TY - GEN A1 - Schneidereit, Toni A1 - Breuß, Michael T1 - Adaptive neural-domain refinement for solving time-dependent differential equations T2 - Advances in Continuous and Discrete Models N2 - A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent differential equations, one can apply the recently developed method of domain segmentation. That is, the domain may be split into several subdomains, on which the optimisation problem is solved. In classic adaptive numerical methods, the mesh as well as the domain may be refined or decomposed, in order to improve the accuracy. Also, the degree of approximation accuracy may be adapted. Therefore, it is desirable to transfer such important and successful strategies to the field of neural-network-based solutions. In the presented work, we propose a novel adaptive neural approach to meet this aim for solving time-dependent problems. To this end, each subdomain is reduced in size until the optimisation is resolved up to a predefined training accuracy. In addition, while the neural networks employed are by default small, we propose a means to adjust also the number of neurons in an adaptive way. We introduce conditions to automatically confirm the solution reliability and optimise computational parameters whenever it is necessary. Results are provided for several initial-value problems that illustrate important computational properties of the method. KW - Neural forms KW - Adaptive neural refinement KW - Domain decomposition KW - Physics-informed neural networks KW - Differential equations Y1 - 2023 U6 - https://doi.org/10.1186/s13662-023-03789-x SN - 2731-4235 IS - 1 ER - TY - GEN A1 - Kahra, Marvin A1 - Breuß, Michael T1 - Properties of Morphological Dilation in Max-Plus and Plus-Prod Algebra in Connection with the Fourier Transformation T2 - Journal of Mathematical Imaging and Vision N2 - The basic filters in mathematical morphology are dilation and erosion. They are defined by a structuring element that is usually shifted pixel-wise over an image, together with a comparison process that takes place within the corresponding mask. This comparison is made in the grey value case by means of maximum or minimum formation. Hence, there is easy access to max-plus algebra and, by means of an algebra change, also to the theory of linear algebra. We show that an approximation of the maximum function forms a commutative semifield (with respect to multiplication) and corresponds to the maximum again in the limit case. In this way, we demonstrate a novel access to the logarithmic connection between the Fourier transform and the slope transformation. In addition, we prove that the dilation by means of a fast Fourier transform depends only on the size of the structuring element used. Moreover, we derive a bound above which the Fourier approximation yields results that are exact in terms of grey value quantisation. KW - Mathematical morphology KW - Fourier transform KW - Dilation KW - Max-plus algebra KW - Slope transform Y1 - 2023 U6 - https://doi.org/10.1007/s10851-022-01138-3 SN - 0924-9907 VL - 65 IS - 4 SP - 577 EP - 591 ER - TY - GEN A1 - Köhler, Alexander A1 - Breuß, Michael T1 - Towards Efficient Time Stepping for Numerical Shape Correspondence T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2312.13841 SP - 1 EP - 12 ER - TY - GEN A1 - Sridhar, Vivek A1 - Breuß, Michael T1 - Morphological Sampling Theorem and its Extension to Grey-value Images T2 - arXiv N2 - Sampling is a basic operation in image processing. In classic literature, a morphological sampling theorem has been established, which shows how sampling interacts by morphological operations with image reconstruction. Many aspects of morphological sampling have been investigated for binary images, but only some of them have been explored for grey-value imagery. With this paper, we make a step towards completion of this open matter. By relying on the umbra notion, we show how to transfer classic theorems in binary morphology about the interaction of sampling with the fundamental morphological operations dilation, erosion, opening and closing, to the grey-value setting. In doing this we also extend the theory relating the morphological operations and corresponding reconstructions to use of non-flat structuring elements. We illustrate the theoretical developments at hand of examples. Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2305.13279 SP - 1 EP - 24 ER - TY - GEN A1 - Sridhar, Vivek A1 - Shahin, Keyvan A1 - Breuß, Michael A1 - Reichenbach, Marc T1 - The Polynomial Connection between Morphological Dilation and Discrete Convolution T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2305.03018 SP - 1 EP - 11 ER - TY - GEN A1 - Masouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Hartmann, Carsten T1 - Long Short-Term Memory Neural Network for Temperature Prediction in Laser Powder Bed Additive Manufacturing T2 - arXiv Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2301.12904 SP - 1 EP - 15 ER - TY - GEN A1 - Radow, Georg A1 - Rodriguez, Giuseppe A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael ED - Cristiani, Emiliano T1 - Photometric Stereo with Non-Lambertian Preprocessing and Hayakawa Lighting Estimation for Highly Detailed Shape Reconstruction T2 - Mathematical Methods for Objects Reconstruction : From 3D Vision to 3D Printing N2 - In many realistic scenarios, the use of highly detailed photometric 3D reconstruction techniques is hindered by several challenges in given imagery. Especially, the light sources are often unknown and need to be estimated, and the light reflectance is often non-Lambertian. In addition, when approaching the problem to apply photometric techniques at real-world imagery, several parameters appear that need to be fixed in order to obtain high-quality reconstructions. In this chapter, we attempt to tackle these issues by combining photometric stereo with non-Lambertian preprocessing and Hayakawa lighting estimation. At hand of a dedicated study, we discuss the applicability of these techniques for their use in automated 3D geometry recovery for 3D printing. KW - Photometric stereo Shape from shading Hayakawa procedure Lighting estimation Oren-Nayar model Lambertian reflector Y1 - 2023 SN - 978-981-99-0775-5 U6 - https://doi.org/10.1007/978-981-99-0776-2_2 SN - 978-981-99-0776-2 SN - 2281-518X SP - 35 EP - 56 PB - Springer CY - Singapore ER - TY - GEN A1 - Kahra, Marvin A1 - Breuß, Michael A1 - Kleefeld, Andreas A1 - Welk, Martin T1 - An Approach to Colour Morphological Supremum Formation using the LogSumExp Approximation T2 - arXiv N2 - Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations. In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric 2×2 matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach. Y1 - 2023 U6 - https://doi.org/10.48550/arXiv.2312.13792 SP - 1 EP - 12 ER - TY - GEN A1 - Köhler, Alexander A1 - Breuß, Michael A1 - Shabani, Shima ED - Frolkovič, P. ED - Mikula, K. ED - Ševčovič, D. T1 - Dictionary learning with the K-SVD algorithm for recovery of highly textured images : an experimental analysis T2 - Proceedings of the Conference Algoritmy 2024 N2 - Image recovery by dictionary learning is of potential interest for many possible applications. To learn a dictionary, one needs to solve a minimization problem where the solution should be sparse. The K-SVD formalism, which is a generalization of the K-means algorithm, is one of the most popular methods to achieve this aim. We explain the preprocessing that is needed to bring images into a manageable format for the optimization problem. The learning process then takes place in terms of solving for sparse representations of the image batches. The main contribution of this paper is to give an experimental analysis of the recovery for highly textured imagery. For our study, we employ a subset of the Brodatz database. We show that the recovery of sharp edges plays a considerable role. Additionally, we study the effects of varying the number dictionary elements for that purpose. KW - Image recovery KW - Dictionary learning KW - Sparse representation KW - Textured images Y1 - 2024 UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2199 SN - 978-80-89829-33-0 SP - 264 EP - 273 PB - Jednota slovenských matematikov a fyzikov CY - Bratislava ER - TY - GEN A1 - Khan Mohammadi, Mohsen A1 - Schneidereit, Toni A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael T1 - Investigating Training Datasets of Real and Synthetic Images for Outdoor Swimmer Localisation with YOLO T2 - AI N2 - In this study, we developed and explored a methodical image augmentation technique for swimmer localisation in northern German outdoor lake environments. When it comes to enhancing swimmer safety, a main issue we have to deal with is the lack of real-world training data of such outdoor environments. Natural lighting changes, dynamic water textures, and barely visible swimming