Hard Thresholding Research Articles

Accurate and fast reconstruction for bioluminescence tomography based on adaptive Newton hard thresholding pursuit algorithm.

As a promising noninvasive medical imaging technique, bioluminescence tomography (BLT) dynamically offers three-dimensional visualization of tumor distribution in living animals. However, due to the high ill-posedness caused by the strong scattering property of biological tissues and the limited boundary measurements with noise, BLT reconstruction still cannot meet actual preliminary clinical application requirements. In our research, to recover 3D tumor distribution quickly and precisely, an adaptive Newton hard thresholding pursuit (ANHTP) algorithm is proposed to improve the performance of BLT. The ANHTP algorithm fully combines the advantages of sparsity constrained optimization and convex optimization to guarantee global convergence. More precisely, an adaptive sparsity adjustment strategy was developed to obtain the support set of the inverse system matrix. Based on the strong Wolfe line search criterion, a modified damped Newton algorithm was constructed to obtain optimal source distribution information. A series of numerical simulations and phantom and in vivo experiments show that ANHTP has high reconstruction accuracy, fast reconstruction speed, and good robustness. Our proposed algorithm can further increase the practicality of BLT in biomedical applications.

Reliability assessment of a system with multi‐shock sources subject to dependent competing failure processes under phase‐type distribution

AbstractFor a system affected by multiple shock sources, the system usually experiences not only one failure process. This paper develops a reliability model for systems with multi‐shock sources subject to dependent competing failure processes (DCFPs). DCFPs consist of two failure modes: soft and hard failures. Multiple shock sources act on the system as follows: assuming there aremshock sources in total, thekth shock source works on the system at first until the system fails, and then the next shock source re‐acts on the system. Unlike the methods in other papers, the phase‐type distribution is used to build the hard failure reliability model in this paper. We consider the time lag of impacts and assume that the impact magnitudes do not exceed the hard failure threshold as an element in the transition matrix. At the same time, consider these two situations to establish a reliability model. In addition, we divide shock magnitudes into three areas: dead, nondeadly, and safe zones. An application example of a micro‐engine is studied to describe the availability of the developed reliability model. And we conduct the sensitivity analysis to exemplify the influence of the performance of the micro‐engine with parameter changing. With the proposed model, the reliability analysis is more efficient with multi‐shock sources subject to DCFPs

Iterative 2D sparse signal reconstruction with masked residual updates for automotive radar interference mitigation

Compressive sensing has attracted considerable attention in automotive radar interference mitigation. However, these algorithms usually cannot be applied directly to commercial automotive radar as most of them are computationally intense. In this paper, we therefore introduce a computationally efficient two-dimensional masked residual updates (2D MRU) compressive sensing framework. By utilizing the sparsity of the beat signal in the frequency domain, the range-Doppler (RD) spectrum can be reconstructed with the help of undistorted samples in the beat signal. Unlike the other schemes, where a 2D signal measurement is vectorized into a 1D signal, the proposed 2D MRU can directly take a 2D signal measurement and reconstruct the corresponding RD spectrum. Furthermore, the 2D MRU framework can be easily integrated into well-known optimization schemes such as basis pursuit, iterative hard thresholding, iterative soft thresholding, orthogonal matching pursuit, and approximate message-passing algorithm. In addition to the standard iterative thresholding algorithms, we propose a novel prior-model-based iterative thresholding method to further reduce the computation time and reconstruction error. Theoretical analysis shows that the proposed framework can successfully reconstruct the RD spectrum with high probability. Moreover, numerical experiments demonstrate the superiority of the proposed framework in terms of computational complexity.

A Reputation Game Simulation: Emergent Social Phenomena from Information Theory

AbstractReputation is a central element of social communications, be it with human or artificial intelligence (AI), and as such can be the primary target of malicious communication strategies. There is already a vast amount of literature on trust networks and their dynamics using Bayesian principles and involving Theory of Mind models. An issue for these simulations can be the amount of information that can be stored and managed using discretizing variables and hard thresholds. Here a novel approach to the way information is updated that accounts for knowledge uncertainty and is closer to reality is proposed. Agents use information compression techniques to capture their complex environment and store it in their finite memories. The loss of information that results from this leads to emergent phenomena, such as echo chambers, self‐deception, deception symbiosis, and freezing of group opinions. Various malicious strategies of agents are studied for their impact on group sociology, like sycophancy, egocentricity, pathological lying, and aggressiveness. Our set‐up already provides insights into social interactions and can be used to investigate the effects of various communication strategies and find ways to counteract malicious ones. Eventually this work should help to safeguard the design of non‐abusive AI systems.

