Fast Algorithm Research Articles

Reduction Accelerated Adaptive Step‐Size FISTA Based Smooth‐Lasso Regularization for Fluorescence Molecular Tomography Reconstruction

ABSTRACTIn this paper, a reduced accelerated adaptive fast iterative shrinkage threshold algorithm based on Smooth‐Lasso regularization (SL‐RAFISTA‐BB) is proposed for fluorescence molecular tomography (FMT) 3D reconstruction. This method uses the Smooth‐Lasso regularization to fuse the group sparse prior information which can balance the relationship between the sparsity and smoothness of the solution, simplifying the process of calculation. In particular, the convergence speed of the FISTA is improved by introducing a reduction strategy and Barzilai‐Borwein variable step size factor, and constructing a continuation strategy to reduce computing costs and the number of iterations. The experimental results show that the proposed algorithm not only accelerates the convergence speed of the iterative algorithm, but also improves the positioning accuracy of the tumor target, alleviates the over‐sparse or over‐smooth phenomenon of the reconstructed target, and clearly outlines the boundary information of the tumor target. We hope that this method can promote the development of optical molecular tomography.

Fast mapping algorithm with optimized placement selection for CGRA

Fast mapping algorithm with optimized placement selection for CGRA

An innovative fast iterative process algorithm computerization for intermittency LSSPV generation reconfiguration

An innovative fast iterative process algorithm computerization for intermittency LSSPV generation reconfiguration

Image Enhancement Using Bidimensional Empirical Mode Decomposition and Morphological Operations for Brain Tumor Detection and Classification.

The three steps of brain image processing – preprocessing, segmentation, and classification are becoming increasingly important in patient care. The aim of this article is to present a proposed method in the mentioned three-steps, with emphasis on the preprocessing step, which includes noise removal and contrast enhancement. The fast and adaptive bidimensional empirical mode decomposition and the anisotropic diffusion equation as well as the modified combination of top-hat and bottom-hat transforms are used for noise reduction and contrast enhancement. Fast C-means clustering with enhanced image is used to detect tumors and the tumor cluster corresponds to the maximum centroid. Finally, Ensemble learning is used for classification. The Figshare brain tumor dataset contains magnetic resonance images used for data selection. The optimal parameters for both noise reduction and contrast enhancement are investigated using a tumor contaminated with Gaussian noise. The results are evaluated against state-of-the-art results and qualitative performance metrics to demonstrate the dominance of the proposed approach. The fast C-means algorithm is applied to detect tumors using twelve enhanced images. The detected tumors were compared to the ground truth and showed an accuracy and specificity of 99% each, and a sensitivity and precision of 90% each. Six statistical features are retrieved from 150 enhanced images using wavelet packet coefficients at level 4 of the Daubechies 4 wavelet function. These features are used to develop the classifier model using ensemble learning to create a model with training and testing accuracy of 96.7% and 76.7%, respectively. When this model is applied to classify twelve detected tumor images, the accuracy is 75%; there are three misclassified images, all of which belong to the pituitary disease group. Based on the research, it appears that the proposed approach could lead to the development of computer-aided diagnosis (CADx) software that physicians can use as a reference for the treatment of rain tumor.

Photometric classification of stars around the Milky Way’s central black hole

Context. The presence of young massive stars in the Galactic Centre (GC) raises questions about how such stars could form near the massive black hole Sagittarius A* (Sgr A*). Furthermore, the shape of the initial mass function (IMF) in this region seems to differ from its standard Salpeter/Kroupa law. Due to observational challenges such as extreme extinction and crowding, our understanding of the stellar population in this region remains limited, with spectroscopic data available only for selected small and comparably bright sources. Aims. We aim to improve our knowledge about the distribution and the IMF of young, massive, stars in the vicinity of Sgr A*. Methods. We used intermediate band (IB) photometry to identify candidates for massive young stars. To ensure robust classification, we applied three different, but complementary methods: Bayesian inference, a basic neural network, and a fast gradient-boosted trees algorithm. Results. We obtain spectral energy distributions for 6590 stars, 1181 of which have been previously classified spectroscopically. We identify 351 stars that are classified as early types by all three classification methods, with 155 of them being newly identified candidates. The radial density profiles for late and early-type stars fit well with broken power laws, revealing a break radius of 9.2 ± 0.6″ for early-type stars. The late-type stars show a core-like distribution around Sgr A* while the density of the early-type stars increases steeply towards the black hole, consistent with previous work. We infer a top-heavy IMF of the young stars near Sgr A* (R < 9″), with a power-law of 1.6 ± 0.1. At greater distances from Sgr A* a standard Salpeter/Kroupa IMF can explain the data. Additionally, we demonstrate that IB photometry can also constrain the metallicities of late-type stars, estimating metallicities for over 600 late-type stars. Conclusions. The variation of the IMF with radial distance from Sgr A* suggests that different mechanisms of star formation may have been at work in this region. The top-heavy IMF in the innermost region is consistent with star formation in a disc around Sgr A*.

