Minimum Entropy Algorithm Research Articles

High-Speed Maneuvering Target Inverse Synthetic Aperture Radar Imaging and Motion Parameter Estimation Based on Fast Spare Bayesian Learning and Minimum Entropy

High-speed maneuvering target inverse synthetic aperture radar (ISAR) imaging is always a hot topic in signal processing. High-speed maneuvering targets often have high-order maneuvering characteristics, such as translational and rotational characteristics, which destroy the signal structure of stationary targets and make basic imaging processing methods such as range-Doppler (RD) algorithm no longer suitable. In this paper, a high-resolution imaging method for high-speed maneuvering targets is proposed, which uses the fast sparse Bayesian learning (SBL) algorithm and the minimum entropy algorithm for ISAR high-resolution imaging and motion parameter estimation, respectively. Because SBL makes full use of the characteristics of the target and the environment, it can obtain an ISAR high-resolution image of the maneuvering target. However, the high computational complexity caused by matrix inversion and some matrix operations in SBL iteration limit the practical application of SBL in ISAR imaging. In view of the special structure of the matrix required to be inverted, we propose a fast SBL algorithm, which uses a new decomposition method to obtain the decomposition formula of the inverse matrix. Based on the decomposition factors, the multiplication operation involving the inverse matrix can be quickly calculated using fast Fourier transform (FFT), which greatly improves the computational efficiency. Image entropy represents the sharpness and focusing degree of an image, and so the minimum entropy algorithm can estimate the motion parameters of maneuvering targets more accurately. We combine the minimum entropy algorithm with the fast SBL algorithm to realize phase error correction and high-resolution imaging, which has better noise sensitivity and can obtain the best focusing degree image. Finally, simulation results prove the effectiveness of this algorithm.

Inverse synthetic aperture radar autofocus imaging of block structure targets with sparse aperture

Inverse synthetic aperture radar (ISAR) autofocus imaging performance is challenged by the residual phase errors that arise from the traditional motion compensation methods with sparse aperture. Moreover, sparse reconstruction algorithms usually ignore the block sparsity in the ISAR image, which cannot recover structured information of the block structure target completely. An imaging method based on joint minimum Tsallis entropy and pattern-coupled sparse Bayesian learning algorithm is proposed to achieve ISAR autofocus imaging of block structure targets with sparse aperture. A pattern-coupled hierarchical complex Gaussian prior is utilized to characterize the correlation among ISAR image pixels in the complex domain. Such a prior model has the potential to encourage block-sparse patterns and achieve ISAR sparse aperture imaging of block structure targets without knowing the block partition prior information. The residual phase errors are estimated based on the minimum Tsallis entropy criterion during the sparse reconstruction of ISAR image to achieve ISAR autofocus imaging, which has the advantage of improving the computational efficiency compared with minimum Shannon entropy criterion. The superiority of the proposed algorithm is verified by the experimental results based on both simulated and measured data.

Sparse Aperture Autofocusing and Imaging Based on Fast Sparse Bayesian Learning From Gapped Data

Sparse aperture (SA) autofocusing and imaging is a hot research problem in the signal processing field and has been widely used. Under SA, the absence of echoes destroys the coherence between the pulses, which then affects the autofocusing accuracy of the imaging, leading to defocus of the image. In this paper, a novel SA autofocusing and imaging algorithm based on Sparse Bayesian Learning (SBL) is proposed, which uses a fast SBL algorithm to achieve SA high resolution imaging, and uses the minimum Tsallis entropy algorithm to realize autofocusing. As is known to all, SBL has strong robustness and high precision. Unfortunately, the direct calculation of the inversion and multiplication operations involved in each iteration of SBL results in significant computational costs. In the proposed fast SBL algorithm, the matrix required to be inverted has a special structure. The inverse matrix can then be represented by Gohberg-Semencul (G-S) factorization. And almost all operations except for G-S factorization during each iteration can be completed by fast Fourier transform (FFT) or inverse FFT (IFFT), which greatly reduces the amount of computation by several orders of magnitude. In each SBL iteration, the minimum Tsallis entropy algorithm is used for estimating the phase error, which has better noise sensitivity and obtains the images with the best focused degree. Finally, the effectiveness and high efficiency of the proposed fast algorithm are verified by experimental results obtained by simulation and measured data.

