基于互交替投影的块稀疏正交匹配追踪算法

针对块稀疏信号,理论分析和实验验证均表明算法精确重构的充分条件与矩阵块相关性和子相关性有关。在此基础上,提出了一种基于互交替投影的块稀疏正交匹配追踪算法(mutual alternating projection-block or-thogonal matching pursuit,MAP-BOMP)。该算法利用互交替投影方法不断构造新的测量矩阵和感知矩阵,使得矩阵块相关性和子相关性都很小,从而提高重构概率,并给出明确的算法收敛条件,降低了计算复杂度。通过与大多数已有块稀疏信号重构算法进行实验仿真对比,该算法在重构效果和重构速度上均优于其他算法。     

回溯正则化分段正交匹配追踪算法

针对分段正交匹配追踪（StOMP）算法对信号重构效果较差的问题,提出一种回溯正则化分段正交匹配追踪（BR-StOMP）算法。首先,该算法采用正则化思想选取能量较大的原子,以减少阈值阶段候选集中的原子;然后,利用回溯对原子进行检验,并对解的支撑集中的原子重新筛选一次,同时删除对解的贡献较低的原子,提高算法的重构率;最后,对感知矩阵进行归一化处理,使算法更加简单。仿真结果表明：BR-StOMP算法与正交匹配追踪（OMP）算法相比较峰值信噪比提高8%~10%左右,运行时间减少70%~80%;与StOMP算法相比较,峰值信噪比提高19%~35%。BR-StOMP算法能够精确地恢复信号,重建效果优于OMP算法和StOMP算法。     

一种稀疏自适应的正交互补匹配追踪算法

针对实际应用中信号稀疏度未知的缺点,提出了一种稀疏度自适应的正交互补匹配追踪算法。算法先初始化稀疏度,再通过互补正交匹配追踪重构信号,找到一个支撑集;若支撑集不满足条件,则按指定步长增加稀疏度,再次运用算法进行重构,直到支撑集满足条件,得到最优支撑集。实验结果表明,该算法可以准确有效地重构信号,并且在相同压缩比下,其重构质量（PSNR）优于其他几种算法。     

MISO 系统基于正交匹配追踪算法的参数与时滞联合估计

在有限采样情况下, 研究具有时滞的多输入单输出受控自回归系统的参数辨识和时滞估计问题. 当采样次数少于未知变量数时, 描述系统的方程组是欠定的, 对其目标函数求解是NP-hard 问题, 传统方法无法有效辨识出系统参数. 受压缩感知理论的启发, 基于参数向量所具有的稀疏特性, 提出一种新的阈值正交匹配追踪算法辨识系统的参数和时滞. 仿真实验表明, 所提出的算法能在少量采样时有效地辨识系统参数、估计未知时滞, 同时验证了算法的有效性.

     

Pixel-level image fusion with simultaneous orthogonal matching pursuit

Pixel-level image fusion integrates the information from multiple images of one scene to get an informative image which is more suitable for human visual perception or further image-processing. Sparse representation is a new signal representation theory which explores the sparseness of natural signals. Comparing to the traditional multiscale transform coefficients, the sparse representation coefficients can more accurately represent the image information. Thus, this paper proposes a novel image fusion scheme using the signal sparse representation theory. Because image fusion depends on local information of source images, we conduct the sparse representation on overlapping patches instead of the whole image, where a small size of dictionary is needed. In addition, the simultaneous orthogonal matching pursuit technique is introduced to guarantee that different source images are sparsely decomposed into the same subset of dictionary bases, which is the key to image fusion. The proposed method is tested on several categories of images and compared with some popular image fusion methods. The experimental results show that the proposed method can provide superior fused image in terms of several quantitative fusion evaluation indexes.     

Accelerating 2D orthogonal matching pursuit algorithm on GPU

Two-dimensional orthogonal matching pursuit (2D-OMP) algorithm is an extension of the one-dimensional OMP (1D-OMP), whose complexity and memory usage are lower than the 1D-OMP when they are applied to 2D sparse signal recovery. However, the major shortcoming of the 2D-OMP still resides in long computing time. To overcome this disadvantage, we develop a novel parallel design strategy of the 2D-OMP algorithm on a graphics processing unit (GPU) in this paper. We first analyze the complexity of the 2D-OMP and point out that the bottlenecks lie in matrix inverse and projection. After adopting the strategy of matrix inverse update whose performance is superior to traditional methods to reduce the complexity of original matrix inverse, projection becomes the most time-consuming module. Hence, a parallel matrix–matrix multiplication leveraging tiling algorithm strategy is launched to accelerate projection computation on GPU. Moreover, a fast matrix–vector multiplication, a parallel reduction algorithm, and some other parallel skills are also exploited to boost the performance of the 2D-OMP further on GPU. In the case of the sensing matrix of size 128 \(\times \) 256 (176 \(\times \) 256, resp.) for a 256 \(\times \) 256 scale image, experimental results show that the parallel 2D-OMP achieves 17 \(\times \) to 41 \(\times \) (24 \(\times \) to 62 \(\times \) , resp.) speedup over the original C code compiled with the O \(_2\) optimization option. Higher speedup would be further obtained with larger-size image recovery.     