Single track orbit determination analysis for low Earth orbit with approximated J2 dynamics

In the domain of Space Situational Awareness (SSA), the challenges related to orbit determination and catalog correlation are notably pronounced, exacerbated by data scarcity. This study introduces an initial orbit determination methodology that relies on data obtained from a single surveillance radar, with the need for fast algorithms within an operational context serving as the main design driver. The result is a linearized least-squares fitting procedure incorporating an analytically formulated approximation of the dynamics under the J2 perturbation, valid for short-term propagation. This algorithm utilizes all available observables, including range-rate, distinguishing it from other similar methods. A significant contribution of this paper is the enhancement of estimation quality by incorporating information about the object’s predicted orbital plane into the methodology, a method denoted as OPOD. The proposed methods are evaluated through a series of simulations against a classical range and angles fitting method (GTDS) to examine the effects of track length and measurement density on the quality of full state estimation, including the impact of using arcs that are too short. The OPOD methodology shows promising results throughout a wide range of scenarios.

Fast algorithms for the (k,t)-hypercore maintenance problem on hypergraphs

Fast algorithms for the (k,t)-hypercore maintenance problem on hypergraphs

On resolution coresets for constrained clustering

Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the computations and hence allow to extend algorithms to much larger problem sizes. The present paper deals with a weight-balanced clustering problem, and is specifically motivated by an application in materials science where a voxel-based image is to be processed into a diagram representation. Here, the class of desired coresets is naturally confined to those which can be viewed as lowering the resolution of the input data. While one might expect that such resolution coresets are inferior to unrestricted coreset we prove bounds for resolution coresets which improve known bounds in the relevant dimensions and also lead to significantly faster algorithms in practice.

A clustering-aided multi-agent deep reinforcement learning for multi-objective parallel batch processing machines scheduling in semiconductor manufacturing

Batch processing machines are often the bottleneck in semiconductor manufacturing and their scheduling plays a key role in production management. Pioneer researches on multi-objective batch machines scheduling mainly focus on evolutionary algorithms, failing to meet the online scheduling demand. To deal with the challenges confronted by incompatible job families, dynamic job arrivals, capacitated machines and multiple objectives, we propose a clustering-aided multi-agent deep reinforcement learning approach (CA-MADRL) for the scheduling problem. Specifically, to achieve diverse nondominated solutions, an offline multi-objective scheduling algorithm named Multi-Subpopulation fast elitist Non-Dominated Sorting Genetic Algorithm (MS-NSGA-II) is firstly developed to obtain the Pareto Fronts, and a clustering algorithm based on cosine distance is employed to analyze the distribution of Pareto frontier solution, which would be used to guide reward functions design in multi-agent deep reinforcement learning. To realize multi-objective optimization, several reinforcement learning base models are trained for different optimization directions, each of which composed of batch forming agent and batch scheduling agent. To alleviate time complexity of model training, a parameter sharing strategy is introduced between different reinforcement learning base model. By validating the proposed approach with 16 instances designed based on actual production data from a semiconductor manufacturing company, it has been demonstrated that the approach not only meets the high-frequency scheduling requirements of manufacturing systems for parallel batch processing machines but also effectively reduces the total job tardiness and machine energy consumption.

Anisotropic power diagrams for polycrystal modelling: Efficient generation of curved grains via optimal transport

The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape of individual grains. One major obstacle to the wider adoption of APDs is the computational cost that is associated with their generation. We propose a novel approach to generate APDs with prescribed statistical properties, including fine control over the size of individual grains. To this end, we rely on fast optimal transport algorithms that stream well on Graphics Processing Units (GPU) and handle non-uniform, anisotropic distance functions. This allows us to find large APDs that best fit experimental data and generate synthetic high-resolution microstructures in (tens of) seconds. This unlocks their use for computational homogenisation, which is especially relevant to machine learning methods that require the generation of large collections of representative microstructures as training data. The paper is accompanied by a Python library, PyAPD, which is freely available at: www.github.com/mbuze/PyAPD.

