Gradient Projection For Sparse Reconstruction Research Articles

Adaptive milling chatter identification based on sparse dictionary considering noise estimation and critical bandwidth analysis

As one of the most unfavorable factors, chatter will seriously hinder the improvement of production efficiency. The weak chatter identification is an effective method for stable cutting. In this paper, a weak chatter identification method is developed using sparse dictionary on account of the milling dynamic responses. As the bases for chatter identification, chatter frequencies are calculated based on the milling dynamic equations. In order to decrease false alarm rate due to the measured background noise, the noise estimation based filtering is proposed. Besides, in consideration of the parameter uncertainty, an adaptive critical bandwidth analysis is implemented with the developed energy proportion index in case of missed alarm. Then, the sparse dictionary matrix is constructed based on the obtained chatter frequencies and critical bandwidth. Finally, the gradient projection for sparse reconstruction (GPSR) algorithm is adopted for chatter frequencies extraction. The proposed method can decrease the measured background noise, obtain critical chatter band and extract weak chatter frequencies accurately. Experimental results shows that the developed method can be successful in weak chatter identification.

Void fraction measurement of gas–liquid two-phase flow based on compressed sensing theory and capacitively coupled electrical resistance tomography system

Capacitively coupled electrical resistance tomography (CCERT) is an innovative technique for electrical resistance tomography based on capacitively coupled contactless conductivity detection (C4D). Despite its potential, there are only a few studies on image reconstruction algorithms for CCERT. To address this, a CCERT measurement system is developed, and the compressed sensing (CS) theory is applied to the inverse problem imaging of CCERT to improve the image reconstruction quality and speed. Firstly, a mathematical CCERT image reconstruction model is constructed under CS theory and three algorithms under CS theory are employed to solve the convex optimization problem of the reconstruction model. Then a thresholding operation is applied to obtain the post-processed image and compared it with the classical linear back projection and Landweber algorithms. The simulation results demonstrate that the Barzilai–Borwein gradient projection for sparse reconstruction (GPSR-BB) algorithm yields more satisfactory imaging results than the other four algorithms. Additionally, three sensitivity matrix optimization methods for GPSR-BB algorithm are compared and find that the new method of screening the rows of the sensitivity matrix to zero is more effective than the other two common optimization methods in terms of reconstructed image quality. Finally, the static experiments of void fraction measurement are conducted using the developed CCERT system. The results indicated that the absolute error of void fraction measurement by GPSR-BB algorithm was less than 6.59% in the range of void fraction from 0.90% to 66.29%.

Lightweight computational spectrometer enabled by learned high-correlation optical filters.

A neural network (NN) computational spectrometer has high reconstruction accuracy and a fast operation speed; however, this type of spectrometer also occupies a large amount of storage in an embedded system due to the excessive computation volume. Contrarily, conventional algorithms such as gradient projection for sparse reconstruction (GPSR) take up less storage, but their spectral reconstruction accuracy is much lower than that of an NN. The major reason is that the performance of a GPSR depends greatly on the non-correlation property of optical filters which may pose challenges for optical filters design and fabrication. In this study, a GPSR algorithm, known as NN-GPSR, is applied to achieve high-precision spectral reconstruction enabled by NN-learned highly correlated filters. A group of NN-learned filters shows high-correlation work as the encoder, and an optimized GPSR algorithm works as the decoder. In this case, large computation volume is exempt and prior knowledge of tens of thousands of images are exploited to get appropriate optical filters design. The experiment data indicate that the NN-GPSR performs well in the reconstructing spectrum and requires far less storage.

AFISTA: Accelerated FISTA for sparse signal recovery and compressive sensing

This paper presents a new fast iterative shrinkage-thresholding algorithm, termed AFISTA. The essential idea is to improve the convergence rate of FISTA using a new continuation strategy leading to a less number of iterations compared to FISTA. The convergence theorem of the AFISTA is proposed. In order to further accelerate the AFISTA method, it is equipped with the Barzilai-Borwein (BB) method. Also, for applications with orthogonal sensing matrix A, we proposed a specialized version of the AFISTA method. AFISTA is tailored for solving the basis pursuit problem which can be applied successfully on a variety of problems arising in signal and image processing issues such as sparse signal recovery, signal and image denoising, image restoration, and compressive sensing. To show the efficiency of the method, we compare our results with generalizations of linearized Bregman and fixed - point continuation (FPC) methods in sparse signal recovery applications, with split Bregman method in compressive sensing for sparse MRI and with Gradient projection for sparse reconstruction (GPSR) method in image deconvolution. Numerical results demonstrate that AFISTA overcomes all of the compared methods in convergence rate and some of them in both convergence rate and quality of reconstructed results.

A Fast Barzilai-Borwein Gradient Projection for Sparse Reconstruction Algorithm Based on 3D Modeling: Application to ERT Imaging

Image reconstruction for electrical resistance tomography (ERT) is an ill-posed inverse problem. L1 regularization is used to solve the inverse problem. An effective method of Barzilai-Borwein gradient projection for sparse reconstruction (GPSR-BB) can resolve the inverse problem into bound-constrained quadratic programming and achieve a gradient projection with line search. However, it is computationally expensive to solve the problem when the data dimension is substantial. Hence, a projection method is employed and combined with the GPSR-BB algorithm to improve the real-time performance. The problem can be mainly solved in the Krylov subspace. For comparison, another L1 regularization GPSR-BB method based on the truncated singular value decomposition is also conducted. Both simulation (with 3D modeling) and experimental results demonstrate the new method’s effectiveness in reducing the computational time and improving the image quality.

Application of Barzilai-Borwein gradient projection for sparse reconstruction algorithm to image reconstruction of electrical capacitance tomography

Electrical capacitance tomography (ECT) is one kind of two/three-phase flow parameter visualization measurement technique. Image reconstruction of ECT is an ill-posed problem. Among the two-phase flow regimes, there are such distribution situations as objects being in the centre, objects being rather small or many objects being close to each other, the accuracy of reconstructed images is relatively poor. Based on the fact that the permittivity distribution of these flow regimes satisfies the priori condition of sparsity, the ECT image reconstruction algorithm based on Barzilai-Borwein gradient projection for sparse reconstruction (GPSR-BB) was presented in this paper. Simulation and experimental tests were carried out for the sparse distribution phantoms and experimental results show that the quality of reconstructed images can be enhanced obviously.

Application of Gradient Projection for Sparse Reconstruction to Compressed Sensing for Image Reconstruction of Electrical Capacitance Tomography

The compressed sensing algorithm based on gradient projection for spare reconstruction (CS-GPSR) is applied to electrical capacitance tomography (ECT) image reconstruction in this paper. First, using the orthogonal basis of FFT transformation, the grey signals of original images can be sparse. Secondly, the observation matrix of ECT system was designed by rearranging the exciting-measuring order, and the capacitance measurements and corresponding sensitivity matrix can be obtained. Finally, the reconstructed images can be obtained using CS-GPSR algorithm. Simulation experiments were carried out and the results showed that the reconstructed images with higher quality can be obtained using the presented CS-GPSR algorithm, compared with conventional linear back projection (LBP) and Landweber iterative algorithms.

Single Channel Speech Enhancement using Wiener Filter and Compressive Sensing

<table width="593" border="0" cellspacing="0" cellpadding="0"><tbody><tr><td valign="top" width="387"><p class="Text">The speech enhancement algorithms are utilized to overcome multiple limitation factors in recent applications such as mobile phone and communication channel. The challenges focus on corrupted speech solution between noise reduction and signal distortion. We used a modified Wiener filter and compressive sensing (CS) to investigate and evaluate the improvement of speech quality. This new method adapted noise estimation and Wiener filter gain function in which to increase weight amplitude spectrum and improve mitigation of interested signals. The CS is then applied using the gradient projection for sparse reconstruction (GPSR) technique as a study system to empirically investigate the interactive effects of the corrupted noise and obtain better perceptual improvement aspects to listener fatigue with noiseless reduction conditions. The proposed algorithm shows an enhancement in testing performance evaluation of objective assessment tests outperform compared to other conventional algorithms at various noise type conditions of 0, 5, 10, 15 dB SNRs. Therefore, the proposed algorithm significantly achieved the speech quality improvement and efficiently obtained higher performance resulting in better noise reduction compare to other conventional algorithms. </p></td></tr></tbody></table>

Block based compressive sensing method of microwave induced thermoacoustic tomography for breast tumor detection

Microwave induced thermoacoustic tomography (MITAT) is a developing non-ionized technique which has great potential in early breast tumor detection. In our previous work, an imaging method, CS-MITAT, was proposed, which applied the compressive sensing theory in MITAT and achieved a good image. The method converts a signal model into an unconstrained optimization problem with ℓ1 norm regularization, which only exploits the spatial sparsity of targets. In this paper, based on the block sparsity of thermoacoustic signals and target distribution in MITAT, the signals to be detected can be grouped into several blocks and the summation of ℓ2 norm regularization is used to replace the ℓ1 norm regularization of the CS-MITAT method. The combination of ℓ2 and ℓ1 norm regularizations helps the aggregation of nonzero elements which are accumulated in blocks. A priori structural constraint is added to form a more realistic signal model which can improve the image quality. Compared with the conventional approach of time reversal mirror and the method of gradient projection for sparse reconstruction, the alternating direction method of multipliers is applied to solve the convex optimization problem. Simulations and experiments on a real breast tumor demonstrate the effectiveness of the proposed method.

