L1-norm Research Articles

Robust Blind Text Image Deblurring via Maximum Consensus Framework

The blind text image deblurring problem presents a formidable challenge, requiring the recovery of a clean and sharp text image from a blurry version with an unknown blur kernel. Sparsity-based strategies have demonstrated their efficacy by emphasizing the sparse priors of the latent image and kernel. However, these existing strategies have largely neglected the influence of additional noise, imposing limitations on their performance. To overcome this limitation, we propose a novel framework designed to effectively mitigate the impact of extensive noise prevalent in blurred images. Our approach centers around a robust Maximum Consensus Framework, wherein we optimize the quantity of interest from the noisy blurry image based on the maximum consensus criterion. Furthermore, we propose the integration of the Alternating Direction Method of Multipliers (ADMM) and the Half-Quadratic Splitting (HQS) method to address the computationally intractable L0 norm problem. This innovative strategy enables improvements in the deblurring performance of blurry text images with the additional synthetic noise. Experimental evaluations conducted on various noisy blurry text images demonstrate the superiority of the proposed approach over existing methods.

Stronger and Transferable Node Injection Attacks

Despite the increasing popularity of graph neural networks (GNNs), the security risks associated with their deployment have not been well explored. Existing works follow the standard adversarial attacks to maximize cross-entropy loss within an L-infinity norm bound. We analyze the robustness of GNNs against node injection attacks (NIAs) in black-box settings by allowing new nodes to be injected and attacked. In this work, we propose to design stronger and transferable NIAs. First, we propose margin aware attack (MAA) that uses a maximum margin loss to generate NIAs. We then propose a novel margin and direction aware attack (MDA) that diversifies the initial directions of MAA attack by minimizing the cosine similarity of the injected nodes with respect to their respective random initialization in addition to the maximization of max-margin loss. This makes the NIAs stronger. We further observe that using L2 norm of gradients in the attack step leads to an enhanced diversity amongst the node features, thereby further enhancing the strength of the attack. We incorporate transferability in NIAs by perturbing the surrogate model before generating the attack. An analysis of eigen spectrum density of the hessian of the loss emphasizes that perturbing the weights of the surrogate model improves the transferability. Our experimental results demonstrate that the proposed resilient node injection attack (R-NIA) consistently outperform PGD by margins about 7-15% on both large and small graph datasets. R-NIA is significantly stronger and transferable than existing NIAs on graph robustness benchmarks.

A special fuzzy star-shaped number space with the sendograph metric

As a natural generalization of fuzzy numbers, fuzzy star-shaped numbers play a crucial role in fuzzy mathematics. Let Y be a non-degenerate compact convex subset of the n-dimensional Euclidean space, and let FSz0(Y) be the family consisting of all fuzzy star-shaped numbers with respect to z0 whose supports contained in Y. Using methods from infinite-dimensional topology, we mainly show that the space FSz0(Y) with the topology induced by the sendograph metric is homeomorphic to the separable Hilbert space ℓ2.

A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm. For three classes of packing problems, balance, homothetic and sparse packing, the corresponding new (generalized) models are formulated. Non-overlapping and containment conditions for irregular objects composed by generalized spheres are presented. It is demonstrated that these formulations can be stated for any norm. Different geometrical shapes can be treated in the same way by simply selecting a suitable norm. The approach is applied to generalized spheres defined by Lp norms and their compositions. Numerical solutions of small problem instances obtained by the global solver BARON are provided for two-dimensional objects composed by spheres defined in Lp norms to demonstrate the potential of the approach for a wide range of engineering optimization problems.

Abstract 7392: Machine learning-based identification of H&E-derived morphologic features associated with CD8+ T cell immune exclusion