Phase space framework enables a variable-scale diffraction model for coherent imaging and display

The fast algorithms in Fourier optics have invigorated multifunctional device design and advanced imaging technologies. However, the necessity for fast computations limits the widely used conventional Fourier methods, where the image plane has a fixed size at certain diffraction distances. These limitations pose challenges in intricate scaling transformations, 3D reconstructions, and full-color displays. Currently, the lack of effective solutions makes people often resort to pre-processing that compromises fidelity. In this paper, leveraging a higher-dimensional phase space method, a universal framework is proposed for customized diffraction calculation methods. Within this framework, a variable-scale diffraction computation model is established for adjusting the size of the image plane and can be operated by fast algorithms. The model’s robust variable-scale capabilities and its aberration automatic correction capability are validated for full-color holography, and high fidelity is achieved. The tomography experiments demonstrate that this model provides a superior solution for holographic 3D reconstruction. In addition, this model is applied to achieve full-color metasurface holography with near-zero crosstalk, showcasing its versatile applicability at nanoscale. Our model presents significant prospects for applications in the optics community, such as beam shaping, computer-generated holograms (CGHs), augmented reality (AR), metasurface optical elements (MOEs), and advanced holographic head-up display (HUD) systems.

ECG arrhythmia classification based on the fast ant colony clustering algorithm with improved spatiotemporal feature perception ability

Electrocardiograph (ECG) is one of the most critical physiological signals used for arrhythmia diagnosis. In recent years, ECG arrhythmia classification devices consisting of multi-module sensors, clustering algorithms and neural networks play an important role in monitoring and diagnosing cardiovascular diseases. However, the commonly used ECG arrhythmia classification methods are still facing some problems such as the complex model structure and long running time. To address the above problems, this paper proposes an ECG arrhythmia classification method based on the fast ant colony clustering algorithm with improved spatiotemporal feature perception ability (SFP-FACC), which uses LSTM to fit the cluster centers and avoids the time consumption of updating the cluster centers during the classification process. The spatiotemporal feature perception ability of this model with the dynamic time warping (DTW) algorithm is improved. The classification is achieved by applying the combination of Euclidean distance and DTW. The convergence speed of the model is improved by using dynamic pheromone volatility coefficient; and finally the optimal solution of the model is determined by using radix sort. Based on the MIT-BIH arrhythmia dataset, the overall accuracy of the proposed classification method in this paper achieves 99.04 %, and even the accuracy of certain types of classification achieves 100 %, and the running time is about 3.5 times faster than that of the basic models. The experiments show that the method proposed in this paper has certain advantages.

In-field grading and sorting technology of apples: A state-of-the-art review

Apple is one of the most popular fruits. In-field grading and sorting of apples would enhance growers’ economic benefits by lowering production costs. This study reviews the key components and progress of the quality inspection algorithm for in-field grading and sorting of apples. Four key components (e.g., conveyor, imaging chamber, sorting actuator, and bin filler) are presented in detail, followed by summarizing the shortcomings of these components. The apple’s external (color, size, and defects) and internal quality inspection technologies, such as optical technologies of visible light, near-infrared (NIR), hyperspectral/multispectral imaging (HSI/MSI), and structured illumination (SI) were presented. Despite the excellent detection performance of emerging technologies (e.g., HSI, MSI, and SI), visible light is still dominantly used for in-filed grading. Challenges in getting information on the whole surface area of the apple, uneven lighting, machine size, throughput, and associated costs hamper the commercialization of apple in-field grading and sorting equipment. At present, more efforts should be devoted to internal quality inspection, by developing reliable, fast, and accurate detection equipment and algorithms. With the advancement of sensors and automation algorithms, as well as the emergence of mechanical systems that are suitable for in-field use, it is anticipated that the apple in-field grading and sorting equipment that inspects both external and internal quality will be realized and commercialized in the near future.

Sparse-spike seismic inversion with semismooth newton algorithm solver

Seismic prospecting has been widely used in the exploration and development of underground geological resources, such as mineral products (e.x., coal, uranium deposit), oil and gas, groundwater, and so forth. Seismic impedance is a physical characteristic parameter of underground formation, which can be used in lithologic classification, rock characterization, stratigraphic correlation, and further mineral reservoir prediction, reserve estimation, and so forth. To estimate impedance from seismic data, one must perform reflectivity series inversion first. Under a simple exponential integration transformation, the reflectivity series can give the final estimated impedance. Sparse-spike seismic inversion is the most common method to obtain reflectivity series with high resolution. It adopts a sparse regularization to impose sparsity on reflectivity series. From sparse reflectivity series, the final estimated impedance has blocky features to make formation interfaces and geological edges precise, which is very important to accurately delineate the distribution range of mineral resources. The development of sparse-spike seismic inversion is still facing major challenges of fast optimization algorithms in real-life application, especially for massive seismic data in 3D case. Semismooth Newton algorithm (SNA), which is a second order mehtod and has super-linear, even quadratic convergence rate, is used to solve sparse-spike seismic inversion. The proposed algorithm has been compared with common used algorithms through a synthetic seismic trace and a 3D real seismic data volume. The results show that the proposed algorithm has faster convergence rate and fewer computation time. It provides a new effective algorithm to solve sparse-spike seismic inversion.

