Enhanced sampling schemes for MCMC based blind Bernoulli-Gaussian deconvolution

This paper proposes and compares two new sampling schemes for sparse deconvolution using a Bernoulli-Gaussian model. To tackle such a deconvolution problem in a blind and unsupervised context, the Markov Chain Monte Carlo (MCMC) framework is usually adopted, and the chosen sampling scheme is most often the Gibbs sampler. However, such a sampling scheme fails to explore the state space efficiently. Our first alternative, the K-tuple Gibbs sampler, is simply a grouped Gibbs sampler. The second one, called partially marginalized sampler, is obtained by integrating the Gaussian amplitudes out of the target distribution. While the mathematical validity of the first scheme is obvious as a particular instance of the Gibbs sampler, a more detailed analysis is provided to prove the validity of the second scheme.For both methods, optimized implementations are proposed in terms of computation and storage cost. Finally, simulation results validate both schemes as more efficient in terms of convergence time compared with the plain Gibbs sampler. Benchmark sequence simulations show that the partially marginalized sampler takes fewer iterations to converge than the K-tuple Gibbs sampler. However, its computation load per iteration grows almost quadratically with respect to the data length, while it only grows linearly for the K-tuple Gibbs sampler.     

Bayes computation for life testing and reliability estimation

Powerful computational techniques for estimating the parameters and the reliability function of complex life distributions, using Bayes methods, from complete and type-II censored samples are given. The Gibbs sampler approach brings considerable conceptual and computational simplicity to the calculation of the posterior marginals and reliability. Considering constrained parameter and truncated data problems in multivariate life distributions, the Gibbs sampler procedure is easy to implement for sets of simulated data     

一种新颖的异步多径CDMA信号的 贝叶斯多用户检测方法

马尔可夫链蒙特卡罗(MCMC)方法有效地解决了贝叶斯计算的问题,但是不容易将它应用于有未知干扰用户的异步多径CDMA系统.为了克服这一困难,本文提出一种新颖的贝叶斯多用户检测方法,它首先用线性群盲解相关器对接收信号做预处理,然后再用Gibbs采样(一种典型的MCMC算法)做贝叶斯多用户检测.仿真结果表明,该方法的检测性能明显地优于线性群盲多用户检测,其计算复杂度的增加与小区内用户数目呈线性关系.为了进一步提高本文方法的性能,我们使用两级Gibbs采样,根据第一级Gibbs采样的输出得到更精确的参数估计,并把它用于第二级Gibbs采样中.仿真结果证明,与只使用一级Gibbs采样的方法相比,两级Gibbs采样的检测性能明显地改善了.     

Bayes computation for reliability estimation

Bayes estimation of complicated functions requires simpler estimation techniques due to the mathematical difficulties involved in the classical Bayes approach. Bayes estimation enjoys many approximation techniques and computational methods like Metropolis, and Gibbs sampler. Bayes estimation of the reliability of a mixture inverse Gaussian distribution requires a numerical approach since the calculations are immensely difficult from the exact Bayes point of view. Lack of full conditional prior distributions for all 3 parameters of this particular case makes the use of Gibbs sampler inefficient. Application of the rejection method, however, is reasonable since it is very simple to implement without any constraints on the prior distributions or on the hyper-parameters     

Gradient Pursuits

Sparse signal approximations have become a fundamental tool in signal processing with wide-ranging applications from source separation to signal acquisition. The ever-growing number of possible applications and, in particular, the ever-increasing problem sizes now addressed lead to new challenges in terms of computational strategies and the development of fast and efficient algorithms has become paramount. Recently, very fast algorithms have been developed to solve convex optimization problems that are often used to approximate the sparse approximation problem; however, it has also been shown, that in certain circumstances, greedy strategies, such as orthogonal matching pursuit, can have better performance than the convex methods. In this paper, improvements to greedy strategies are proposed and algorithms are developed that approximate orthogonal matching pursuit with computational requirements more akin to matching pursuit. Three different directional optimization schemes based on the gradient, the conjugate gradient, and an approximation to the conjugate gradient are discussed, respectively. It is shown that the conjugate gradient update leads to a novel implementation of orthogonal matching pursuit, while the gradient-based approach as well as the approximate conjugate gradient methods both lead to fast approximations to orthogonal matching pursuit, with the approximate conjugate gradient method being superior to the gradient method.     

Hierarchical Bayesian Sparse Image Reconstruction With Application to MRFM

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.      

基于联合稀疏近似的彩色图像超分辨率重建

针对常用的超分辨率（SR）算法中彩色图像的处理会出现彩色信息的丢失或处理结果色彩偏差较大的问题,提出基于联合稀疏近似（SSA）的彩色图像SR重建方法（SR-SSA）。将多通道数据进行联合稀疏编码（SC）,并保证它们具有相同的稀疏性模式;同时考虑了彩色图像的各通道数据,并兼顾了它们之间的相关性,增强了先验知识的表达能力。...     