Abstract Background: Immune exclusion is characterized by a predominance of CD8+ T cells in the stroma of the tumor microenvironment (TME) which are not in contact with tumor cells. Immune exclusion is a significant obstacle to effective cancer immunotherapy and reversing it has emerged as a new therapeutic opportunity. However, the objective assessment of immune exclusion remains a challenge due to the complexity of the TME and the need for immunostaining to quantify CD8+ cells in tumor and stroma. While artificial intelligence (AI) models applied to H&E images can quantify spatial tissue and cell features at scale, they are unable to identify the molecular subtypes of cells. Here we describe the development of a machine learning model that classifies tumors by their CD8-defined immune phenotypes using features extracted from H&E whole slide images alone. Methods: Al-powered TME models (PathAI PathExplore™) were deployed on H&E images from 39 non-small lung cancer (NSCLC) and triple-negative breast cancer (TNBC) samples. CD8-based assessment of immune phenotypes was done using an adjacent section. 115 H&E-derived features from each of the 25 tumor samples (12 NSCLC, 13 TNBC) classified as immune excluded and 7 tumor samples (3 NSCLC, 4 TNBC) classified as immune infiltrated were used as input into a feature selection process to identify the subset of H&E features predictive of immune phenotype. The feature selection process was driven by an ensemble L1 norm support vector machine (Ens-L1-SVM) model containing 500 L1-SVM base models each trained by 80% of the data. The degree of immune exclusion was determined in the feature space by the distance to the separation hyperplane defined by the model. Out-of-bag error estimation was employed on the remaining 20% of data from each base model to assess model performance. Results: The Ens-L1-SVM model identified 6 H&E features predictive of CD8-defined immune phenotypes, including the density ratio of lymphocytes to macrophages in the cancer epithelium, the density of fibroblasts, and the spatial distributions of cancer cells, macrophages, and lymphocytes. Immune phenotypes were classified by the Ens-L1-SVM model with an estimated accuracy of 97%. Additionally, all selected features and their direction of association aligned with prior knowledge of the mechanisms or manifestations of immune exclusion or infiltration in the TME. Conclusion: This work illustrated that morphologic features derived from H&E images using AI-powered models can be effective predictors of CD8-defined immune exclusion, providing an option for patient stratification by immune phenotype using widely-available H&E images. While the Ens-L1-SVM model showed robust performance on a small number of samples and is expected to have good generalizability due to the linear nature of the model, additional validation across diverse datasets and various tumor indications is needed. Citation Format: Yanchao Wang, Fredrick D. Gootkind, Florent Peyraud, Jean-Philippe Guégan, Antoine Italiano, G. Travis Clifton, Laura A. Dillon, Xinwei Sher. Machine learning-based identification of H&E-derived morphologic features associated with CD8+ T cell immune exclusion [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7392.

Frozen is better than learning: A new design of prototype-based classifier for semantic segmentation

Semantic segmentation models comprise an encoder to extract features and a classifier for prediction. However, the learning of the classifier suffers from the ambiguity which is caused by two factors: (1) the weights of a classifier for similar categories may have positive similarities lowing the performance for similar categories, named correlation ambiguity, and (2) the classifier is prone to predict the category with a larger ℓ2 norm and vice versa, termed prior ambiguity. To comedy the issues, we propose Category-Basis Prototype (CBP), frozen and mutually orthogonalized prototypes with equalℓ2norm. Orthogonalization prevents the prototypes from being similar to each other and the equality decouples the prediction from the ℓ2 norm. To better shape the feature space, we propose Online Centroid Contrastive Loss (OCCL) equipped with centroid and category-level losses. Experiments show that our method yields compelling results over two widely applied benchmarks indicating the effectiveness of our methods.

Locking-free isogeometric discretizations of linear plane Timoshenko rods: LAS elements

We make use of linear plane curved Timoshenko rods as a model problem to study how to overcome shear and membrane locking in NURBS-based discretizations. In this work, we propose lumped-assumed-strain (LAS) elements, a projection-based assumed-strain treatment that removes shear and membrane locking for a very broad range of slenderness ratios. For a NURBS patch with basis functions of degree p and Cp−1 continuity across element boundaries, the space of the assumed strains is defined on a B-spline patch with the same elements, but using basis functions of degree p−1 and Cp−2 continuity across element boundaries. The assumed strains are obtained by performing a L2 projection of the compatible strains at the patch level in which the consistent mass matrix is substituted with the lumped mass matrix. Our numerical investigations suggest that LAS elements need either the same or slightly finer mesh resolutions than B̄ elements in order for the relative errors in L2 norm of the unknowns and the stress resultants to be all below 1%. However, LAS elements are significantly more computationally efficient than B̄ elements for a given mesh. The use of C1-continuous quadratic LAS elements with 2 Gauss–Legendre quadrature points per element exhibit superconvergence of the stress resultants for most slenderness ratios, making it a particularly cost-effective choice of obtaining accurate results. When compared with linear Lagrange B̄ elements with 2 Gauss–Legendre quadrature points per element, C1-continuous quadratic LAS elements with 2 Gauss–Legendre quadrature points per element require far fewer elements in order to obtain relative errors in L2 norm of the unknowns and the stress resultants smaller than 1%.