Study on Multiple Fractal Analysis and Response Characteristics of Acoustic Emission Signals from Goaf Rock Bodies.

Based on the actual monitoring data of the acoustic emission (AE) ground pressure monitoring and positioning system, this paper introduces fractal theory and the multifractal detrended fluctuation analysis (MF-DFA) method to estimate the waveform multifractal spectrum of goaf rock acoustic emission signals and investigate multifractal time-varying response characteristics. The research results show that the wavelet hard thresholding method has the best noise reduction effect on the original signal, and the box counting dimension has a strong waveform identification effect. Before deformation damage occurs, fractal spectral width Δα shows an increase and then decrease and the fluctuation scale factor Δf(α) decreases and then increases. When damage occurs, fractal spectral width Δα decreases and then stabilizes and concentrates. Simultaneously, the fluctuation scale factor Δf(α) keeps decreasing until the lowest point, and then shows an increasing trend until it reaches a stable state. This study is of great significance to the stability evaluation and disaster early warning of mine goaf.

Study on the Wavelet Threshold Noise Reduction Technique Based on MATLAB

In the process of image processing, image acquisition, conversion and transmission are often affected by imaging equipment and external environmental noise impact, so that the image degradation. The follow-up image processing of digital image noise influence is bigger, so there are very important realistic meanings to remove image noise. Image denoising is an extensive image pretreatment technology, the purpose is to improve the image SNR, highlight the expectations of the image features. Modern image noise reduction technology is very much, and each has its advantages and disadvantages, in the process of image processing, image acquisition, conversion and transmission are often affected by imaging equipment and external environmental noise impact, so that the image degradation. The follow-up image processing of digital image noise influence is bigger, so there are very important realistic meanings to remove image noise. Image denoising is an extensive image pretreatment technology, the purpose is to improve the image SNR, highlight the expectations of the image features. Modern image noise reduction technology is very much, and each has its advantages and disadvantages, among them, wavelet threshold denoising is a denoising technique can have good treatment of Gauss noise, wavelet threshold denoising is divided into soft threshold and hard threshold denoising, for different noise, can take different threshold denoising, can get very good the effect of. MATLAB is a very good software, and her language is simple and powerful, can finish all kinds of simulation of signal processing, especially the simulation of image denoising. Among them, wavelet threshold denoising is a denoising technique can have good treatment of Gauss noise, wavelet threshold denoising is divided into soft threshold and hard threshold denoising, for different noise, can take different threshold denoising, can get very good effect. MATLAB is a very good software, and her language is simple and powerful, can finish all kinds of simulation of signal processing, especially the simulation of image denoising.

MoËT: Mixture of Expert Trees and its application to verifiable reinforcement learning

Rapid advancements in deep learning have led to many recent breakthroughs. While deep learning models achieve superior performance, often statistically better than humans, their adoption into safety-critical settings, such as healthcare or self-driving cars is hindered by their inability to provide safety guarantees or to expose the inner workings of the model in a human understandable form. We present MoËT, a novel model based on Mixture of Experts, consisting of decision tree experts and a generalized linear model gating function. Thanks to such gating function the model is more expressive than the standard decision tree. To support non-differentiable decision trees as experts, we formulate a novel training procedure. In addition, we introduce a hard thresholding version, MoËTh, in which predictions are made solely by a single expert chosen via the gating function. Thanks to that property, MoËTh allows each prediction to be easily decomposed into a set of logical rules in a form which can be easily verified. While MoËT is a general use model, we illustrate its power in the reinforcement learning setting. By training MoËT models using an imitation learning procedure on deep RL agents we outperform the previous state-of-the-art technique based on decision trees while preserving the verifiability of the models. Moreover, we show that MoËT can also be used in real-world supervised problems on which it outperforms other verifiable machine learning models.

Indicators and criteria of consciousness: ethical implications for the care of behaviourally unresponsive patients