Partition function estimation of Gibbs random field images usingMonte Carlo simulations

A Monte Carlo simulation technique for estimating the partition function of a general Gibbs random field image is proposed. By expressing the partition function as an expectation, an importance sampling approach for estimating it using Monte Carlo simulations is developed. As expected, the resulting estimators are unbiased and consistent. Computations can be performed iteratively by using simple Monte Carlo algorithms with remarkable success, as demonstrated by simulations. The work concentrates on binary, second-order Gibbs random fields defined on a rectangular lattice. However, the proposed methods can be easily extended to more general Gibbs random fields. Their potential contribution to optimal parameter estimation and hypothesis testing problems for general Gibbs random field images using a likelihood approach is anticipated     

融合暗原色先验和稀疏表示的水下图像复原

由于水下图像成像过程中受光的散射、噪声干扰等因素影响,致使图像质量严重退化。为了去除模糊和抑制噪声,改善水下图像质量,该文提出一种融合暗原色先验和稀疏表示的水下图像复原新方法。该方法首先利用暗原色先验理论计算水下图像的暗原色,然后基于稀疏表示理论对暗原色进行去噪和优化,基于改进后的暗原色计算水体透射率和光照强度以计算最终复原结果,可以同时达到去模糊和去噪的良好效果。实验结果表明,提出的方法有效提高了图像的平均梯度和信息熵等图像像素,从而改善了图像的质量。     

Robust online tracking via sparse gradient convolution networks

Convolution networks trained offline have recently exhibited promising performance in object tracking tasks. However, offline training is time-consuming and their performance heavily rely on the category of auxiliary training sets. In this paper, we propose a sparse gradient convolution network without pretraining for object tracking. This approach combines shallow convolutional networks and traditional methods (gradient features and sparse representations) to avoid the offline training. In the first frame, we utilize the sparse representation method to learn a series of gradient-based local patches served as fixed filters, and they are used to convolving the input image in the subsequent frames to encode local structural information. Then, we stack all the local structure features to construct global spatial structure features, and the inner geometric layout information is preserved. Moreover, sparse coding and online updating are used to overcome issues related to target appearance variations. Qualitative and quantitative evaluations based on a challenging benchmark dataset demonstrate the effectiveness of the proposed algorithm against several state-of-the-art tracking methods.     

Image compressive sensing via hybrid regularization combining centralized group sparse representation and deep denoiser prior

To effectively solve the ill-posed image compressive sensing (CS) reconstruction problem, it is essential to properly exploit image prior knowledge. In this paper, we propose an efficient hybrid regularization approach for image CS reconstruction, which can simultaneously exploit both internal and external image priors in a unified framework. Specifically, a novel centralized group sparse representation (CGSR) model is designed to more effectively exploit internal image sparsity prior by suppressing the group sparse coding noise (GSCN), i.e., the difference between the group sparse coding coefficients of the observed image and those of the original image. Meanwhile, by taking advantage of the plug-and-play (PnP) image restoration framework, a state-of-the-art deep image denoiser is plugged into the optimization model of image CS reconstruction to implicitly exploit external deep denoiser prior. To make our hybrid internal and external image priors regularized image CS method (named as CGSR-D-CS) tractable and robust, an efficient algorithm based on the split Bregman iteration is developed to solve the optimization problem of CGSR-D-CS. Experimental results demonstrate that our CGSR-D-CS method outperforms some state-of-the-art image CS reconstruction methods (either model-based or deep learning-based methods) in terms of both objective quality and visual perception.     

Simultaneous wavelet estimation and deconvolution of reflectionseismic signals

The problem of simultaneous wavelet estimation and deconvolution is investigated with a Bayesian approach under the assumption that the reflectivity obeys a Bernoulli-Gaussian distribution. Unknown quantities, including the seismic wavelet, the reflection sequence, and the statistical parameters of reflection sequence and noise are all treated as realizations of random variables endowed with suitable prior distributions. Instead of deterministic procedures that can be quite computationally burdensome, a simple Monte Carlo method, called Gibbs sampler, is employed to produce random samples iteratively from the joint posterior distribution of the unknowns. Modifications are made in the Gibbs sampler to overcome the ambiguity problems inherent in seismic deconvolution. Simple averages of the random samples are used to approximate the minimum mean-squared error (MMSE) estimates of the unknowns. Numerical examples are given to demonstrate the performance of the method     

A NOVEL DETECTOR FOR UPLINK CDMA SYSTEM WITH UNKNOWN INTERFERENCE

In this letter, the detection of asynchronous DS-CDMA signal with multipath fading and interference from neighboring cells is studied. A novel multiuser detector based on Gibbs sampler is proposed, in which Gibbs sampler is employed to perform the Bayesian multiuser detection according to the linear group-blind decorrelator output. Since Gibbs sampler is dependent of parameter estimation that can be improved by the output of the detector, an enhanced Gibbs sampier based detector using the improved parameter estimation is put forward. The novel multiuser detection technique has the advantages of high performance and wide applications. Computer simulations show its effectiveness.     