LSFSR: Local label correlation-based sparse multilabel feature selection with feature redundancy

In recent studies, existing multilabel feature selection models have focused on either considering the relationship between labels or the redundancy between features. Furthermore, they only use simple sparsity constraints to process high-dimensional data without the intrinsic relationships between features and labels. These issues can have a great impact on the classification effectiveness of feature selection. To address these limitations, this article describes a new local label correlation-based sparse multilabel feature selection approach with feature redundancy. First, a new loss function is established among the matrices of samples, label coefficients, and labels. Then, the Frobenius norm is imposed to investigate the potential relationships between features and labels. The weight matrix is sparsified by the l2,1 norm to ensure that the new loss function has high interpretability. Second, a manifold constraint is employed to capture the local geometric structure between labels and to delve deeper into the latent information among the local labels. Then manifold constraints and Laplacian scores are combined for embedding feature selection to guide the exploration of hidden latent label. Finally, by considering the differences between the feature scores and the redundancy between the samples, feature redundancy is analyzed via the modified cosine similarity, and a candidate feature subset with low redundancy is generated. The l2 norm is used to select features with low redundancy while preserving sparsity, and a novel objective function is developed to optimize this solution. Thus, a sparse feature selection algorithm via local label correlation and feature redundancy is designed, and has demonstrated remarkable classification effectiveness in comparative experiments conducted on 21 multilabel datasets.

Higher order Galerkin finite element method for [formula omitted]-dimensional generalized Benjamin–Bona–Mahony–Burgers equation: A numerical investigation

In this article, we study solitary wave solutions of the generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equation using higher-order shape elements in the Galerkin finite element method (FEM). Higher-order elements in FEMs are known to produce better results in solution approximations; however, these elements have received fewer studies in the literature. As a result, for the finite element analysis of the gBBMB equation, we consider Lagrange quadratic shape functions. We employ the Galerkin finite element approximation to derive a priori error estimates for semi-discrete solutions. For fully discrete solutions, we adopt the Crank–Nicolson approach, and to handle nonlinearity, we utilize a predictor–corrector scheme with Crank–Nicolson extrapolation. Additionally, we perform a stability analysis for time using the energy method. In the space, O(h3) convergence in L2(Ω) norm and O(h2) convergence in H1(Ω) norm are observed. Furthermore, an optimal O(Δt2) convergence in the maximum norm for the temporal direction is also obtained. We test the theoretical results on a few numerical examples in one- and two-dimensional spaces, including the dispersion of a single solitary wave and the interaction of double and triple solitary waves. To demonstrate the efficiency and effectiveness of the present scheme, we compute L2 and L∞ normed errors, along with the mass, momentum, and energy invariants. The obtained results are compared with the existing literature findings both numerically and graphically. We find quadratic shape functions improve accuracy in mass, momentum, energy invariants and also give rise to a higher order of convergence for Galerkin approximations for the considered nonlinear problems.

Optimal non-absolute domains for the Hardy operator minus identity

We characterize the optimal non-absolute domain for the Hardy operator minus the identity, in the Lebesgue space Lp(0,∞), 1≤p≤∞. We also address a similar question for the dual Hardy operator minus the identity.

Optimal decay rates and space–time analyticity of solutions to the Patlak-Keller–Segel equations

Based on some new elementary estimates for the space–time derivatives of the heat kernel, we use a bootstrapping approach to establish quantitative estimates on the optimal decay rates for the Lq(Rd) (1≤q≤∞, d∈N) norm of the space–time derivatives of solutions to the (modified) Patlak-Keller–Segel equations with initial data in L1(Rd), which implies the joint space–time analyticity of solutions. When the L1(Rd) norm of the initial datum is small, the upper bound for the decay estimates is global in time, which yields a lower bound on the growth rate of the radius of space–time analyticity in time. As a byproduct, the space analyticity is obtained for any initial data in L1(Rd). The decay estimates and space–time analyticity are also established for solutions bounded in both space and time variables. The results can be extended to a more general class of equations.

CM-YOLOv8: Lightweight YOLO for Coal Mine Fully Mechanized Mining Face.