BackgroundAssessing consciousness in other subjects, particularly in non-verbal and behaviourally disabled subjects (e.g., patients with disorders of consciousness), is notoriously challenging but increasingly urgent. The high rate of misdiagnosis among disorders of consciousness raises the need for new perspectives in order to inspire new technical and clinical approaches.Main bodyWe take as a starting point a recently introduced list of operational indicators of consciousness that facilitates its recognition in challenging cases like non-human animals and Artificial Intelligence to explore their relevance to disorders of consciousness and their potential ethical impact on the diagnosis and healthcare of relevant patients. Indicators of consciousness mean particular capacities that can be deduced from observing the behaviour or cognitive performance of the subject in question (or from neural correlates of such performance) and that do not define a hard threshold in deciding about the presence of consciousness, but can be used to infer a graded measure based on the consistency amongst the different indicators. The indicators of consciousness under consideration offer a potential useful strategy for identifying and assessing residual consciousness in patients with disorders of consciousness, setting the theoretical stage for an operationalization and quantification of relevant brain activity.ConclusionsOur heuristic analysis supports the conclusion that the application of the identified indicators of consciousness to its disorders will likely inspire new strategies for assessing three very urgent issues: the misdiagnosis of disorders of consciousness; the need for a gold standard in detecting consciousness and diagnosing its disorders; and the need for a refined taxonomy of disorders of consciousness.

Variational Model for Single-Image Reflection Suppression Based on Multiscale Thresholding.

Reflections often cause degradation in image quality for pictures taken through glass medium. Removing the undesired reflections is becoming increasingly important. For human vision, it can produce much more pleasing results for multimedia applications. For machine vision, it can benefit various applications such as image segmentation and classification. Reflection removal is itself a highly illposed inverse problem that is very difficult to solve, especially for a single input image. Existing methods mainly rely on various prior information and assumptions to alleviate the ill-posedness. In this paper, we design a variational model based on multiscale hard thresholding to both effectively and efficiently suppress image reflections. A direct solver using the discrete cosine transform for implementing the proposed variational model is also provided. Both synthetic and real glass images are used in the numerical experiments to compare the performance of the proposed algorithm with other representative algorithms. The experimental results show the superiority of our algorithm over the previous ones.

“Terrace compression method” and its application in heterogeneity contour detection of transmission images

In multispectral transmission images, the strong scattering characteristics of biological tissues make the acquired signal weak and the image blurred, which brings difficulties to the contour detection of heterogeneity. The precision of image data can be improved by the modulation–demodulation technique, but the improvement of data effective bits also brings data redundancy. This paper proposes the “terrace compression method” and applies it to the detection of heterogeneity contours in transmission images. Experiments are designed to demonstrate the effectiveness of the proposed method. Four types of LEDs with different center wavelengths loaded with sinusoidal signals are used as the illumination sources respectively to acquire image sequences, and four single-wavelength images are demodulated by fast Fourier transform. The grayscale values of the demodulated images are sorted from low to high, several grayscale hard thresholds are set based on the quantity threshold obtained from the minimum size of the predicted detection target, and the grayscale values are divided into different intervals based on the grayscale hard thresholds. Then, the grayscale values below the threshold in each interval are combined to the minimum value of that interval. Finally, the Sobel operator is used to extract the heterogeneity contours. This method can realize image filtering, reduce data redundancy and enhance image gradient, which provides a new idea for heterogeneity contour detection of multispectral transmission images.

Different thresholding methods on Nearest Shrunken Centroid algorithm

This article considers the impact of different thresholding methods to the Nearest Shrunken Centroid algorithm, which is popularly referred as the Prediction Analysis of Microarrays (PAM) for high-dimensional classification. PAM uses soft thresholding to achieve high computational efficiency and high classification accuracy but in the price of retaining too many features. When applied to microarray human cancers, PAM selected 2611 features on average from 10 multi-class datasets. Such a large number of features make it difficult to perform follow up study. One reason behind this problem is the soft thresholding, which is known to produce biased parameter estimate in regression analysis. In this article, we extend the PAM algorithm with two other thresholding methods, hard and order thresholding, and a deep search algorithm to achieve better thresholding parameter estimate. The modified algorithms are extensively tested and compared to the original one based on real data and Monte Carlo studies. In general, the modification not only gave better cancer status prediction accuracy, but also resulted in more parsimonious models with significantly smaller number of features.

Partial gradient optimal thresholding algorithms for a class of sparse optimization problems

The optimization problems with a sparsity constraint is a class of important global optimization problems. A typical type of thresholding algorithms for solving such a problem adopts the traditional full steepest descent direction or Newton-like direction as a search direction to generate an iterate on which a certain thresholding is performed. Traditional hard thresholding discards a large part of a vector, and thus some important information contained in a dense vector has been lost in such a thresholding process. Recent study (Zhao in SIAM J Optim 30(1): 31–55, 2020) shows that the hard thresholding should be applied to a compressible vector instead of a dense vector to avoid a big loss of information. On the other hand, the optimal k-thresholding as a novel thresholding technique may overcome the intrinsic drawback of hard thresholding, and performs thresholding and objective function minimization simultaneously. This motivates us to propose the so-called partial gradient optimal thresholding (PGOT) method and its relaxed versions in this paper. The PGOT is an integration of the partial gradient and the optimal k-thresholding technique. The solution error bound and convergence for the proposed algorithms have been established in this paper under suitable conditions. Application of our results to the sparse optimization problems arising from signal recovery is also discussed. Experiment results from synthetic data indicate that the proposed algorithm is efficient and comparable to several existing algorithms.

