Minimum Entropy Method Research Articles

A Fast and Robust Range Alignment Method for ISAR Imaging Based on a Deep Learning Network and Regional Multi-Scale Minimum Entropy Method

In inverse synthetic aperture radar (ISAR) imaging, range alignment (RA) is crucial for translational compensation. To address the need for rapidity and accuracy in the RA process, a fast and robust range alignment method is proposed based on a deep learning network and minimum entropy (ME) method. The proposed method consists primarily of two components: the CNN-RNN attention mechanism network (CRAN) architecture and the regional multi-scale minimum entropy (RMSME) method. The main distinction of this method from existing approaches lies in its utilization of a deep learning network for rapid coarse alignment, followed by the search for minimum entropy within local regions at multiple scales. The integration strategy effectively addresses the current challenges of poor generalization in deep learning networks and low efficiency in the traditional ME method. The experimental results of simulation data indicate that the proposed method achieves the best range alignment performance compared to RNN, CRAN, and the traditional ME method. The experimental results of the measured data further validate the practicality of the proposed method. This research provides reference significance for the joint application of deep learning and traditional methods in the RA process.

A novel spaceborne ISAR imaging approach for space target with high-order translational motion compensation and spatial variant MTRC correction

ABSTRACT For spaceborne ISAR imaging of space targets, due to the high-speed relative motion between the radar and targets, both the translational and rotational motion exhibit the high-order characteristics. Conventional translational motion compensation (TMC) methods are ineffective in handling such high-order translational motion. Moreover, the migration through resolution cell (MTRC) stems from the presence of the high-order spatial variant phase of the echo signal, resulting in severe defocusing of ISAR images. In this paper, a novel spaceborne ISAR imaging approach for space targets is proposed, which incorporates the high-order TMC and the high-order MTRC correction. First, the slant range model for spaceborne ISAR imaging is derived as a third-order polynomial form. Based on this model, a modified high-order TMC method is proposed, which utilizes the minimum entropy method combined with the Broyden – Fletcher – Goldfarb – Shanno (BFGS) algorithm. The proposed method leverages orbital model information to obtain the initial TMC coefficients, enabling TMC to be completed more accurately and effectively. Then, a modified polynomial keystone transform (PKT) is proposed to correct the high-order MTRC. The PKT-based method effectively addresses both the high-order and first-order MTRC corrections simultaneously. Finally, a spaceborne ISAR imaging approach is proposed to obtain well-focused ISAR images. Simulated and real data results validate the analysis of the spaceborne ISAR imaging model and demonstrate the effectiveness of the spaceborne imaging approach for space targets proposed in this paper.

Adaptive cascade detection of weak magnetic anomalies based on marine predators algorithm-stochastic resonance

Magnetic anomaly detection is a new technology for underground or underwater ferromagnetic targets using the physical principle that ferromagnetic targets will be long-term magnetized by the geomagnetic field to generate abnormal magnetic fields. This technology is often used in underwater security, mineral exploration, and other areas. But it is quite challenging to effectively detect weak magnetic anomaly signals in a complex underwater environment. Therefore, we propose an adaptive cascade weak magnetic anomaly detection method based on Marine Predators Algorithm-Stochastic Resonance (MPA-SR). According to the characteristics of magnetic anomaly signals, the cascade detection method of low-pass filtering, stochastic resonance, and threshold detection is designed to improve the detection probability of magnetic anomaly signals. In addition, the Marine predator algorithm with optimized initialization strategy and step size control parameters is used to improve the stochastic resonance system to adaptively detect the magnetic anomaly signal in more applications. The simulation results show that the signal-to-noise ratio (SNR) of the output signal of the MPA-SR method is 2.41 dB higher than the input signal, and the detection probability of the method is 57% higher than that of the minimum entropy (ME) method under the same low SNR environment. The method can provide the theoretical basis and empirical reference for further application of magnetic anomaly data like identifying, locating, and tracking underwater magnetic targets.