With the continuous development of deep learning, the application of object detection based on deep neural networks in the coal mine has been expanding. Simultaneously, as the production applications demand higher recognition accuracy, most research chooses to enlarge the depth and parameters of the network to improve accuracy. However, due to the limited computing resources in the coal mining face, it is challenging to meet the computation demands of a large number of hardware resources. Therefore, this paper proposes a lightweight object detection algorithm designed specifically for the coal mining face, referred to as CM-YOLOv8. The algorithm introduces adaptive predefined anchor boxes tailored to the coal mining face dataset to enhance the detection performance of various targets. Simultaneously, a pruning method based on the L1 norm is designed, significantly compressing the model's computation and parameter volume without compromising accuracy. The proposed algorithm is validated on the coal mining dataset DsLMF+, achieving a compression rate of 40% on the model volume with less than a 1% drop in accuracy. Comparative analysis with other existing algorithms demonstrates its efficiency and practicality in coal mining scenarios. The experiments confirm that CM-YOLOv8 significantly reduces the model's computational requirements and volume while maintaining high accuracy.

Adaptive least-squares finite element methods: Guaranteed upper bounds and convergence in L2 norm of the dual variable

We consider adaptive least-squares finite element methods. First, we develop a guaranteed upper bound for the dual error in the L2 norm, and this can be used as a stopping criterion for the adaptive procedures. Secondly, based on the a posteriori error estimates for the dual variable, we develop an error indicator that identifies the local area to refine, and establish the convergence of the adaptive procedures based on the Dörfler's marking strategy. Our convergence analysis is valid for the entire range of the bulk parameter 0<Θ≤1 and it shows the effect of bulk parameter and reduction factor of elements on the convergence rate. Confirming numerical experiments are provided.

Capacitary maximal inequalities and applications

In this paper we introduce capacitary analogues of the Hardy-Littlewood maximal function,MCf(x):=supr>0⁡1C(B(x,r))∫B(x,r)|f|dC, for C= the Hausdorff content or a Riesz capacity. For these maximal functions, we prove a strong-type (p,p) bound for 1<p≤+∞ on the capacitary integration spaces Lp(C) and a weak-type (1,1) bound on the capacitary integration space L1(C). We show how these estimates clarify and improve the existing literature concerning maximal function estimates on capacitary integration spaces. As a consequence, we deduce correspondingly stronger differentiation theorems of Lebesgue-type, which in turn, by classical capacitary inequalities, yield more precise estimates concerning Lebesgue points for functions in Sobolev spaces.

Gabor frames on finite non-cyclic Abelian groups

We attempt to analyze Gabor frames for L2 spaces on finite non cyclic abelian groups from their natural perspectives and establish their equivalence with Gabor frames on the isomorphic product groups of finite cyclic groups by means of unitary and non unitary invertible linear transformations. Gabor frames and their canonical dual frames on finite non cyclic groups are identified as the images of the same Gabor frame on a finite product of finite cyclic groups under invertible linear transformations.

Global well-posedness and large time behavior for the inviscid Oldroyd-B model

In this paper, we consider the 3-dimensional incompressible inviscid Oldroyd-B model. Firstly, we establish the global existence of the solutions for the inviscid Oldroyd-B model with different coupling coefficient k>0. Then, we show the connection between the solution with the parameter k that is the reciprocal of Weissenberg number. On one hand, we prove that the solutions (u,τ) depend continuously on the parameter k>0, though (u,τ) corresponds to different decays rate for different k. On the other hand, when k→0 in large time, we prove that there is a gap between the L2 norm of solution uk(t,x) to the model of parameter k>0 with the L2 norm of solution u0(t,x) to the model of parameter k=0. In a word, we prove that the larger positive k induces the faster decay rate of the solution, but k cannot go to zero, or the dissipation will vanish instantly.

Robust treatment planning for small animal radio-neuromodulation using focused kV x-ray beams.