Exploiting prior knowledge in compressed sensing to design robust systems for endoscopy image recovery

In this work, we investigate compressed sensing (CS) techniques based on the exploitation of prior knowledge to support telemedicine. In particular, prior knowledge is obtained by computing the probability of appearance of non-zero elements in each row of a sparse matrix, which is then employed in sensing matrix design and recovery algorithms for CS systems. A robust sensing matrix is designed by jointly reducing the average mutual coherence and the projection of the sparse representation error. A Probability-Driven Normalized Iterative Hard Thresholding (PD-NIHT) algorithm is developed as the recovery method, which also exploits the prior knowledge of the probability of appearance of non-zero elements and can bring performance benefits. Simulations for synthetic data and different organs of endoscopy image are carried out, where the proposed sensing matrix and PD-NIHT algorithm achieve a better performance than previously reported algorithms.

Fully learnable deep wavelet transform for unsupervised monitoring of high-frequency time series

High-frequency (HF) signals are ubiquitous in the industrial world and are of great use for monitoring of industrial assets. Most deep-learning tools are designed for inputs of fixed and/or very limited size and many successful applications of deep learning to the industrial context use as inputs extracted features, which are a manually and often arduously obtained compact representation of the original signal. In this paper, we propose a fully unsupervised deep-learning framework that is able to extract a meaningful and sparse representation of raw HF signals. We embed in our architecture important properties of the fast discrete wavelet transform (FDWT) such as 1) the cascade algorithm; 2) the conjugate quadrature filter property that links together the wavelet, the scaling, and transposed filter functions; and 3) the coefficient denoising. Using deep learning, we make this architecture fully learnable: Both the wavelet bases and the wavelet coefficient denoising become learnable. To achieve this objective, we propose an activation function that performs a learnable hard thresholding of the wavelet coefficients. With our framework, the denoising FDWT becomes a fully learnable unsupervised tool that does not require any type of pre- or postprocessing or any prior knowledge on wavelet transform. We demonstrate the benefits of embedding all these properties on three machine-learning tasks performed on open-source sound datasets. We perform an ablation study of the impact of each property on the performance of the architecture, achieve results well above baseline, and outperform other state-of-the-art methods.

Multi-source fault diagnosis of chiller plant sensors based on an improved ensemble empirical mode decomposition Gaussian mixture model

As the core of the heating, ventilation, and air-conditioning (HVAC) control system, the sensor directly determines whether the HVAC control system is running normally. Poor natural and artificial environments can cause sensors to simultaneously fault, called multi-source sensor faults. Compared to the other methods, the Gaussian mixture model (GMM) has a better effect on high-dimensional data classification. In this paper, an improved ensemble empirical mode decomposition hard threshold denoising (EEMD-HTD) is first proposed to denoise the collected data and highlight each sensor’s fault characteristics. Secondly, the single-source and multi-source faults of the sensors are analyzed by the GMM at different points. The above fault diagnosis processes are collectively referred to as EEMD-HTD-GMM. Experimental results show that the EEMD-HTD-GMM has a higher diagnostic ability and distinguishes between the fault types that cause GMM classification confusion.

A globally convergent approximate Newton method for non-convex sparse learning

Newton-type greedy pursuit methods have been shown to work favorably for cardinality-constrained sparse learning problems. The appealing sparsity recovery performance of the existing Newton-type greedy pursuit methods, however, is typically guaranteed within a local neighborhood around the target solution. To address this limitation, we present in this paper a novel approximate Newton pursuit method for sparse learning with linear models. The computation procedure of our method iterates between constructing an inexact Newton-type quadratic majorization to the global empirical risk and solving the quadratic approximation via iterative hard thresholding. Provable global guarantees on mean squared prediction error, which is less understood for prior methods, are provided for our method. Numerical evidence is provided to show the advantages of our approach over the prior methods.

Clustering of sequential repeated superresolution localizations via linear assignment problem

Many fluorescence superresolution techniques, such as (d)STORM, PALM, and DNA-PAINT, generate datasets wherein multiple sequential localizations may arise from a single blinking event of an emitter. These repeated localizations not only hinder interpretation and analysis of such datasets, but also represent an incomplete use of the fluorescence photons. Such localizations are typically combined into a single localization either by clustering with hard distance and time thresholds, or by classical hypothesis testing assuming Gaussian localization errors.