persons are key issues to address. We account for these difficulties by adopting an effective background removal technique with available training data. This allows us to edit swimmers into natural environment backgrounds for use in subsequent image augmentation. We created 17 training datasets with real images, synthetic images, and a mixture of both to investigate different aspects and characteristics of the proposed approach. The datasets were used to train YOLO architectures for possible future applications in real-time detection. The trained frameworks were then tested and evaluated on outdoor environment imagery acquired using a safety drone to investigate and confirm their usefulness for outdoor swimmer localisation. Y1 - 2024 U6 - https://doi.org/10.3390/ai5020030 SN - 2673-2688 VL - 5 IS - 2 SP - 576 EP - 593 PB - MDPI AG CY - Basel ER - TY - GEN A1 - Köhler, Alexander A1 - Kahra, Marvin A1 - Breuß, Michael T1 - A First Approach to Quantum Logical Shape Classification Framework T2 - Mathematics N2 - Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to devise suitable applications. This article aims to propose for the first time an approach using quantum logic in image processing for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way, we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification, we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables us to initiate the principal component analysis. Through experiments, we explore the possibility of distinguishing between different geometrical objects and discuss the results in terms of quantum logical interpretation. KW - quantum logic KW - principal component analysis KW - shape classification KW - Hilbert spaces KW - eigenvectors Y1 - 2024 U6 - https://doi.org/10.3390/math12111646 SN - 2227-7390 VL - 12 IS - 11 PB - MDPI AG CY - Basel ER - TY - GEN A1 - Kahra, Marvin A1 - Breuß, Michael A1 - Kleefeld, Andreas A1 - Welk, Martin T1 - An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation T2 - Lecture Notes in Computer Science N2 - Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations. In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach. KW - mathematical morphology KW - colour image KW - matrix-valued image KW - symmetric matrix KW - transitivity Y1 - 2024 SN - 9783031577925 U6 - https://doi.org/10.1007/978-3-031-57793-2_25 SN - 0302-9743 VL - 14605 SP - 325 EP - 337 PB - Springer Nature Switzerland CY - Cham ER - TY - GEN A1 - Schneidereit, Slavomira A1 - Yarahmadi, Ashkan Mansouri A1 - Schneidereit, Toni A1 - Breuß, Michael A1 - Gebauer, Marc T1 - YOLO-Based Object Detection in Industry 4.0 Fischertechnik Model Environment T2 - Lecture Notes in Networks and Systems N2 - In this paper we extensively explore the suitability of YOLO architectures to monitor the process flow across a Fischertechnik Industry 4.0 application. Specifically, different YOLO architectures in terms of size and complexity design along with different prior-shapes assignment strategies are adopted. To simulate the real world factory environment, we prepared a rich dataset augmented with different distortions that highly enhance and in some cases degrade our image qualities. The degradation is performed to account for environmental variations and enhancements opt to compensate the color correlations that we face while preparing our dataset. The analysis of our conducted experiments shows the effectiveness of the presented approach evaluated using different measures along with the training and validation strategies that we tailored to tackle the unavoidable color correlations that the problem at hand inherits by nature. KW - Object detection KW - Image augmentation KW - Classification KW - YOLO KW - Fischertechnik industry KW - Industry 4.0 Y1 - 2024 SN - 9783031477232 U6 - https://doi.org/10.1007/978-3-031-47724-9_1 SN - 2367-3370 VL - 823 SP - 1 EP - 20 PB - Springer Nature Switzerland CY - Cham ER - TY - GEN A1 - Hajighasemi, Saeide A1 - Breuß, Michael T1 - An Improved Frankot and Chellappa Method for Surface Normal Integration Using Fuzzy Concepts T2 - Preprints.org N2 - In this paper, we propose the Fuzzy formulation of the classic Frankot-Chellappa method by which surfaces can be reconstructed using normal vectors. In the Fuzzy formulation, the surface normal vectors may be uncertain or ambiguous. The underlying model yields a Fuzzy Poisson partial differential equation, where it is imperative to give meaningful