Profiling complex volatile components by HS-GC-MS and entropy minimization software: An example on Ligusticum chuanxiong Hort.

Volatile oil, as an important bioactive fraction of medicinal herbs, is comprised of a diversity of compounds. At present, gas chromatography-mass spectrometry (GC-MS) is one of the mainstream approaches to profiling these complex components. However, GC-MS faces the major bottleneck in data analysis, such as co-elution of more than one compound, and interference caused by high background noise; this usually makes an operator have to spend a lot of time and effort in optimizing experimental conditions. Taking Chuanxiong Rhizoma (the dry rhizome of Ligusticum chuanxiong Hort., abbreviated as “CR”) as an example, this study is intended to provide a feasible, quick and cost-effective solution for compound identification based on the chemometric method of entropy minimization (EM) algorithm. Ten batches of geo-authentic CR and eight batches of adulterants including Fuxiong (FX), Shanchuanxiong (SCX) and Cnidii Rhizoma (CNR) were determined by headspace GC-MS. FX and SCX were rhizomes of L. chuanxiong but subjected to improper harvest time. CNR was the dried rhizome of Cnidium officinale Makino. The co-eluting and overlapping peaks and low-concentration peaks with high background were precisely reconstructed by EM algorithm, and then the reconstructed pure mass spectra of each component were compared with the ion fragment information in NIST library for qualitative identification. EM algorithm proves to be capable of delivering results with increased accuracy and high confidence. Moreover, by the GC-MS approach established in this work, the volatile chemical profiles of FX, SCX, and CNR, were quite distinct from those of geo-authentic CR, suggesting that the adulterants should not be confused with CR in clinical practice and pharmaceutical industry. In brief, the advanced EM algorithm is envisioned to be applied to a variety of medicinal herbs, enabling rapid and accurate identification of volatile phytochemicals.

Ground Moving Target Imaging for Highly Squint SAR by Modified Minimum Entropy Algorithm and Spectrum Rotation

Ground moving target (GMT) is displaced and defocused in conventional synthetic aperture radar (SAR) image due to the residual phase error of non-cooperative GMT motion. In this study, a GMT imaging (GMTIm) method is proposed for highly squint SAR. As the squint angle become large, the displace and defocus effect of the GMT image become severe and the geometry distortion of the GMT image cannot be ignored. The proposed method first deduced the two-dimensional (2-D) frequency domain signal of the GMT and the bulk compression function of the Range Migration Algorithm (RMA) in highly squint SAR. Then GMT ROI data are extracted and a modified minimum entropy algorithm (MMEA) is proposed to refocus the GMT image. MMEA introduces the idea of bisection into the iteration process to converge more efficiently than the previous minimum entropy method. To overcome the geometry distortion of the GMT image, an equivalent squint angle spectrum rotation method is proposed. Finally, to suppress the GMT image sidelobe, the sparse characteristic of GMT is considered and a sparse enhancement method is adopted. The proposed method can realize GMTIm in highly squint SAR where the squint angle reaches to 75 degrees. The PSNR and ISLR of point target in highly squint SAR is close to that in side-looking SAR. The simulated point target data and ship data are used to validate the effectiveness of the proposed method.

Fast ISAR motion compensation using improved stage-by-stage approaching algorithm

This paper proposes a fast inverse synthetic aperture radar (ISAR) motion compensation (MOCOM) method. The various motion compensation methods using minimum entropy algorithm such as stage-by-stage approaching (SSA) algorithm were reported recently. However, the computational efficiency and the clearance of the ISAR image were hard to achieve simultaneously. In particular, as the number of the local minima in the entropy curve increases, the processing time takes longer to find the global minimum. In this paper, we propose a new MOCOM algorithm based on an improved SSA algorithm to reduce the processing time. The proposed algorithm uses the envelope value as the fitness function instead of the entropy value, so the number of the local minima in the entropy curve is reduced. Therefore, the entropy curve becomes simple and the required number of the phase error samples is reduced. In the simulation, the processing time is improved by 88.8% than the conventional SSA algorithm. Also, in the experiment, the processing time is improved by 87.9% ∼ 89.2%.