A Review on Adaptive Hierarchy Segmentation of Bone Cancer Using Neural Network in MATLAB

Abstract: Medical imaging is critical in the diagnosis and treatment of illness, the detection of tumours and the early detection of malignant cells. Microscopic pictures have traditionally been used to detect bone characteristics as a conventional technique. Using micro radiography, which requires several exposures and is labor-intensive, these pictures were captured. This method is unable to distinguish between malignant and non-cancerous cells since the pictures are filled with noise. Image processing analysis has to be automated and dependable in order to be effective. Denoising is the initial step in image processing, and it must be done without interfering with the diagnostic information in the process. Noise and blur are introduced in the picture during the earlier step. We've built soft and hard threshold with a variety of coefficients and measured the threshold in order to obtain exact picture processing. Pre-processing approaches for removing noise and obtaining smooth pictures were discussed throughout our presentation. The picture quality will be improved and false segments will be removed as a result of this procedure. The K-means method was used to identify the presence of bone cancer and to assess its stage, while edge segmentation was employed to smooth out the image. GA analysis relies heavily on the ability to discriminate between benign and malignant bone tumour development. The primary goal of our study was to accurately forecast or identify bone tumours at the appropriate time and stage. Using our image processing and genetic method, we were able to accurately identify bone tumours, which would then aid in the right treatment of therapy. Keywords: Cancer, bone cancer, osteosarcoma, Ewing, image segmentation, edge based segmentation, region based segmentation

Towards better characterization of global warming impacts in the environment through climate classifications with improved global models

AbstractClimate classifications are useful to synthesize the physical state of the climate with a proxy that can be directly related to biota. However, they present a potential drawback, namely a strong sensitivity because of the use of hard thresholds (step functions). Thus, minor discrepancies in the base data produce large differences in the type of climate. However, such an a priori limitation is also a strength because such sensitivity can be used to better gauge model performance. Although previous attempts of classifying climates of the world using global climate model outputs were encouraging, the applicability of their classifications to impact studies has been limited by past model issues. Notwithstanding the persistence of certain imperfections and limitations in current models, the high‐quality physical simulations from phase six of the Coupled Intercomparison Project (CMIP6) has opened new possibilities in the field, thanks to their improved representation of atmospheric and oceanic physics. The purpose of this paper is twofold: to show that climate classifications from CMIP6 are sufficiently robust for use in impact studies, and to use those classifications for identifying error sources and potential issues that deserve further attention in models. Thus, 52 CMIP6 climate models were evaluated by using three climate classifications schemes, classical Köppen, extended‐Köppen, and modified Thornthwaite. We first assessed model ability to reproduce present climate types by comparing their outputs with observational data. Models performed best for the Köppen and extended‐Köppen classification methods (Cohen's kappa κ = 0.7), and had moderate scores for the Thornthwaite climate classification (κ = 0.4). By tracing back the observed biases, we were able to pinpoint the misrepresentation of dry climates as a major source of error. Another finding was that most models still had some difficulties in representing the seasonal variability of precipitation over several monsoonal regions, thereby yielding the wrong climate type there. Models were also evaluated for future climate. Substantial changes in climate types are projected in the SSP5‐8.5 scenario. These changes include a shrinkage of polar/frigid climates (22%) and an increase of dry climates (7%).

Iterative Newton hard thresholding‐based approach for cosparse recovery of mmWave massive MIMO channels

SummaryMillimeter wave (mmWave) massive multiple‐input multiple‐output (MIMO) channels are cosparse in nature. These cosparse channels share common cosparsity properties, which is interesting when it comes to estimating a large number of mmWave mMIMO channels. Therefore, the channel estimation (CE) problem can be solved by exploiting the cosparsity and common cosupport properties. Specifically, the CE problem can be formulated as a cosparse signal recovery problem, which can be solved using an analysis operator (AO) and the iterative hard thresholding (IHT) algorithm. Prior analysis‐based compressive sensing (ACS) CE techniques adopt an overcomplete AO, which leads usually to a suboptimal solution that cannot guarantee CE accuracy. In this paper, we firstly propose a projected subgradient (PSG) scheme for AO learning. Then, using the previously learned AO, we propose an iterative Newton hard thresholding (INHT)‐based ACS‐CE algorithm. The effectiveness of the proposal has been proven by computational complexity analysis and numerical simulations.