Diffusion Mixture Minimum Total Error Entropy Adaptive Filtering Algorithm and Its Performance Analysis

The distributed adaptive filtering algorithms applied in the error-in-variables (EIV) model consider that both input and output signals suffer from noise disturbance for practical applications. However, the traditional distributed adaptive filtering algorithms applied in the EIV model cannot combat non-Gaussian noises well. To address this issue, this paper develops a mixture minimum total error entropy (MMTE) method and its diffusion mixture minimum total error entropy (DMMTE) algorithm. The proposed DMMTE has the significant performance improvement in non-Gaussian noises, and is more general than the diffusion minimum total error entropy (DMTE) algorithm. To select mixture coefficient effectively, a variable mixture coefficient method is further proposed to generate a variable DMMTE (VDMMTE) algorithm. Moreover, the local mean stability analysis and steady-state performance analysis of DMMTE are presented. Simulations verify the correctness of the theoretical analysis and illustrate the performance superiority of the proposed DMMTE.

Investment benefit evaluation of wind power energy storage based on improved minimum cross entropy method

Investment benefit evaluation of wind power energy storage based on improved minimum cross entropy method

Investment benefit evaluation of wind power energy storage based on improved minimum cross entropy method

Investment benefit evaluation of wind power energy storage based on improved minimum cross entropy method

An approach to prevent weight manipulation by minimum adjustment and maximum entropy method in social network group decision making.

In social network group decision making (SN-GDM) problem, subgroup weights are mostly unknown, many approaches have been proposed to determine the subgroup weights. However, most of these methods ignore the weight manipulation behavior of subgroups. Some studies indicated that weight manipulation behavior hinders consensus efficiency. To deal with this issue, this paper proposes a theoretical framework to prevent weight manipulation in SN-GDM. Firstly, a community detection based method is used to cluster the large group. The power relations of subgroups are measured by the power index (PI), which depends on the subgroups size and cohesion. Then, a minimum adjustment feedback model with maximum entropy is proposed to prevent subgroups' manipulation behavior. The minimum adjustment rule aims for 'efficiency' while the maximum entropy rule aims for 'justice'. The experimental results show that the proposed model can guarantee the rationality of weight distribution to reach consensus efficiently, which is achieved by maintaining a balance between 'efficiency' and 'justice' in the mechanism of assigning weights. Finally, the detailed numerical and simulation analyses are carried out to verify the validity of the proposed method.

Remanufacturing lead time planning of the medical device with multi-refurbishing steps

This research is motivated by the challenges a ventilator remanufacturer encountered during the COVID-19 pandemic: (i) three refurbishing steps, namely, disassembling, sterilising, and reconditioning, which reduce the yield rates of reused components and thus complicating the remanufacturing process, are required to satisfy the compulsory hygienic regulations; and (ii) the lead time to procuring new components become rather variable because of the paralysed global logistics, thereby prolonging the remanufacturing time. To minimise the total remanufacturing costs, mathematical models are built to derive the optimal remanufacturing lead time analytically for one- and two-component cases and numerical studies are conducted to investigate the behaviour of the remanufacturing process. Four managerial insights are provided to improve the remanufacturing performance: (i) The minimum relative entropy method could approximate the optimal remanufacturing lead time with higher precision because the remanufacturing time might be multi-modal distributed. (ii) Increasing the yield rates at all refurbishing steps could shorten the remanufacturing lead time but does not lower the total cost necessarily. (iii) Investment in reducing the refurbishing lead times might not be economically efficient, whereas shortening the procurement lead time could lower the cost dramatically. (iv) Stock-based strategy for the components with low holding cost could help simplify the remanufacturing process and save the multi-skilled labour cost.