Image smoothing using regularized entropy minimization and self-similarity for the quantitative analysis of drug diffusion.

Targetable drug delivery is an important method for the treatment of liver tumors. For the quantitative analysis of drug diffusion, the establishment of a method for information collection and characterization of extracellular space is developed by imaging analysis of magnetic resonance imaging (MRI) sequences. In this paper, we smoothed out interferential part in scanned digital MRI images. Making full use of priors of low rank, nonlocal self-similarity, and regularized sparsity-promoting entropy, a block-matching regularized entropy minimization algorithm is proposed. Sparsity-promoting entropy function produces much sparser representation of grouped nonlocal similar blocks of image by solving a nonconvex minimization problem. Moreover, an alternating direction method of multipliers algorithm is proposed to iteratively solve the problem above. Experiments on simulated and real images reveal that the proposed method obtains better image restorations compared with some state-of-the-art methods, where most information is recovered and few artifacts are produced.

Flow-Based Clustering on Directed Graphs: A Structural Entropy Minimization Approach

In this study, we focus on flow-based clustering on directed graphs and propose a localized algorithm for this problem. Flow-based clustering in networks requires a set of closely related vertices where the flow amount getting into it is larger than that going out of it. It is able to formulate a variety of practical problems, such as fund-raising set detection in financial networks and influential document clustering in citation networks, etc. Methodologically, we propose the new concept of two-dimensional structural entropy on directed graphs, and based on this, a local structural entropy minimization algorithm for detecting the flow-based community structure of networks is designed. We adopt our algorithm for the problem of fund-raising set detection in financial networks, in which vertices represent accounts, edges represent transactions between two accounts, and weights represent money amounts of transactions. In our experiments, the local two-dimensional structure entropy minimization algorithm is devoted to find a fund-raising community which involves a given input account. We conduct experiments on both synthetic and real fund-raising datasets. The experimental results demonstrate that, given a fixed account, our algorithm is able to efficiently locate a fund-raising community (if any) for which the fund flowing into the community is much higher than that flowing out, and the transactions within the community are relatively denser (fund amount based) than that of inter-community. For a synthetic ground-truth fund-raising community, we adjust the parameters to change its fund-raising tendency. The results for the synthetic datasets show that our algorithm obtains higher precision and recall rates as this tendency gets stronger with each single factor varing. For a real fund-raising community embedded in a simulated capital flow network, our algorithm also find it with high precision and recall rates. The experiments for both scenarios verify the effectiveness of our algorithm.

Iterative minimum entropy algorithm for refocusing of moving targets in SAR images

In this study, an iterative minimum entropy algorithm is proposed for synthetic aperture radar (SAR) refocusing on moving targets with data of the defocused region of interest (ROI). The image entropy of the ROI data is modelled as a function of the phase compensation parameter. Then, an image entropy surrogate function is constructed to iteratively estimate the phase compensation parameter. With the convergence of iterative estimation of the phase compensation parameter, a refocused image of the moving target can be achieved. By directly operating on the small-size defocused ROI data, the computational burden is significantly reduced and most of the clutter is suppressed. Different from the existing ROI-based methods for SAR refocusing of moving targets, the proposed algorithm does not need any prior parameters. The performance of the proposed algorithm is demonstrated by using simulated data and real SAR data. Compared with some existing methods, the proposed method can produce slightly better-refocusing effect with less computational complexity.