representations of Fuzzy derivatives. The solution of the resulting Fuzzy model is approached numerically. To this end, a fuzzy formulation for the discrete sine transform method is explored, which results in a fast, accurate and robust method for surface reconstruction. In experiments we consider specifically the robustness with respect to noisy surface normal vectors. KW - Surface normal integration; Frankot-Chellappa method; Fuzzy derivatives; Fuzzy partition; Fuzzy Poisson equation Y1 - 2024 U6 - https://doi.org/10.20944/preprints202411.0742.v1 PB - MDPI AG ER - TY - GEN A1 - Köhler, Alexander A1 - Breuß, Michael A1 - Shabani, Shima T1 - Dictionary Learning with the K-SVDAlgorithm for Recovery of Highly Textured Images T2 - Preprints.org N2 - Image recovery by dictionary learning is of potential interest for many possible applications. To learn a dictionary, one needs to solve a minimization problem where the solution should be sparse. The K-SVD formalism, which is a generalization of the K-means algorithm, is one of the most popular methods to achieve this aim. We explain the preprocessing that is needed to bring images into a manageable format for the optimization problem.The learning process then takes place in terms of solving for sparse representations of the image batches. The main contribution of this paper is to give an experimental analysis of the recovery for highly textured imagery. For our study, we employ a subset of the Brodatz database. We show that the recovery of sharp edges plays a considerable role. Additionally, we study the effects of varying the number dictionary elements for that purpose. Y1 - 2024 U6 - https://doi.org/10.20944/preprints202406.0355.v1 PB - MDPI AG ER - TY - GEN A1 - Köhler, Alexander A1 - Kahra, Marvin A1 - Breuß, Michael T1 - A First Approach to Quantum Logical Shape Classification Framework T2 - Preprints.org N2 - Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to device suitable applications. This article aims to propose for the first time an approach to use quantum logic in image processing at hand of a process for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables to initiate the principal component analysis. At hand of experiments, we explore the possibility to distinguish between different geometrical objects and discuss the results in terms of quantum logical interpretation. Y1 - 2024 U6 - https://doi.org/10.20944/preprints202402.1042.v1 PB - MDPI AG ER - TY - GEN A1 - Khan Mohammadi, Mohsen A1 - Schneidereit, Toni A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael T1 - Investigating training datasets of real and synthetic images for swimmer localisation with YOLO T2 - Preprints.org N2 - In this paper we develop and explore a methodical pipeline for swimmer localisation in outdoor environments. The developed framework is intended to be used for enhancing swimmer safety. A main issue we deal with by the proposed approach is the lack of real world training data in such outdoor environments. Natural lighting changes, dynamic water textures and possibly barely visible swimming persons are key elements to approach. We account for these difficulties by adopting an effective background removal technique with available training data. This allows us to edit swimmers into natural environment backgrounds for the use in subsequent image augmentation. We created 17 training datasets with real images, synthetic images and a mixture of both to investigate different aspects and characteristics of the proposed approach. The datasets are used to train a YOLO architecture for the possible future application in real-time detection. The trained framework is then tested and evaluated on outdoor environment imagery acquired by a safety drone to investigate and confirm the usefulness for outdoor swimmer localisation. Y1 - 2024 U6 - https://doi.org/10.20944/preprints202402.0446.v1 PB - MDPI AG ER - TY - GEN A1 - Shabani, Shima A1 - Breuß, Michael T1 - Semi-Monotone Goldstein Line Search Strategy with Application in Sparse Recovery T2 - arXiv N2 - Line search methods are a prominent class of iterative methods to solve unconstrained minimization problems. These methods produce new iterates utilizing a suitable step size after determining proper directions for minimization. In this paper we propose a semi-monotone line search technique based on the Goldstein quotient for dealing with convex non-smooth optimization problems. The method allows to employ large step sizes away from the optimum thus improving the efficacy compared to standard Goldstein approach. For the presented line search method, we prove global convergence to a stationary point and local R-linear convergence rate in strongly convex cases. We report on some experiments in compressed sensing. By comparison with several state-of-the-art algorithms in the field, we demonstrate the competitive performance of the proposed approach and specifically its high efficiency. Y1 - 2025 U6 - https://doi.org/https://doi.org/10.48550/arXiv.2503.13099 SP - 1 EP - 12 ER - TY - GEN A1 - Shabani, Shima A1 - Khoshghiaferezaee, Mohammadsadegh A1 - Breuß, Michael T1 - Sparse dictionary learning for image recovery by iterative shrinkage T2 - arXiv N2 - In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage operation. As the mathematical setting of these methods, we consider an online approach as algorithmical basis together with the basis pursuit denoising problem that arises by the convex optimization approach to the dictionary learning problem. By a dedicated construction of datasets and corresponding dictionaries, we study the effect of enlarging the underlying learning database on reconstruction quality making use of several error measures. Our study illuminates that the choice of the optimization method may be practically important in the context of availability of training data. In the context of different settings for training data as may be considered part of our study, we illuminate the computational efficiency of the assessed optimization methods. Y1 - 2025 U6 - https://doi.org/10.48550/arXiv.2503.10732 SP - 1 EP - 19 ER - TY - GEN A1 - Schneidereit, Toni A1 - Gohrenz, Stefan A1 - Breuß, Michael T1 - Object detection characteristics in a learning factory environment using YOLOv8 N2 - AI-based object detection, and efforts to explain and investigate their characteristics, is a topic of high interest. The impact of, e.g., complex background structures with similar appearances as the objects of interest, on the detection accuracy and, beforehand, the necessary dataset composition are topics of ongoing research. In this paper, we present a systematic investigation of background influences and different features of the object to be detected. The latter includes various materials and surfaces, partially transparent and with shiny reflections in the context of an Industry 4.0 learning factory. Different YOLOv8 models have been trained for each of the materials on different sized datasets, where the appearance was the only changing parameter. In the end, similar characteristics tend to show different behaviours and sometimes unexpected results. While some background components tend to be detected, others with the same features are not part of the detection. Additionally, some more precise conclusions can be drawn from the results. Therefore, we contribute a challenging dataset with detailed investigations on 92 trained YOLO models, addressing some issues on the detection accuracy and possible overfitting. Y1 - 2025 U6 - https://doi.org/https://doi.org/10.48550/arXiv.2503.10356 VL - 2503.10356 SP - 1 EP - 18 ER - TY - GEN A1 - Kahra, Marvin A1 - Breuß, Michael T1 - Colour morphological distance ordering based on the Log-Exp-Supremum T2 - arXiv N2 - Mathematical morphology, a field within image processing, includes various filters that either highlight, modify, or eliminate certain information in images based on an application's needs. Key operations in these filters are dilation and erosion, which determine the supremum or infimum for each pixel with respect to an order of the tonal values over a subset of the image surrounding the pixel. This subset is formed by a structuring element at the specified pixel, which weighs the tonal values. Unlike grey-scale morphology, where tonal order is clearly defined, colour morphology lacks a definitive total order. As no method fully meets all desired properties for colour, because of this difficulty, some limitations are always present. This paper shows how to combine the theory of the log-exp-supremum of colour matrices that employs the Loewner semi-order with a well-known colour distance approach in the form of a pre-ordering. The log-exp-supremum will therefore serve as the reference colour for determining the colour distance. To the resulting pre-ordering with respect to these distance values, we add a lexicographic cascade to ensure a total order