In preclinical radio-neuromodulation research, small animal experiments are pivotal for unraveling radiobiological mechanism, investigating prescription and planning techniques, and assessing treatment effects and toxicities. However, the target size inside a rat brain is typically in the order of sub-millimeters. The small target inside the visual cortex neural region in rat brain with a diameter of around 1mm was focused in this work to observe the physiological change of this region. Delivering uniform doses to the small target while sparing health tissues is challenging. Focused kV x-ray technique based on modern x-ray polycapillary focusing lens is a promising modality for small animal radio-neuromodulation. The current manual planning method could lead to sub-optimal plans, and the positioning uncertainties due to mechanical accuracy limitations, animal immobilization, and robotic arm motion are not considered. This work aims to design a robust inverse planning method to optimize the intensities of focused kV x-ray beams located in beam trajectories to irradiate small mm-sized targets in rat brains for radio-neuromodulation. Focused kV x-ray beams were generated through polycapillary x-ray focusing lenses on achieving small (≤0.3mm) focus perpendicular to the beam. The beam trajectories were manually designed in 3D space in scanning-while-rotating mode. Geant4 Monte Carlo (MC) simulation generated a dose calculation matrix for each focused kV x-ray beam located in beam trajectories. In the proposed robust inverse planning method, an objective function combining a voxel-wise stochastic programming approach and L1 norm regularization was established to overcome the positioning uncertainties and obtain a high-quality plan. The fast iterative shrinkage thresholding algorithm (FISTA) was utilized to solve the objective function and obtain the optimal intensities. Four cases were employed to validate the feasibility and effectiveness of the proposed method. The manual and non-robust inverse planning methods were also implemented for comparison. The proposed robust inverse planning method achieved superior dose homogeneity and higher robustness against positioning uncertainties. On average, the clinical target volume (CTV) homogeneity index (HI) of robust inverse plan improved to 13.3 from 22.9 in non-robust inverse plan and 53.8 in manual plan if positioning uncertainties were also present. The average bandwidth at D90 was reduced by 6.5Gy in the robust inverse plan, compared to 9.6Gy in non-robust inverse plan and 12.5Gy in manual plan. The average bandwidth at D80 was reduced by 3.4Gy in robust inverse plan, compared to 5.5Gy in non-robust inverse plan and 8.5Gy in manual plan. Moreover, the dose delivery time of manual plan was reduced by an average reduction of 54.7% with robust inverse plan and 29.0% with non-robust inverse plan. Compared to manual and non-robust inverse planning methods, the robust inverse planning method improved the dose homogeneity and delivery efficiency and was resistant to the uncertainties, which are crucial for radio-neuromodulation utilizing focused kV x-rays.

New completeness theorems on the boundary in elasticity

The completeness on the boundary (in the sense of Picone) of certain systems related to the III and IV BVPs for the elasticity system is proved. The completeness is obtained in both Lp (1⩽1<∞) and uniform norms.

The effect of talker intelligibility on adaptation to an unfamiliar accent

Listening effort, as indexed by task-evoked pupil response, increases as the intelligibility of second language (L2) speech decreases, and this processing cost is mitigated by experience with talkers of the same accent (Porretta and Tucker, 2019). Prior research has shown that listeners can adapt to unfamiliar L2-accented speech and generalize the adaptation to different L2-accented talkers with the same L1 (Bradlow and Bent, 2008). The current study investigates what type of L2-accented speech exposure (high or low intelligibility) best reduces later listening effort to a novel talker of the same accent. We hypothesize that exposure to highly intelligible L2 speech supports adaptation to the features of an accent because it allows listeners to map accented tokens to the talker’s intended lexical representations. Alternatively, adaptation to a less intelligible talker may require exposure to other low-intelligibility speech, which is characterized by features that deviate more significantly from L1 norms. To test this, participants were exposed to simple sentences spoken in English by either L1 talkers, highly intelligible L2 talkers, or less intelligible L2 talkers. At test, all participants listened to different sentences spoken by a previously unheard L2 talker while listening effort was measured via pupillometry. Data collection is ongoing.

Efficient methods for iterative ultrasound image reconstruction using L1 and L2 norm regularization

Ultrasound image reconstruction can be posed as an inverse problem, with image pixels as parameters to a model of wave propagation that are estimated from raw ultrasound channel data. Such framework allows one to make assumptions about channel signals and image properties in form of regularization that can be used to improve reconstruction accuracy in the presence of electronic and acoustic noise. A simple model assumes spherical wave propagation from point sources in a homogeneous medium, similar to delay-and-sum (DAS) beamforming; solving such problems numerically can require many iterations and can result in blurred images when traditional L2 norm regularization is used. We use Fast Iterative Shrinkage Thersholding Algorithm (FISTA) to reduce the number of iterations to less than 10, and to apply L1-norm regularization to the data, which improves edge sharpness and image contrast. We demonstrate the concept using FIELD II simulated ultrasound signals from point, speckle, and anechoic targets with controlled levels of electronic and speckle noise. The FISTA-reconstructed point targets show reduced sidelobe levels by 15 dB compared to the traditional DAS image, and the reduction in full-width at half maximum by a factor of 2. We also implement iterative reconstruction in omega-k frequency domain, which allows factoring the forward and adjoint operators at each spatial frequency and paves the way for an intuitive and more memory efficient, multi-threaded implementation of the method.