Three-dimensional Geometry Reconstruction of Ship Targets with Complex Motion for Interferometric ISAR with Sparse Aperture

Three-Dimensional (3-D) Interferometric Inverse Synthetic Aperture Radar (InISAR) imaging system based on the orthogonal double baseline can achieve the 3-D geometric reconstruction of a target effectively, which is extremely helpful in target classification and identification. However, only sparse aperture measurements are available in the actual imaging process, which might pose some challenges to the traditional InISAR imaging algorithms. In this study, a new method of 3-D InISAR imaging of a ship with sparse aperture is presented. Minimum entropy algorithms are adopted to realize motion compensation and image coregistration of the sparse echoes. A gradient-based technique is used to achieve highly accurate signal reconstruction for the sparse aperture. A two-Dimensional (2-D) ISAR image was achieved with azimuth compression via the parameters-estimation method, and the 3-D reconstruction of a ship was achieved via the interference approach. The obtained simulation results validate the feasibility of the presented approach.

A new and fast correntropy-based method for system identification with exemplifications in low-SNR communications regime

One of the most significant issues in machine learning is system identification with many applications, e.g., channel estimation (CE) in digital communications. Introducing a new correntropy-based method, this paper deals with the comparison between mean square error (MSE) and information theoretic measures in non-Gaussian noise channel estimation, by analyzing the MSE, minimum error entropy (MEE) and correntropy algorithms in several channel models utilizing neural networks. The first contribution of this paper is introducing a new correntropy-based conjugate gradient (CCG) method and applying it in the CE problem, which this new algorithm converges faster than standard maximum correntropy criterion algorithm. Aiming at this contribution, the better convergence rate is discussed analytically and it is proved that the CCG could converge to the optimal solution quadratically. Next, the performance of an extended MSE algorithm is compared with information theoretic criteria; in addition, a comparison between MEE and correntropy-based algorithm is presented. The Monte Carlo results illustrate that correntropy and MEE outperform MSE algorithm in low-SNR communications especially in the presence of impulsive noise. Then, we apply the trained neural networks in the receiver as an equalizer to obtain the intended performance for different SNR values.

Dynamic background noise removal from overlapping GC-MS peaks via an entropy minimization algorithm

An entropy minimization approach is applied as a dynamic background noise removal system. Clean and pure mass spectra were extracted from overlapping GC-MS peaks and led to the accurate identification of chemical compounds.

Convergence of Gradient Descent for Minimum Error Entropy Principle in Linear Regression

We study the convergence of minimum error entropy (MEE) algorithms when they are implemented by gradient descent. This method has been used in practical applications for more than one decade, but there has been no consistency or rigorous error analysis. This paper gives the first rigorous proof for the convergence of the gradient descent method for MEE in a linear regression setting. The mean square error is proved to decay exponentially fast in terms of the iteration steps and of order $O(\frac{1}{m})$ in terms of the sample size $m$ . The mean square convergence is guaranteed when the step size is chosen appropriately and the scaling parameter is large enough.

Diffusion maximum correntropy criterion algorithms for robust distributed estimation

Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adapt then combine MCC and combine then adapt MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distributed estimation are in general based on the mean square error (MSE) criterion, which is desirable when the measurement noise is Gaussian. In non-Gaussian situations, especially for the impulsive-noise case, MCC based methods may achieve much better performance than the MSE methods as they take into account higher order statistics of error distribution. The proposed methods can also outperform the robust diffusion least mean p-power (DLMP) and diffusion minimum error entropy (DMEE) algorithms. The mean and mean square convergence analysis of the new algorithms are also carried out.

Analysis of Four Components of Asphalt Based on Entropy Minimization Algorithm

Analysis of Four Components of Asphalt Based on Entropy Minimization Algorithm

Minimum Error Entropy Algorithms with Sparsity Penalty Constraints

Recently, sparse adaptive learning algorithms have been developed to exploit system sparsity as well as to mitigate various noise disturbances in many applications. In particular, in sparse channel estimation, the parameter vector with sparsity characteristic can be well estimated from noisy measurements through a sparse adaptive filter. In previous studies, most works use the mean square error (MSE) based cost to develop sparse filters, which is rational under the assumption of Gaussian distributions. However, Gaussian assumption does not always hold in real-world environments. To address this issue, we incorporate in this work an l1-norm or a reweighted l1-norm into the minimum error entropy (MEE) criterion to develop new sparse adaptive filters, which may perform much better than the MSE based methods, especially in heavy-tailed non-Gaussian situations, since the error entropy can capture higher-order statistics of the errors. In addition, a new approximator of l0-norm, based on the correntropy induced metric (CIM), is also used as a sparsity penalty term (SPT). We analyze the mean square convergence of the proposed new sparse adaptive filters. An energy conservation relation is derived and a sufficient condition is obtained, which ensures the mean square convergence. Simulation results confirm the superior performance of the new algorithms.