基于随机支撑挑选的广义正交匹配追踪算法

针对广义正交匹配追踪（GOMP）算法复杂度高、重构时间长的问题,提出了一种基于随机支撑挑选的GOMP（StoGOMP）算法。首先引入随机支撑挑选的策略,在每次迭代中随机生成一个概率值。然后通过比较此概率值与预设概率值的大小来决定候选支撑集的挑选方式：若此概率值小于预设概率值,则采用匹配计算方式;否则,采用随机选择方式。最后根据得到的候选支撑来更新残差。这种方式充分考虑了算法单次迭代复杂度和迭代次数之间的平衡,减少了算法的计算量。一维随机信号重构实验结果表明,在预设概率值为0.5、稀疏度为20时,StoGOMP算法相较GOMP算法达到100%重构成功率所需的采样数减少了9.5%。实际图像重构实验结果表明,所提出的算法具有与GOMP算法相当的重构精度,且在采样率为0.5时,所提算法的重构时间相较于原算法减少了27%以上,这说明StoGOMP算法能够有效减少信号的重构时间。     

正交匹配追踪算法的优化设计与FPGA实现

设计了一种基于FPGA的正交匹配追踪(Orthogonal Matching Pursuit,OMP)算法的硬件优化结构,对OMP算法进行了改进,大大减少了乘法运算次数;在矩阵分解部分采用了交替柯列斯基分解(Alternative Cholesky Decomposition,ACD)方法避免开方运算,以减小计算延迟,整个系统采用并行计算、资源复用技术,在提高运算速度的同时减少资源利用。在Quartus II开发环境下对该设计进行了RTL级描述,在Altera公司的Cyclone II EP2C70F672C6上进行综合并完成时序仿真,仿真结果验证了设计的正确性。     

3D sparse signal recovery via 3D orthogonal matching pursuit

Though many three-dimensional (3D) compressive sensing schemes have been proposed, recovery algorithms in most of these schemes are designed for 1D or 2D signals, which cause some serious drawbacks, e.g., huge memory usage, and high decoder complexity. This paper proposes a 3D separable operator (3DSO) which is able to completely exploit the spatial and spectral correlation to sparsify and samples the 3D signal in three dimensions. A 3D orthogonal matching pursuit (3D-OMP) algorithm is then employed to recover the 3D sparse signal, which is able to reduce the computational complexity of the decoder significantly with guaranteed accuracy. In the proposed algorithm, we represent each 3D signal as a weighted sum of 3D atoms, which allow us to sample the 3D signal with 3D separable sensing operator. Then the best matched atoms are selected to construct the 3D support set, and the 3D signal is optimally recovered from the 3D support set in the sense of the least squares. Experimental results show that the 3D-OMP approach achieves higher recovery quality but requires less computational time than the Kronecker Compressive Sensing (KCS) scheme.     

2D sparse signal recovery via 2D orthogonal matching pursuit

Recovery algorithms play a key role in compressive sampling (CS).Most of current CS recovery algo-rithms are originally designed for one-dimensional (1D) signal,while many practical signals are two-dimensional (2D).By utilizing 2D separable sampling,2D signal recovery problem can be converted into 1D signal recovery problem so that ordinary 1D recovery algorithms,e.g.orthogonal matching pursuit (OMP),can be applied directly.However,even with 2D separable sampling,the memory usage and complexity at the decoder are still high.This paper develops a novel recovery algorithm called 2D-OMP,which is an extension of 1D-OMP.In the 2D-OMP,each atom in the dictionary is a matrix.At each iteration,the decoder projects the sample matrix onto 2D atoms to select the best matched atom,and then renews the weights for all the already selected atoms via the least squares.We show that 2D-OMP is in fact equivalent to 1D-OMP,but it reduces recovery complexity and memory usage significantly.What’s more important,by utilizing the same methodology used in this paper,one can even obtain higher dimensional OMP (say 3D-OMP,etc.) with ease.     

一种基于FPGA实现的优化正交匹配追踪算法设计

针对压缩感知重构算法中正交匹配追踪(OMP)算法在每次迭代中不能选取最优原子问题,对OMP算法进行优化设计,保证了每次迭代的当前观测信号余量最小,并提出了一种基于FPGA实现的优化OMP算法硬件结构设计。在矩阵分解部分采用了修正乔列斯基(Cholesky)分解方法,回避开方运算,以减少计算延时,易于FPGA实现。整个系统采用并行计算、资源复用技术,在提高运算速度的同时减少资源利用。在Quartus II开发环境下对该设计进行了RTL级描述,并在FPGA仿真平台上进行仿真验证。仿真结果验证了设计的正确性。     