A reweighted alternating direction method of multipliers for joint phase adjustment and ISAR imaging

ABSTRACT In view of inverse synthetic aperture radar (ISAR) imaging, sparse aperture not only affects the imaging quality of traditional range Doppler (RD) algorithm but also increases the difficulty of translational motion compensation (TMC). For the purpose of reducing the influence of motion errors on the target imaging, reweighted alternating direction method of multipliers (RADMM) is proposed to realize the joint processing of phase adjustment and ISAR imaging. Combined with pattern-coupled sparse structure (PCSS) information of the target, the reweighted norm minimization problem is established first. Then, the minimum entropy method is adopted to estimate the phase error, and the iterative process of RADMM is deduced. Finally, the experimental results based on two sets of measured data demonstrate the validity of the proposed algorithm under the conditions of noise and sparse aperture.

Translational Motion Compensation for ISAR Imaging Based on Range Joint Fast Orthogonal Matching Pursuit Algorithm

Accurate translational motion compensation (TMC) is the key procedure of inverse synthetic aperture radar (ISAR) imaging. Under the condition of sparse aperture, the correlation of adjacent pulses is severely destroyed, which brings a few challenges to TMC and imaging. Thus, this paper proposes a novel TMC method for ISAR imaging. In this technique, the signal model of joint phase adjustment and ISAR imaging is established first. Then, the process of TMC is designed. That is, after range alignment with improved global minimum entropy (IGME), the range joint fast orthogonal matching pursuit (RJFOMP) algorithm is applied to ISAR imaging, and the minimum entropy method (MEM) is adopted to estimate the phase error. Meanwhile, the joint optimization of phase adjustment and ISAR imaging is realized through the cyclic iteration. Extensive experiments based on both simulated and measured data demonstrate that the proposed TMC method is effective for two modes of motion errors, which are named as coherent mode (CM) and non-coherent mode (NCM), respectively. When RJFOMP is used for joint phase adjustment and ISAR imaging, it has excellent imaging performance under noisy and sparse conditions.

The influence of discretization of the flat's area on its selling time

Many of the variables that describe property attributes are continuous. Additionally, during the digitization of the real estate market, analysts have access to a large amount of information. This overload of information (many observations, many attributes) makes it difficult to analyse the data and identify patterns. For continuous variables, therefore, discretization is recommended, which among other things: speeds up calculations, increases the transparency of results, facilitates interpretation, allows the use of variables with outliers.The subject of the study is a mixed property offered for sale. The authors study the time of sale of properties depending on their area, using the method of duration analysis and the Kaplan-Meier estimator. However, these methods require attributes to be in categorical, nominal or symbolic form. In real estate research, continuous variables are most often discretized using expert knowledge and a lack of proposed solutions to this problem in the literature. There is also a lack of research on comparing the effectiveness of different discretization methods. Therefore, the paper proposes a discretization of real estate area according to thirteen selected methods. The result of the discretization should be, among others, disjoint intervals and significantly different time of sale in selected subgroups, which was the basis for assessing the effectiveness of selected methods.Due to the large number of observations (3,732), methods referring to the number of observations and the range of values proved unsuitable, with equal-frequency methods generating a larger number of classes than equal-width methods. As a result of using methods discretizing the variable into too few classes (4), selling time did not differ significantly among subgroups. The best results were obtained using the minimum entropy method and expert indication of the interval span. The results can be used in the practice of selling residential real estate, as preliminary information about the time of sale depending on the area of the flat.

An Efficient Multichannel SAR Channel Phase Error Calibration Method Based on Fine-Focused HRWS SAR Image Entropy

