茨矩阵行列式曲线,分析了接收天线间相关性以及收发天线数目的最大值对于两发多收单用户MIMO系统功率偏移的影响,得出了给定天线阵列长度情况下,功率偏移极值点的基本公式。仿真结果表明,可以利用极值点公式选择合理的接收天线数目,实现最优功率偏移。     

一种利用最大特征矢量的Toeplitz去相干方法

 本文针对相干源的DOA估计问题,利用最大特征值对应的特征矢量(简记为最大特征矢量),提出了一种新的Toeplitz去相干方法.该方法用最大特征矢量构造了一个Toeplitz矩阵来估计相干源的波达方向,实现简单,不损失阵列孔径.相对于常规的去相干算法具有更好的估计性能,特别是在低信噪比情况下,且能估计更多相干源.理论分析和仿真结果均验证了该方法的有效性.     

A parallel algorithm solving a tridiagonal Toeplitz linear system

A new tridiagonal Toeplitz linear system (TTLS) solver is proposed. The solver first decomposes an n-dimensional strictly diagonally dominant TTLS equation into a number of m-dimensional subsystems employing a modified Gaussian elimination method. An analytic solution of a continued fraction is obtained to derive the solver. The solver based on the modified Gaussian elimination method fully exploits parallelism. Computation and communication complexities of the proposed algorithm are all shown to be O(n/m).     

A bit-level systolic array for digital contour smoothing

Linear operators for digital contour smoothing are described. These operators are defined by circulant Toeplitz matrices and allow to smooth digital contours in the least-squares sense. They minimize the undersampling, digitizing and quantizing error and allow to calculate invariants, such as curvature, which are not possible to calculate without smoothing. A bit-level systolic array which is capable of realizing the proposed operator is described. This array is easy to implement in VLSI, because the array cells involved are very simple. Furthermore, the array is completely pipelined on the bit-level, so that it operates with a high clock frequency achieving very high throughputs.     

More IMPATIENT: A gridding-accelerated Toeplitz-based strategy for non-Cartesian high-resolution 3D MRI on GPUs

Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code.     

一类Toeplitz三对角方程组的一种分布式并行算法

文中提出一类Toeplitz三对角方程组的一种分布式并行算法。该算法以系数矩阵的分解为基础,充分利用了系数矩阵结构的特殊性,算法因并行化而引入的冗余计算量非常少,算法的通信机制简单,通信量仅与处理 机台数p有关,与方程组规模n无关,算法具有很高的并行效率,理论分析和数值试验表明,其加速比Sp(n)→p(n→ ∞）,此为线性加速比的理想情况。文中给出了算法在分布存储多计算机系统上的数值试验结果。