Hardware-friendly fast rate-distortion optimization algorithm for AV1 encoder

Hardware-friendly fast rate-distortion optimization algorithm for AV1 encoder

Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximation

Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous conclusions. In this article a new MSSA method is proposed, named RObust Diagonalwise Estimation of SSA (RODESSA), which is robust against the presence of cellwise and casewise outliers. In particular, the decomposition step of MSSA is replaced by a new robust low-rank approximation of the trajectory matrix that takes its special structure into account. A fast algorithm is constructed, and it is proved that each iteration step decreases the objective function. In order to visualize different types of outliers, a new graphical display is introduced, called an enhanced time series plot. An extensive Monte Carlo simulation study is performed to compare RODESSA with competing approaches in the literature. A real data example about temperature analysis in passenger railway vehicles demonstrates the practical utility of the proposed approach.

A fast combinatorial algorithm for the bilevel knapsack problem with interdiction constraints

A fast combinatorial algorithm for the bilevel knapsack problem with interdiction constraints

Target-oriented image-domain elastic least-squares reverse time migration

Elastic least-squares reverse time migration (ELSRTM), as an imaging method, offers advantages over conventional elastic reverse time migration (ERTM), including higher resolution, better amplitude balancing, reduced crosstalk, and broader bandwidth. However, conventional ELSRTM involves iterative processes in the data domain, resulting in high computational costs. Moreover, since time is continuous during data domain extrapolation, it cannot solely focus on the target area within the subsurface medium. In contrast, image-domain ELSRTM (IDELSRTM) exhibits high computational efficiency and the ability to image target area. Currently, research on image-domain least-squares reverse time migration is predominantly focused on the acoustic wave assumption, despite elastic waves being closer to the actual subsurface medium and providing richer imaging information. In this study, within the framework of data domain ELSRTM, we derived the objective function for the IDELSRTM and introduced an L1 regularization term under the L2 norm to enhance inversion stability. We devised an inversion strategy employing the fast iterative shrinkage-thresholding algorithm (FISTA). Furthermore, drawing from the point spread functions theory in optics, we derived the mapping relationship between the elastic multi-parameter point spread functions (PSF) and the elastic multi-parameter Hessian matrix, and the relationship between the Hessian matrix and the ERTM images. We provided the computational method for the elastic multi-parameter Hessian matrix and utilized it as the linearized forward operator for IDELSRTM. Through numerical experiments, we further elucidated the relationship between the ERTM images and the Hessian matrix under the framework of IDELSRTM, along with the sources of crosstalk in ERTM. Applying our proposed target-oriented IDELSRTM method to layered models and the Marmousi2 model, we demonstrated its effectiveness in improving imaging resolution and quality with only a marginal increase in computational overhead compared to conventional ERTM.

CatReNet: interactive analysis of (auto-) catalytic reaction networks.

Catalytic reaction networks serve as fundamental models for understanding biochemical systems. CatReNet is a novel software designed to facilitate interactive analysis of such networks. It offers fast and exact algorithms for computing various types of self-sustaining autocatalytic subnetworks, including so-called CAFs (constructively autocatalytic food-generated networks), RAFs (reflexively autocatalytic food-generated networks), and pseudo-RAFs. It provides dynamic visualizations to aid exploration and understanding. This open-source Java application runs on Linux, MacOS, and Windows. It is available at https://github.com/husonlab/catrenet under a GPL3 license.

Correction of ‘J. Laderman, V. Pan, X.–H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-588’

In this article, we corrected the trilinear formula for triple disjoint matrix multiplication given in the article ‘J. Laderman, V. Pan, X. H. Sha, On practical Algorithms for Accelerated Matrix Multiplication, Linear Algebra and its Applications. Vol. 162-164 (1992) pp. 557-588’, which is incorrect for matrix dimensions equal to two or greater. That formula is a base of two algorithms, for disjoint and single matrix multiplication. The necessary correction made the amount of non–scalar products rise, slightly increasing the algorithm time complexity. We also corrected explicit formulas, in the bilinear form, for triple disjoint matrix multiplication. They are explicit, and thus convenient for the practical use of the fast matrix multiplication algorithms in question.