Azimuth multichannel synthetic aperture radar (SAR) is a useful approach to solving minimum antenna area constraint and realizing high resolution and wide swath (HRWS) imaging by multichannel signal reconstruction. However, channel phase error will significantly degrade the reconstruction performance and leads to azimuth ghost. This article presents an efficient minimum entropy channel error estimation method based on fine-focused SAR image. The multichannel SAR images are obtained by using Range-Doppler imaging algorithm applied for preprocessed data of each channel. Then, the reconstruction and the residual range cell migration and residual second range compression compensation are performed to achieve multichannel fine-focused SAR images. After overlapping these multichannel fine-focused SAR images and iteratively calibrating the channel phase error, fine-focused HRWS SAR image can be achieved. Therefore, the SAR image used in the channel error estimation process can directly obtain the fine focused HRWS SAR image after minimum entropy iteration without additional imaging operations. Compared with the minimum entropy method by using the coarse-focused SAR image based on azimuth deramp, redundant reconstruction, and imaging operations are avoided. Thus, error estimation and imaging processing procedures are optimized. Processing efficiency improvement are analyzed, and simulation and acquired data processing verify the effectiveness of the proposed method.

Performance Assessment of MIMO System With Non-Gaussian Disturbances

Performance assessment of control loops is of great importance for industrial production. This paper proposes a novel performance assessment and controller tuning method for non-Gaussian MIMO feedback control systems. First, an algorithm based on minimum entropy and mutual information projection to latent structure (ME-PLS) is proposed to replace the canonical correlation analysis algorithm (CCA). The ME-PLS algorithm decomposes the system data into independent components related to inputs and outputs, and this algorithm applies to both Gaussian and non-Gaussian systems. Each pair of principal components represents a virtual non-Gaussian control loop. Next, the performance of each virtual loop is calculated separately with the non-Gaussian minimum entropy method. Finally, a least absolute deviation iterative algorithm based on the CARMA model (CARMA-LADI) is given to identify the parameters of each virtual loop and to give the actual controller tuning directions based on the relationships obtained by the ME-PLS algorithm.

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.

Weak magnetic anomaly signal detection based on the entropy of mixed differential signal

Magnetic anomaly detection is of great significance in geological exploration and underwater target detection. However, the magnetic anomaly signal is not easy to be detected because of its weakness relative to the magnetic environmental noise, and the detection probability of the magnetic anomaly signal is affected by signal frequency. We propose a mixed differential minimum entropy method which can detect the weak magnetic anomaly signal. The proposed method combines the coherence difference method with the synchronous reference subtraction method in preprocess, which can suppress common-mode noise in the signal and relax the limitation of the frequency of the magnetic anomaly signal on the detection ability. Using the concept of entropy to describe the preprocessed signal can eliminate the residual high-frequency noise and further improve the signal-to-noise ratio of the target signal. Results show that the proposed method may effectively improve the signal-to-noise ratio and increase the frequency range of the magnetic anomaly signal, which has better detection performance than that of traditional method.

Kernel gradient descent algorithm for information theoretic learning

Information theoretic learning is a learning paradigm that uses concepts of entropies and divergences from information theory. A variety of signal processing and machine learning methods fall into this framework. Minimum error entropy principle is a typical one amongst them. In this paper, we study a kernel version of minimum error entropy methods that can be used to find nonlinear structures in the data. We show that the kernel minimum error entropy can be implemented by kernel based gradient descent algorithms with or without regularization. Convergence rates for both algorithms are deduced.

A Modified Factorized Geometrical Autofocus Method for Wide Angle SAR

Wide-Angle (WA) synthetic aperture radar (SAR) has shown remarkable performance in high-resolution mapping, and its mostly used imaging algorithm, fast factorized back projection (FFBP), is efficient, robust, and of low computational complexity. However, trajectory deviations and the system calibration error, introduced by low measurement accuracy, dramatically degrade FFBP's performance. This article proposes the modified factorized geometrical autofocus (MFGA) method for WA-SAR to address the above problems in FFBP. MFGA implements the phase gradient algorithm on defocus subimages at first. Then, a factorized geometrical error hypothesis between subimages is proposed. And the corresponding defocus factors are classified as three independent parts: image distortion, spectrum migration, and phase error. To deal with those problems, MFGA introduces image registration techniques and a maximum sharpness method to calibrate image distortion and phase error. Moreover, in MFGA, based on minimum entropy and least square method, a Doppler spectrum migration correction algorithm is proposed to correct spectrum migration. In the FFBP chain, MFGA is used on subimages refocus and fusion until obtaining a full-resolution image. In our experiments, we compared MFGA and other time-domain autofocus algorithms using simulated data and real data obtained by helicopter and airship with false trajectory and system calibration parameters. The results show that MFGA performs better in terms of the peak to side-lobe ratio, the azimuth resolution, the refocused images' entropy, and processing time consumption. The better performance demonstrates MFGA's advantages in addressing trajectory deviations and the system calibration error for WA-SAR.

