Backtracking-based matching pursuit method for distributed compressed sensing

In this paper, we study a distributed compressed sensing (DCS) problem in which we need to recover a set of jointly sparse vectors from the measurements. A Backtracking-based Adaptive Orthogonal Matching Pursuit (BAOMP) method to approximately sparse solutions for DCS is proposed. It is an iterative approach where each iteration consists of consecutive forward selection to adaptively choose several atoms and backward removal stages to detect the previous chosen atoms’ reliability and then delete the unreliable atoms at each iteration. Also, unlike its several predecessors, the proposed method does not require the sparsity level to be known as a prior which makes it a potential candidate for many practical applications, when the sparsity of signals is not available. We demonstrate the reconstruction ability of the proposed algorithm on both synthetically generated data and image using Normal and Binary sparse signals, and the real-life electrocardiography (ECG) data, where the proposed method yields less reconstruction error and higher exact recovery rate than other existing DCS algorithms.     

Parallel compressive sampling matching pursuit algorithm for compressed sensing signal reconstruction with OpenCL

Compressive sensing (CS) is a new signal processing method, which was developed recent years. CS can sample signals with a frequency far below the Nyquist frequency. CS can also compress the signals while sampling, which can reduce the usage of resources for signal transmission and storage. However, the reconstruction algorithm used in the corresponding decoder is highly complex and computationally expensive. Thus, in some specific applications, e.g., remote sensing image processing for disaster monitoring, the CS algorithm usually cannot satisfy the time requirements on traditional computing platforms. Various studies have shown that many-core computing platforms such as OpenCL are among the most promising platforms that are available for real-time processing because of their powerful floating-point computing capabilities. In this study, we present the design and implementation of parallel compressive sampling matching pursuit (CoSaMP), which is an OpenCL-based parallel CS reconstruction algorithm, as well as some optimization strategies, such as access efficiency, numerical merge, and instruction optimization. Based on experiments using remote sensing images with different sizes, we demonstrated that the proposed parallel algorithm can achieve speedups of about 41 times and 58 times on AMD HD7350 and NVIDIA K20Xm platforms, respectively, without modifying the application code.     

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.     

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     

基于一次投影子空间追踪的压缩感知信号重构

为了降低信号重构算法的复杂度,实现对稀疏度未知信号的重构,提出了一种基于一次投影子空间追踪(OPSP)的信号重构方法。首先根据约束等距性质确定信号稀疏度的上下界,并将最接近上下界中值的整数作为稀疏度的估计值;然后在子空间追踪(SP)算法的框架下,去掉了迭代中观测向量在支撑集上的投影过程,降低了算法的复杂度。为了更准确地衡量算法的重构性能,提出用完整信号的重构概率作为衡量算法重构性能的指标。与传统的SP算法相比,所提算法可以重构稀疏度未知的信号,且重构时间短,重构概率高。仿真结果验证了该算法的有效性。     

基于压缩感知的后退型自适应匹配追踪算法

基于压缩感知理论的重建关键在于从压缩感知得到的低维数据中精确恢复出原始的高维稀疏数据。针对目前大多数算法都建立在稀疏度已知的基础上,提出一种后退型固定步长自适应匹配追踪重建算法,能够在稀疏度未知的条件下获得图像的精确重建。该算法通过较大固定步长的设置,保证待估信号支撑集大小的稳步快速增加;以相邻阶段重建信号的能量差为迭代停止条件,在迭代停止后通过简单的正则化方法向后剔除多余原子保证精确重建。实验结果表明,该算法在保证测量次数的条件下可以获得快速的精确重建。     

Improved sparsity adaptive matching pursuit algorithm based on compressed sensing

Traditional greedy algorithms need to know the sparsity of the signal in advance, while the sparsity adaptive matching pursuit algorithm avoids this problem at the expense of computational time. To overcome these problems, this paper proposes a variable step size sparsity adaptive matching pursuit (SAMPVSS). In terms of how to select atoms, this algorithm constructs a set of candidate atoms by calculating the correlation between the measurement matrix and the residual and selects the atom most related to the residual. In determining the number of atoms to be selected each time, the algorithm introduces an exponential function. At the beginning of the iteration, a larger step is used to estimate the sparsity of the signal. In the latter part of the iteration, the step size is set to one to improve the accuracy of reconstruction. The simulation results show that the proposed algorithm has good reconstruction effects on both one-dimensional and two-dimensional signals.     