NOVEL JAMMING SUPPRESSION METHOD USING POLARIZATION SAR DATA

Barrage and deceptive jamming can mask the synthetic aperture radar (SAR) signals and render SAR useless. In this paper, a novel jamming suppression method based on polarization SAR (PolSAR) is proposed. After range compression, the barrage jamming has a noise-like characteristic while the real echo and deceptive jamming are focused. According to this, the barrage jamming is removed via a minimum entropy algorithm. Based on the difierent polarization characteristics between deceptive jamming and the real echo, the deceptive jamming can be suppressed by phase compensation in doppler domain. Simulation results are shown to demonstrate the validity of the proposed method.

A Robust Channel-Calibration Algorithm for Multi-Channel in Azimuth HRWS SAR Imaging Based on Local Maximum-Likelihood Weighted Minimum Entropy

High-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) is an essential tool for modern remote sensing. To effectively deal with the contradiction problem between high-resolution and low pulse repetition frequency and obtain an HRWS SAR image, a multi-channel in azimuth SAR system has been adopted in the literature. However, the performance of the Doppler ambiguity suppression via digital beam forming processing suffers the losses from the channel mismatch. In this paper, a robust channel-calibration algorithm based on weighted minimum entropy is proposed for the multi-channel in azimuth HRWS SAR imaging. The proposed algorithm is implemented by a two-step process. 1) The timing uncertainty in each channel and most of the range-invariant channel mismatches in amplitude and phase have been corrected in the pre-processing of the coarse-compensation. 2) After the pre-processing, there is only residual range-dependent channel mismatch in phase. Then, the retrieval of the range-dependent channel mismatch in phase is achieved by a local maximum-likelihood weighted minimum entropy algorithm. The simulated multi-channel in azimuth HRWS SAR data experiment is adopted to evaluate the performance of the proposed algorithm. Then, some real measured airborne multi-channel in azimuth HRWS Scan-SAR data is used to demonstrate the effectiveness of the proposed approach.

Semi-supervised learning of hidden conditional random fields for time-series classification

Annotating class labels of a large number of time-series data is generally an expensive task. We propose novel semi-supervised learning algorithms that can improve the classification accuracy significantly by exploiting a relatively larger amount of unlabeled data in conjunction with a few labeled samples. Our algorithms utilize the unlabeled data as regularizers for opting for classifiers with stronger certainty on the unlabeled data. For the state-of-the-art conditional probabilistic sequence model called the hidden conditional random field, we first suggest the entropy minimization algorithm that was previously applied for static classification setups. More sophisticated margin-based approaches are then introduced, motivated by the semi-supervised support vector machines originally aimed for non-sequential data. We provide effective ways to incorporate and minimize the hat loss function for sequence data via probabilistic treatment in a principled manner. We show the performance improvement achieved by our methods on several semi-supervised time-series data classification scenarios.

Deep-Ultraviolet (UV) Resonance Raman Spectroscopy as a Tool for Quality Control of Formulated Therapeutic Proteins

A deep-ultraviolet (UV) Raman spectrometer with excitation source tunable from 193 to 210 nm has been built and characterized. The dispersion of the spectrometer over the entire range was measured and described theoretically. The relative sensitivity of the spectrometer was estimated using the integrated intensity ratio of two Raman bands of cyclohexane. Resonance Raman spectra of three formulated insulin products were measured and compared. A band-targeted entropy minimization algorithm was applied to the collected spectra for mixture analysis of insulin products. We conclude that it is feasible to develop robust qualitative methods for quality control of protein-based formulated drug using DUVRR spectroscopy.