Adaptive Magnetic Anomaly Detection Method with Ensemble Empirical Mode Decomposition and Minimum Entropy Feature

Due to the fast attenuation of the magnetic field along with the distance, the magnetic anomaly generated by the remote magnetic target is usually buried in the magnetic noise. In order to improve the performance of magnetic anomaly detection (MAD) with low SNR, we propose an adaptive method of MAD with ensemble empirical mode decomposition (EEMD) and minimum entropy (ME) feature. The magnetic data is decomposed into the multiple intrinsic modal functions (IMFs) with different scales by EEMD. According to a defined criterion, the magnetic noise and magnetic signal are reconstructed based on IMFs, respectively. Entropy feature of reconstructed magnetic signal is extracted based on the probability density function (PDF) of the noise which is updated by the reconstructed magnetic noise. Compared to the traditional minimum entropy method, the entropy feature extracted by the proposed method is more obvious. The magnetic anomaly is detected whenever the entropy feature drops below the threshold. Thus, it is effective for revealing the weak magnetic anomaly by the proposed method. The measured magnetic noise is used to validate the performance of the proposed method. The results show that the detection probability of the proposed method is higher with low input SNR.

Real-Time Localization Approach for Maize Cores at Seedling Stage Based on Machine Vision

To realize quick localization of plant maize, a new real-time localization approach is proposed for maize cores at the seedling stage, which can meet the basic demands for localization and quantitative fertilization in precision agriculture and reduce environmental pollution and the use of chemical fertilizers. In the first stage, by taking pictures of maize at the seedling stage in a field with a monocular camera, the maize is segmented from the weed background of the picture. And then the three most-effective methods (i.e., minimum cross entropy, ISODATA, and the Otsu algorithm) are found from six common segmentation algorithms after comparing the accuracy rate of extracting maize and the time efficiency of segmentation. In the second stage, plant core from segmented maize image is recognized, and localized, based on different brightness of the rest part of maize core and plant. Then the geometric center of maize core is considered as localization point. the best effect of extracting maize core was found from the minimum cross entropy method based on gray level. According to experimental validation using many field pictures, under weedy conditions on sunny days, the proposed method has a minimum recognition rate of 88.37% for maize cores and is more robust at excluding weeds.

The multivariate adaptive design for efficient estimation of the time course of perceptual adaptation.

In experiments on behavioral adaptation, hundreds or even thousands of trials per subject are often required in order to accurately recover the many psychometric functions that characterize adaptation's time course. More efficient methods for measuring perceptual changes over time would be beneficial to such efforts. In this article, we propose two methods to adaptively select the optimal stimuli sequentially in an experiment on adaptation: These are the minimum entropy (ME) method and the match probability (MP) method. The ME method minimizes the uncertainty about the joint posterior distribution of the function parameters at each trial and is mathematically equivalent to Zhao, Lesmes, and Lu's (2019) method, which efficiently measures time courses of perceptual change by maximizing information gain. The MP method selects the next stimulus that makes the value of the psychometric function closest to .5-that is, where the probability of choosing either one of the two options for each stimulus is closest to .5. We extended Zhao et al.'s (2019) work by evaluating the ME method in a new domain (contrast adaptation) with two simulation studies that compared it to MP and two other methods (i.e., traditional staircase and random methods), and also explored the optimal block length. ME outperformed the other three methods in general, and using fewer longer blocks generally produced better parameter recovery than using more shorter blocks.