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.     

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.     

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。     

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.     

Residual domain dictionary learning for compressed sensing video recovery

Multimedia Tools and Applications - For compressed sensing (CS) recovery, the reconstruction quality is highly dependent on the sparsity level of the representation for the signal. Motivated by the...     

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。     

Image compressed sensing recovery via nonconvex garrote regularization

Multimedia Tools and Applications - Sparsity inducing model is one of the most important components of image compressed sensing (CS) recovery methods. These models are built on the image prior...     

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。     

压缩感知与动态纹理模型的视频信号分类

针对视频数据的动态纹理特性,提出结合视频压缩感知技术,首先通过压缩采样技术对视频数据进行采样,得到少量的采样数据;然后建立线性动态系统模型,通过少量的压缩采样数据直接估计出模型参数;最后通过计算模型间的马氏距离实现动态纹理视频数据的分类。实验结果表明,提出的压缩感知参数估计方法在20%的低采样率情况下,对交通视频数据的分类正确率达到87%以上。     

基于压缩感知的阵列信号测向方法研究

针对阵列信号处理中传统测向方法在实际应用中存在采样数据量过大,同时需满足空间采样定理的问题,设计了随机线性阵列采样系统。在不满足空间采样定理的情况下,利用目标信号源在空间角度上的稀疏性,提出了在超完备冗余字典框架下将压缩感知理论应用于阵列高分辨测向的方法。计算机仿真结果表明了该算法在抗噪声性能上具有一定的鲁棒性,与传统测向方法相比,实现了在较低信噪比下只需少量采样点就可以达到高分辨测向的目的,降低了运算量。     

A compressed sensing approach for efficient ensemble learning

This paper presents a method for improved ensemble learning, by treating the optimization of an ensemble of classifiers as a compressed sensing problem. Ensemble learning methods improve the performance of a learned predictor by integrating a weighted combination of multiple predictive models. Ideally, the number of models needed in the ensemble should be minimized, while optimizing the weights associated with each included model. We solve this problem by treating it as an example of the compressed sensing problem, in which a sparse solution must be reconstructed from an under-determined linear system. Compressed sensing techniques are then employed to find an ensemble which is both small and effective. An additional contribution of this paper, is to present a new performance evaluation method (a new pairwise diversity measurement) called the roulette-wheel kappa-error. This method takes into account the different weightings of the classifiers, and also reduces the total number of pairs of classifiers needed in the kappa-error diagram, by selecting pairs through a roulette-wheel selection method according to the weightings of the classifiers. This approach can greatly improve the clarity and informativeness of the kappa-error diagram, especially when the number of classifiers in the ensemble is large. We use 25 different public data sets to evaluate and compare the performance of compressed sensing ensembles using four different sparse reconstruction algorithms, combined with two different classifier learning algorithms and two different training data manipulation techniques. We also give the comparison experiments of our method against another five state-of-the-art pruning methods. These experiments show that our method produces comparable or better accuracy, while being significantly faster than the compared methods.     

A semi fragile watermarking algorithm based on compressed sensing applied for audio tampering detection and recovery

Research on audio tampering detection and recovery plays an important role in the field of audio integrity, and authenticity certification. Generally, we use technology of fragile/semi fragile watermarking to detect and recover tampered audio. In this study, a new scheme for watermark embedding, tampering detection, and recovery is proposed. In the new scheme, we get the compressed version of original audio signal using compressed sensing technology and apply discrete wavelet transform (DWT) to each audio frame. In process of embedding, a new self-adaptive algorithm is proposed. Watermark is the quantized reference value of original framed audio signal and tampering location data, and is embedded in the region with low energy of high frequency coefficients and high energy of low frequency coefficients respectively after 2-level DWT. In process of detection, we locate tampered areas by comparing the value of generated random number and extracted watermark after XOR operation with the extracted location data. As for speech, we set a threshold to judge whether it is tampered or not. At last, we extract watermark in areas which are not damaged and get the recovered signal after decompression. Experiments and analysis show that signal after embedding has at least 5 dB higher average signal-to-noise ratio than others, and broken frames and groups can be detected exactly. When signal is destroyed by 20%, 98% of the corpus is intelligible after recovery, and even destroyed by 50%, 80% of the corpus recovered is also intelligible. Compared with other recovery algorithms, audio signal recovered by our proposal has a higher signal-to-noise ratio and a better robustness to some signal processing. When tampering rate is 50%, the average detection rate is over 93%, which indicates that our method is workable.

     

A new construction of compressed sensing matrices for signal processing via vector spaces over finite fields

As an emerging sampling technique, Compressed Sensing provides a quite masterly approach to data acquisition. Compared with the traditional method, how to conquer the Shannon/Nyquist sampling theorem has been fundamentally resolved. In this paper, first, we provide deterministic constructions of sensing matrices based on vector spaces over finite fields. Second, we analyze two kinds of attributes of sensing matrices. One is the recovery performance with respect to compressing and recovering signals in terms of restricted isometry property. In particular, we obtain a series of binary sensing matrices with sparsity level that are quite better than some existing ones. In order to save the storage space and accelerate the recovery process of signals, another character sparsity of matrices has been taken into account. Third, we merge our binary matrices with some matrices owning low coherence in terms of an embedding manipulation to obtain the improved matrices still having low coherence. Finally, compared with the quintessential binary matrices, the improved matrices possess better character of compressing and recovering signals. The favorable performance of our binary and improved matrices have been demonstrated by numerical simulations.

     

Kernel matching pursuit for large datasets

Kernel matching pursuit is a greedy algorithm for building an approximation of a discriminant function as a linear combination of some basis functions selected from a kernel-induced dictionary. Here we propose a modification of the kernel matching pursuit algorithm that aims at making the method practical for large datasets. Starting from an approximating algorithm, the weak greedy algorithm, we introduce a stochastic method for reducing the search space at each iteration. Then we study the implications of using an approximate algorithm and we show how one can control the trade-off between the accuracy and the need for resources. Finally, we present some experiments performed on a large dataset that support our approach and illustrate its applicability.