and a unique result. The objective of this approach is to identify the original colour within the structuring element that most closely resembles a supremum, which fulfils a number of desired properties. Consequently, this approach avoids the false-colour problem. The behaviour of the introduced operators is illustrated by application examples of dilation and closing for synthetic and natural images. Y1 - 2025 U6 - https://doi.org/https://doi.org/10.48550/arXiv.2503.11329 SP - 1 EP - 13 ER - TY - CHAP A1 - Kahra, Marvin A1 - Breuß, Michael T1 - Colour morphological distance ordering based on the log-exp-supremum T2 - Scale space and variational methods in computer vision : 10th international conference, SSVM 2025, Dartington, UK, May 18–22, 2025, proceedings, part II N2 - Mathematical morphology, a field within image processing, incorporates a variety of filters that either highlight, modify, or eliminate specific information within a mask that traverses the image. Key operations in these filters are dilation and erosion, which determine the supremum or infimum for each pixel with respect to an order of the tonal values over a subset of the image surrounding the pixel. This subset is formed by a structuring element at the specified pixel, which weighs the tonal values. Unlike grey-scale morphology, where tonal order is clearly defined, colour morphology lacks a definitive total order. As no method fully meets all desired properties for colour, because of this difficulty, some limitations are always present. This paper shows how to combine the theory of the log-exp-supremum of colour matrices that employs the Loewner semi-order with a well-known colour distance approach in the form of a pre-ordering. The log-exp-supremum will therefore serve as the reference colour for determining the colour distance. To the resulting pre-ordering with respect to these distance values, we add a lexicographic cascade to ensure a total order and a unique result. The objective of this approach is to identify the original colour within the structuring element that most closely resembles a supremum, which fulfils a number of desired properties. Consequently, this approach avoids the false-colour problem. The behaviour of the introduced operators is illustrated by application examples of dilation and closing for synthetic and natural images. KW - Mathematical colour morphology KW - Matrix-valued image KW - Colour distance KW - Multivariate ordering Y1 - 2025 SN - 9783031923685 U6 - https://doi.org/https://doi.org/10.1007/978-3-031-92369-2_20 SN - 0302-9743 SP - 258 EP - 270 PB - Springer Nature Switzerland CY - Cham ER - TY - CHAP A1 - Shabani, Shima A1 - Breuß, Michael T1 - Semi-monotone Goldstein line search strategy with application in sparse recovery T2 - Scale space and variational methods in computer vision : 10th international conference, SSVM 2025, Dartington, UK, May 18–22, 2025, proceedings, part II N2 - Line search methods are a prominent class of iterative methods to solve unconstrained minimization problems. These methods produce new iterates utilizing a suitable step size after determining proper directions for minimization. In this paper we propose a semi-monotone line search technique based on the Goldstein quotient for dealing with convex non-smooth optimization problems. The method allows to employ large step sizes away from the optimum thus improving the efficacy compared to standard Goldstein approach. For the presented line search method, we prove global convergence to a stationary point and local R-linear convergence rate in strongly convex cases. We report on some experiments in compressed sensing. By comparison with several state-of-the-art algorithms in the field, we demonstrate the competitive performance of the proposed approach and specifically its high efficiency. KW - Line search method KW - Non-smooth optimization KW - Non-monotone technique KW - Goldstein quotient KW - Sparse recovery KW - Compressed sensing KW - Global convergence KW - R-linear convergence Y1 - 2025 SN - 9783031923685 U6 - https://doi.org/https://doi.org/10.1007/978-3-031-92369-2_6 SN - 0302-9743 SP - 69 EP - 81 PB - Springer Nature Switzerland CY - Cham ER - TY - GEN A1 - Castillo, Susana A1 - Cunningham, Douglas William A1 - Winger, Christian A1 - Breuß, Michael T1 - Morphological Amoeba-based Patches for Exemplar-Based Inpainting T2 - Journal of WSCG Y1 - 2018 SN - 1213-6972 VL - 26 IS - 2 SP - 112 EP - 121 ER -