Forward-backward pursuit method for distributed compressed sensing

In this paper, a forward-backward pursuit method for distributed compressed sensing (DCSFBP) is proposed. In contrast to existing distributed compressed sensing (DCS), it is an adaptive iterative approach where each iteration consists of consecutive forward selection and backward removal stages. And it not needs sparsity as prior knowledge and multiple indices are identified at each iteration for recovery. These make it a potential candidate for many practical applications, when the sparsity of signals is not available. Numerical experiments, including recovery of random sparse signals with different nonzero coefficient distributions in many scenarios, in addition to the recovery of sparse image and the real-life electrocardiography (ECG) data, are conducted to demonstrate the validity and high performance of the proposed algorithm, as compared to other existing DCS algorithms.     

改进的压缩采样匹配追踪算法

针对压缩采样匹配追踪( CoSaMP)算法重构精度相对较差的问题,为了提高算法的重构性能,提出了一种基于伪逆处理改进的压缩采样匹配追踪( MCoSaMP)算法。首先,在迭代前,对观测矩阵进行伪逆处理,以此来降低原子间的相干性,从而提高原子选择的准确性;然后,结合正交匹配追踪算法( OMP),将OMP算法迭代K次后的原子和残差作为CoSaMP算法的输入;最后,每次迭代后,通过判断残差是否小于预设阈值来决定算法是否终止。实验结果表明,无论是对一维高斯随机信号还是二维图像信号,MCoSaMP算法的重构效果优于CoSaMP算法,能够在观测值相对较少的情况下,实现信号的精确重构。     

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。     

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。     

SOSP: a stepwise optimal sparsity pursuit algorithm for practical compressed sensing

Compressed Sensing (CS), as a promising paradigm for acquiring signals, is playing an increasing important role in many real-world applications. One of the major components of CS is sparse signal recovery in which greedy algorithm is well-known for its speed and performance. Unfortunately, in many classic greedy algorithms, such as OMP and CoSaMP, the real sparsity is a key prior information, but it is blind. In another words, the true sparsity is not available for many practical applications. Due to this disadvantage, the performance of these algorithms are significantly reduced. In order to avoid too much dependence of classic greedy algorithms on the true sparsity, this paper proposed an efficient reconstruction greedy algorithm for practical Compressed Sensing, termed stepwise optimal sparsity pursuit (SOSP). Differs from the existing algorithms, the unique feature of SOSP algorithm is that the assumption of sparsity is needed instead of the true sparsity. Hence, the limitations of sparsity in practical application can be tackled. Based on an arbitrary initial sparsity satisfying certain conditions, the SOSP algorithm employs two variable step sizes to hunt for the optimal sparsity step by step by comparing the final reconstruction residues. Since the proposed SOSP algorithm preserves the ideas of original algorithms and innovates the prior information of sparsity, thus it is applicable to any effective algorithm requiring known sparsity. Extensive experiments are conducted in order to demonstrate that the SOSP algorithm offers a superior reconstruction performance in terms of discarding the true sparsity.

     

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.     

Construction of compressed sensing matrices for signal processing

To cope with the huge expenditure associated with the fast growing sampling rate, compressed sensing (CS) is proposed as an effective technique of signal processing. In this paper, first, we construct a type of CS matrix to process signals based on singular linear spaces over finite fields. Second, we analyze two kinds of attributes of sensing matrices. One is the recovery performance corresponding to compressing and recovering signals. In particular, we apply two types of criteria, error-correcting pooling designs (PD) and restricted isometry property (RIP), to investigate this attribute. Another is the sparsity corresponding to storage and transmission signals. Third, in order to improve the ability associated with our matrices, we use an embedding approach to merge our binary matrices with some other matrices owing low coherence. At last, we compare our matrices with other existing ones via numerical simulations and the results show that ours outperform others.     

Automated identification of thoracolumbar vertebrae using orthogonal matching pursuit

A computer-assisted system that can automatically provide rapid localization and accurate labeling of vertebral disks and bodies is a highly desirable tool due to the large demand for the diagnostic imaging and surgical planning of the vertebral column structures. However, a reliable detection and definitive labeling of vertebrae can be difficult due to factors such as the limited imaging coverage and various vertebral anomalies particularly in the thoracolumbar and lumbosacral junctions. In this paper, we investigate the problem of identifying the last thoracic and first lumbar vertebrae in CT images. The main purpose of this study is to improve the accuracy of labeling vertebrae of an automatic spine labeling system especially when the field of view is limited in the lower spine region. We present a dictionary-based classification method using a cascade of simultaneous orthogonal matching pursuit classifiers on 2D vertebral regions extracted from the maximum intensity projection images. The performance of the proposed method in terms of accuracy and speed has been validated by experimental results on hundreds of CT images collected from various clinical sites.     

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.