Adaptive Grouping Distributed Compressive Sensing Reconstruction of Plant Hyperspectral Data.

With the development of hyperspectral technology, to establish an effective spectral data compressive reconstruction method that can improve data storage, transmission, and maintaining spectral information is critical for quantitative remote sensing research and application in vegetation. The spectral adaptive grouping distributed compressive sensing (AGDCS) algorithm is proposed, which enables a distributed compressed sensing reconstruction of plant hyperspectral data. The spectral characteristics of hyperspectral data are analyzed and the joint sparse model is constructed. The spectral bands are adaptively grouped and the hyperspectral data are compressed and reconstructed on the basis of grouping. The experimental results showed that, compared with orthogonal matching pursuit (OMP) and gradient projection for sparse reconstruction (GPSR), AGDCS can significantly improve the visual effect of image reconstruction in the spatial domain. The peak signal-to-noise ratio (PSNR) at a low sampling rate (the sampling rate is lower than 0.2) increases by 13.72 dB than OMP and 1.66 dB than GPSR. In the spectral domain, the average normalized root mean square error, the mean absolute percentage error, and the mean absolute error of AGDCS is 35.38%, 31.83%, and 33.33% lower than GPSR, respectively. Additionally, AGDCS can achieve relatively high reconstructed efficiency.

一种改进的稀疏信号重构的梯度投影算法

压缩感知理论作为一种全新的信号采集、编解码理论，已被广泛地应用于图像处理、模式识别、自动控制和生物传感等领域，并展现出强大的力量。为了更快速地求解压缩感知问题，在稀疏信号重构的Barzilai-Borwein (B-B)梯度投影(Barzilai-Borwein Gradient Projection for Sparse Reconstruction, GPSR-BB)算法的基础上，采用预测校正的技巧，提出了一种改进的梯度投影算法。该算法首先由常数步长的梯度投影产生一个预测点，再根据预测点及B-B方法计算步长得到新的迭代点。新算法单步迭代计算同样简单，且采用预测校正技巧可使迭代点更接近问题的解，从而可望减少算法的总的迭代次数。对随机生成的测试问题进行数值实验，数值结果表明新算法的运行时间要少于GPSR-BB算法。 As a novel sampling, coding and decoding theory, compressed sensing has been a powerful tool which was widely used to the fields of image processing, pattern recognition, automatic control, biological sensors and so on. Based on the Barzilai-Borwein (B-B) gradient projection for sparse reconstruction (GPSR-BB), this paper proposed a new algorithm by using predictor-corrector technique for solving compressed sensing problem fast. In the new algorithm, a predicted point was first generated by traditional gradient projection and then a new iteration point was obtained with B-B method according to the predicted point. In our algorithm, the calculation of a single iteration is also simple, and by using predictor-corrector technique, the iteration point may be closer to the solution of the problem, thereby the number of the iteration would be reduced. Numerical results show that the running time of the new algorithm is less than GPSR-BB for some randomly generated test problems.

An efficient iterative CBCT reconstruction approach using gradient projection sparse reconstruction algorithm.

The purpose of this study is to develop a fast and convergence proofed CBCT reconstruction framework based on the compressed sensing theory which not only lowers the imaging dose but also is computationally practicable in the busy clinic. We simplified the original mathematical formulation of gradient projection for sparse reconstruction (GPSR) to minimize the number of forward and backward projections for line search processes at each iteration. GPSR based algorithms generally showed improved image quality over the FDK algorithm especially when only a small number of projection data were available. When there were only 40 projections from 360 degree fan beam geometry, the quality of GPSR based algorithms surpassed FDK algorithm within 10 iterations in terms of the mean squared relative error. Our proposed GPSR algorithm converged as fast as the conventional GPSR with a reasonably low computational complexity. The outcomes demonstrate that the proposed GPSR algorithm is attractive for use in real time applications such as on-line IGRT.

Hybrid Norm Pursuit Method for Hyperspectral Image Reconstruction

This paper proposes a hybrid $l_{0}$ and $l_{1}$ norm pursuit (HNP) method for reconstructing hyperspectral image with high speed and high fidelity. The HNP method provides an approximate result by a simple and fast $l_{0}$ norm algorithm [such as the orthogonal matching pursuit (OMP)] first and then regulates it to an accurate result by a good but slow $l_{1}$ norm algorithm [such as the gradient projection for sparse reconstruction (GPSR)]. We build a mathematic model for the HNP method and formulate it to be a constraint optimization problem. How to choose the best switch point is investigated to ensure that the HNP method is able to provide the best reconstruction performance. Experimental results demonstrate that the HNP method is fast and offers high accuracy for hyperspectral image reconstruction and classification.