Novel FPGA implementations of Walsh-Hadamard transforms for signalprocessing

The paper describes two approaches suitable for a field-programmable gate-array (FPGA) implementation of fast Walsh-Hadamard transforms. These transforms are important in many signal-processing applications including speech compression, filtering and coding. Two novel architectures for the fast Hadamard transforms using both a systolic architecture and distributed arithmetic techniques are presented. The first approach uses the Baugh-Wooley multiplication algorithm for a systolic architecture implementation. The second approach is based on both a distributed arithmetic ROM and accumulator structure, and a sparse matrix-factorisation technique. Implementations of the algorithms on a Xilinx FPGA board are described. The distributed arithmetic approach exhibits better performances when compared with the systolic architecture approach     

Multi-stage image denoising based on correlation coefficient matching and sparse dictionary pruning

We present a novel image denoising method based on multiscale sparse representations. In tackling the conflicting problems of structure extraction and artifact suppression, we introduce a correlation coefficient matching criterion for sparse coding so as to extract more meaningful structures from the noisy image. On the other hand, we propose a dictionary pruning method to suppress noise. Based on the above techniques, an effective dictionary training method is developed. To further improve the denoising performance, we propose a multi-stage sparse coding framework where sparse representations are obtained in different scales to capture multiscale image features for effective denoising. The multi-stage coding scheme not only reduces the computational burden of previous multiscale denoising approaches, but more importantly, it also contributes to artifact suppression. Experimental results show that the proposed method achieves a state-of-the-art denoising performance in terms of both objective and subjective quality and provides significant improvements over other methods at high noise levels.     

基于l0正则化的增量低秩特征学习目标跟踪

为了提高生成型目标跟踪算法在遮挡、背景干扰 等复杂条件下的性能,在稀疏编码模型中引入l₀范数正 则化约束,以减少冗余编码信息并改善目标表观重构效果。同时提出一种新的基于非凸近端 加速梯度的快速迭代算法, 解决由此产生的非凸非光滑优化问题。设计了一种增量低秩学习策略,和传统方法需 要将目标观测数据作为 一个整体进行低秩学习不同,本文方法通过l₀正则化稀疏编码能够有效地对目标低秩特 征子空间进行在线学习和更 新。在多个视频序列上的实验表明:基于l₀正则化的增量低秩学习方法能有效提高目标 跟踪算法的准确率和鲁棒性; 和8种优秀的跟踪算法相比,本文算法在中心误差稳健性和重叠率稳健性两个指标上都取得 了最好结果。     

结合稀疏表示与匹配梯度分布的图像复原

针对基于稀疏表示的传统图像复原方法无法准确恢 复图像小尺度细节的不足,提出了一种结合稀疏 表示与匹配梯度分布的图像复原方法。首先在稀疏表示图像复原模型的基础上,利用参数化 的超拉 普拉斯分布估计原始图像的梯度分布;然后,通过对图像的梯度分布进行全局约束,利用梯 度直方图匹配 操作匹配图像梯度分布,使复原图像的梯度分布尽可能接近原始图像。仿真实验结果表明 , 本文算法能够取得较优的复原效果, 并且能以较高精度复原图像的细节信息。     

局部非负稀疏编码的高光谱目标检测方法研究

基于稀疏编码的高光谱图像处理算法能够挖掘高光谱高维数据空间中潜在的数据相关性,能自然地贴近光谱信号的本质特征。本文提出基于非负稀疏编码的高光谱目标检测算法。与经典稀疏编码模型相比,非负稀疏编码对编码系数进行非负约束,一方面使得线性编码具有明确的物理解释,另一方面增强了系数的可分性与稳健性。算法首先通过双窗口设计构造局部动态字典,然后利用目标和背景在动态字典上编码的稀疏性差异进行阈值分割最后通过统计判决实现目标检测。仿真数据以及真实数据实验结果证明了算法的有效性。      

Bayesian inference for partially accelerated life tests using Gibbs sampling

We consider a life testing situation in which several groups of items are put, at different instances, on the partially accelerated life test proposed by DeGroot and Goel [Naval Research Logistics Quarterly, 1979. 26, 223–235]. The combined failure time data are then used to derive empirical Bayes estimators for the failure of the exponential life length under normal conditions. The estimation which is implemented using the Gibbs sampler Monte-Carlo-based approach, illustrates once again the ease with which these new types of estimation problems often requiring sophisticated numerical or analytical expertise, can be handled using the sampling based approach.     

Bayesian approach to parameter estimation and interpolation oftime-varying autoregressive processes using the Gibbs sampler

A nonstationary time series is one in which the statistics of the process are a function of time; this time dependency makes it impossible to utilise standard analytically defined statistical estimators to parameterise the process. To overcome this difficulty, the time series is considered within a finite time interval and is modelled as a time-varying autoregressive (AR) process. The AR coefficients that characterise this process are functions of time, represented by a family of basis vectors. The corresponding basis coefficients are invariant over the time window and have stationary statistical properties. A method is described for applying a Markov chain Monte Carlo method known as the Gibbs sampler to the problem of estimating the parameters of such a time-varying autoregressive (TVAR) model, whose time dependent coefficients are modelled by basis functions. The Gibbs sampling scheme is then extended to include a stage which may be used for interpolation. Results on synthetic and real audio signals show that the model is flexible, and that a Gibbs sampling framework is a reasonable scheme for estimating and characterising a time-varying AR process