基于优化正交匹配追踪和深度置信网的声音识别

针对各种环境声音对声音事件识别的影响,提出一种基于优化的正交匹配追踪（OOMP）和深度置信网（DBN）的声音事件识别方法。首先,利用粒子群优化（PSO）算法优化OMP稀疏分解,在实现正交匹配追踪（OMP）的快速稀疏分解的同时,保留声音信号的主体部分,抑制噪声对声音信号的影响;接着,对重构声音信号提取Mel频率倒谱系数（MFCC）、OMP时-频特征和基音频率（Pitch）特征,组成OOMP的复合特征;最后,使用DBN对提取的OOMP特征进行特征学习,并对40种声音事件在不同环境不同信噪比下进行识别。实验结果表明,OOMP特征结合DBN的方法适用于各种环境声下的声音事件识别,而且能有效地识别各种环境下的声音事件,即使在信噪比（SNR）为0 dB的情况下,仍然能保持平均60%的识别率。     

基于灰度共生矩阵和同步正交匹配追踪的分形图像压缩

针对传统分形图像压缩中存在计算复杂度高以及编码时间较长的问题,提出了一种基于灰度共生矩阵纹理特征的正交化分形编码算法.首先,从特征提取和图像检索的角度建立起范围块和域块之间的相似性度量矩阵,由此将全局搜索转化为局域搜索来缩减码本;然后,定义一个新的规范块作为新的灰度描述特征,从而简化了块之间的变换过程;最后,引入同步正...     

基于压缩感知信号重建的自适应正交多匹配追踪算法*

近年来出现的压缩感知理论为信号处理的发展开辟了一条新的道路,不同于传统的奈奎斯特采样定理,它指出只要信号具有稀疏性或可压缩性,就可以通过少量随机采样点来恢复原始信号。在研究和总结传统匹配算法的基础上,提出了一种新的自适应正交多匹配追踪算法(adaptive orthogonal multi matching pursuit,AOMMP)用于稀疏信号的重建。该算法在选择原子匹配迭代时分两个阶段,引入自适应和多匹配的原则,加快了原子的匹配速度,提高了匹配的准确性,实现了原始信号的精确重建。最后与传统OMP算法     

基于辅助模型正交匹配追踪的多输入系统迭代辨识算法

针对含有未知时滞的多输入输出误差系统的时滞与参数辨识问题,提出一种基于辅助模型的正交匹配追踪迭代算法.首先,由于各输入通道的时滞未知,通过设定输入回归长度,对系统模型进行过参数化,得到一个高维的辨识模型,且辨识模型中参数向量为稀疏向量;然后,基于辅助模型思想和正交匹配追踪算法,在每次迭代过程中,对参数向量和辅助模型的输出进行交互估计,即利用正交匹配追踪算法获得参数向量的估计,再利用参数估计值计算辅助模型的输出,并用辅助模型的输出值代替信息向量中的不可测信息项以更新参数估计;最后,根据参数向量的稀疏特征,获得系统的时滞估计.所提出算法可以利用少量的采样数据信息同时获得系统参数和时滞的估计值.仿真结果表明了所提出算法的有效性.     

基于改进OMP算法的毫米波大规模MIMO混合预编码设计

针对全连接单用户毫米波大规模MIMO系统,以最大化系统可达和速率为目标,提出一种基于改进的正交匹配追踪（orthogonal matching pursuit,OMP）算法的混合预编码方案。在既有的基于OMP算法的混合预编码基础上,首先,针对其迭代次数过多的问题,受多步长思想的启发,从阵列响应集合中选取与射频链路数目相等的最优的前多列矢量,从而求得模拟预编码矩阵;其次,针对其求逆运算复杂度高的问题,利用Hlder不等式及Schatten范数来逼近待优化的目标函数,从而求得最优的数字预编码矩阵。仿真结果表明,所提基于改进的OMP算法的混合预编码方案有效降低了运算复杂度,且在数据流数目与射频链数目相差较小时,其系统性能更优。     

基于运动估计与回溯自适应正交匹配追踪的视频压缩传感

为了解决传统视频压缩传感方法中对视频逐帧单独重构所产生的图像模糊,将压缩传感理论与MPEG标准视频编码的相关技术相结合,提出了一种基于运动估计与运动补偿的视频压缩传感方法,以消除视频信号在空域和时域上的冗余。该方法在充分考虑视频序列时域相关性的同时,首先对视频图像进行前、后向和双向预测和补偿,然后采用回溯自适应正交匹配追踪(BAOMP)算法,对运动预测残差进行重构,最后实现当前帧的重构。实验结果表明,该方法较逐帧重构的视频图像质量有较大改善,且可获得更高的峰值信噪比。     

基于辅助变量的压缩采样匹配追踪闭环系统辨识方法

针对被控对象和反馈通道均具有未知时滞的闭环系统,提出一种基于辅助变量的压缩采样匹配追踪辨识方法.该方法利用辅助变量方法对压缩采样匹配追踪算法进行改进,获得过参数化辨识模型稀疏参数向量的估计,根据稀疏向量的结构得到前向通道的参数估计和时滞估计,进而根据模型等价原理获得反馈通道的参数估计.仿真结果表明,所提出方法仅需少量的迭代即可获得这类闭环系统参数与时滞的有效估计.