An effective approach to attenuate random noise based on compressive sensing and curvelet transform

Random noise attenuation is an important step in seismic data processing. In this paper, we propose a novel denoising approach based on compressive sensing and the curvelet transform. We formulate the random noise attenuation problem as an L 1 norm regularized optimization problem. We propose to use the curvelet transform as the sparse transform in the optimization problem to regularize the sparse coefficients in order to separate signal and noise and to use the gradient projection for sparse reconstruction (GPSR) algorithm to solve the formulated optimization problem with an easy implementation and a fast convergence. We tested the performance of our proposed approach on both synthetic and field seismic data. Numerical results show that the proposed approach can effectively suppress the distortion near the edge of seismic events during the noise attenuation process and has high computational efficiency compared with the traditional curvelet thresholding and iterative soft thresholding based denoising methods. Besides, compared with f-x deconvolution, the proposed denoising method is capable of eliminating the random noise more effectively while preserving more useful signals.

A fast time-difference inverse solver for 3D EIT with application to lung imaging.

A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

Compressive Hyperspectral Imaging via Approximate Message Passing

We consider a compressive hyperspectral imaging reconstruction problem, where three-dimensional spatio-spectral information about a scene is sensed by a coded aperture snapshot spectral imager (CASSI). The CASSI imaging process can be modeled as suppressing three-dimensional coded and shifted voxels and projecting these onto a two-dimensional plane, such that the number of acquired measurements is greatly reduced. On the other hand, because the measurements are highly compressive, the reconstruction process becomes challenging. We previously proposed a compressive imaging reconstruction algorithm that is applied to two-dimensional images based on the approximate message passing (AMP) framework. AMP is an iterative algorithm that can be used in signal and image reconstruction by performing denoising at each iteration. We employed an adaptive Wiener filter as the image denoiser, and called our algorithm "AMP-Wiener." In this paper, we extend AMP-Wiener to three-dimensional hyperspectral image reconstruction, and call it "AMP-3D-Wiener." Applying the AMP framework to the CASSI system is challenging, because the matrix that models the CASSI system is highly sparse, and such a matrix is not suitable to AMP and makes it difficult for AMP to converge. Therefore, we modify the adaptive Wiener filter and employ a technique called damping to solve for the divergence issue of AMP. Our approach is applied in nature, and the numerical experiments show that AMP-3D-Wiener outperforms existing widely-used algorithms such as gradient projection for sparse reconstruction (GPSR) and two-step iterative shrinkage/thresholding (TwIST) given a similar amount of runtime. Moreover, in contrast to GPSR and TwIST, AMP-3D-Wiener need not tune any parameters, which simplifies the reconstruction process.

Medical Image Compressed Sensing Reconstruction

In order to improve the speed of compressed sensing image reconstruction algorithm, a two step rapid gradient projection for sparse reconstruction in medical image reconstruction is proposed. in traditional gradient projection for sparse reconstruction algorithm, the searching direction is alternate between the negative gradient direction when the direction is ill, the searching speed is slow. Now we search with two step gradient projection, the speed is increased when meets the ill-condition. Compared with the original GPSR algorithm, the TSGPSR algorithm not only accelerate the speed of operation, but also improves the accuracy of the reconstruction. and exhibits higher robustness under different noise intensities.

Basis Mismatch in a Compressively Sampled Photonic Link

To accurately reproduce an incoming signal, compressive sampling requires that the signal have a sparse representation from within a finite basis or dictionary of vectors. If the incoming signal cannot be sparsely represented by vectors within the given basis or dictionary-a situation sometimes termed basis mismatch-then reconstruction error or failure is likely. In this letter, we present both simulated and experimental results showing the influence of basis mismatch on the ability of a photonic compressive sampling system to accurately reconstruct harmonic signals. Our reconstruction algorithm utilizes gradient projection for sparse reconstruction coupled with a discrete Fourier basis.

Research of Adaptive Gradient Projection Algorithm on Remote Sensing Image Reconstruction

In order to improve the low efficient and the noise effect of remote sensing image reconstruction, an algorithm of adaptive dual gradient projection for sparse reconstruction of compressed sensing theory is proposed. Point to the high frequency noise of remote sensing image, the ADGPSR algorithm pursuits the projection direction in two conjudate directions, thus the high frequency noise effect is overcame. Experiment results show that, compared with the GPSR algorithm, the ADGPSR algorithm on remote sensing image improves the signals reconstruction accuracy.

Adaptive Dual Conjudate Gradient Projection Algorithm for Compressed Sensing Image Reconstruction

In order to improve the quality of noise signals reconstruction method, an algorithm of adaptive dual gradient projection for sparse reconstruction of compressed sensing theory is proposed. In ADGPSR algorithm, the pursuit direction is updated in two conjudate directions, the better original signals estimated value is computed by conjudate coefficient. Thus the reconstruction quality is improved. Experiment results show that, compared with the GPSR algorithm, the ADGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.