Compressive_Sensing
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PE-CSNet: An equivariant network architecture with learnable patch-based sparse representation
2026-08-11 04:11:27Kai Li, Haitao Long, Bo Zhang, Haiwen Zhang, Zhi ZhouAbstract
Compressive sensing (CS) enables accurate signal reconstruction from sparse measurements and is widely applied in medical imaging, remote sensing, and image compression. However, designing an effective, task-specific sparse transform and the corresponding optimization procedure for high-quality CS remains challenging. This process typically requires expert domain knowledge and laborious parameter tuning. To address this issue, we present a Patch-based Equivariant deep unrolling architecture, termed PE-CSNet, for accurate CS recovery. While traditional CS methods generally use predefined patch-based transform sparsity, we generalize this idea by incorporating learnable transform sparsity that adapts to the specific CS task through an optimization-driven process. Specifically, we first establish a generalized patch-based CS model, which we solve via a block coordinate descent (BCD) algorithm. The BCD solver is then unrolled into a deep neural network, where all parameters of both the CS model and solver are learned through end-to-end training. To improve data efficiency, we introduce a stochastic equivariant training strategy that exploits the patch-wise structure of the network, enabling PE-CSNet to learn effectively even from limited data. We further provide a simpler, parameter-shared version of PE-CSNet and briefly discuss its convergence as an iterative solver. For practical applications, the network uses stage-specific (non-shared) parameters to enhance its expressive power and thereby improve its performance. On the tasks of CS magnetic resonance imaging (CS-MRI) and CS coded diffraction patterns (CS-CDP), PE-CSNet achieves state-of-the-art accuracy with fast computational speed, outperforming traditional methods and existing deep unrolling methods.
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URL
https://arxiv.org/abs/2608.14708
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Small, Bias-Free, Blind and Convolutional Denoiser: A compact ConvNeXt U-Net for blind Gaussian color-image denoising
2026-07-24 13:31:22Nikolas MarkouAbstract
We describe and evaluate BF-ConvUNeXt, a compact bias-free ConvNeXt U-Net for blind additive-white-Gaussian-noise color image denoising, combining four existing ingredients so a single property survives end to end: a frozen depthwise Gabor stem (oriented band-pass, zero trainable parameters), a Laplacian-pyramid encoder routing the high-frequency residual into each skip connection, a ConvNeXt-V1 U-Net body, and bias-free construction throughout (no additive bias, linear head, LeakyReLU, variance-only batch norm). Together these make the 0.82M-parameter network exactly degree-1 homogeneous at inference, D(alpha y) = alpha D(y), licensing a Miyasawa/Tweedie score reading of the residual and blind generalization across noise levels from one model. We train a single blind model on a noise-sigma curriculum (sigma approximately 6.4 to 64, 0-255 scale); it extrapolates past that ceiling without a cliff, degrading smoothly to 22.8 dB at sigma=150 and 20.0 dB at sigma=200. Evaluated unchanged on four standard color sets (CBSD68, Kodak24, McMaster, Urban100) at sigma in {15,25,50}, it matches or beats DnCNN and FFDNet on every set and level, averaging about +0.7 dB over DnCNN. Against heavyweight CNN/transformer state of the art it trails by a small margin (roughly 0.3-1.7 dB depending on set) at 1/15 to 1/39 of their parameters. The homogeneity is inference-only and checkpoint-specific, and the learned residual is a local, not global, score (non-conservative Jacobian), so plug-and-play/RED guarantees do not transfer; it still drives stochastic sampling and linear inverse problems (inpainting, super-resolution, deblurring, compressive sensing).
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URL
https://arxiv.org/abs/2607.22793
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Mathematics of Data Science
2026-07-11 08:31:44Afonso S. Bandeira, Amit Singer, Thomas StrohmerAbstract
This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principal Component Analysis 4. Linear Regression and Regularization 5. Graphs, Networks, and Clustering 6. Nonlinear Dimension Reduction and Diffusion Maps 7. Linear Dimension Reduction via Random Projections 8. Optimization for Data Science 9. Classification 10. A Mathematical Introduction to Deep Learning 11. Large Sample Limit of Graph Laplacians 12. Community 13. Concentration of Measure and Gaussian Analysis 14. Matrix Concentration Inequalities 15. Compressive Sensing and Sparsity 16. Low-Rank Matrix Recovery
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URL
https://arxiv.org/abs/2607.11938
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Plug-and-Play Volumetric Reconstruction for Compressive Sensing Light-Sheet Microscopy
2026-07-02 03:26:30Jianqing Jia, Yi Gong, Xinyuan Zhang, Jichen Chai, Yichen Ding, Yifei LouAbstract
We investigate volumetric reconstruction for compressive sensing light-sheet microscopy (CS-LSM), where fast volumetric imaging is achieved by encoding multiple axial planes into each camera exposure. To recover the underlying volume from highly multiplexed measurements, we propose a plug-and-play (PnP) framework that flexibly incorporates any user-specified denoiser into the reconstruction process. Building on a slice-based formulation, we further introduce an axial-coupled model that exploits correlations between adjacent slices to improve volumetric continuity. For efficient computation, we derive a Woodbury-based update for the data-consistency step in both the slice-based and axial-coupled formulations, and employ a Gauss-Seidel sweep for the denoising step in the axial-coupled model. Under a weakly convex regularization assumption, we establish subsequential convergence of the proposed algorithm. Experiments on synthetic and real zebrafish-heart data demonstrate that the proposed framework successfully recovers cellular structures from compressed measurements, and provide practical insights into the comparative performance of commonly used denoisers within the PnP framework under the CS-LSM setup.
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URL
https://arxiv.org/abs/2607.01654
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STRIDE: Training Data Attribution via Sparse Recovery from Subset Perturbations
2026-06-03 17:59:36Rishit Dagli, Abir Harrasse, Luke Zhang, Florent Draye, Amirali Abdullah, Bernhard Sch\"olkopf, Zhijing JinAbstract
Training Data Attribution (TDA) seeks to trace a model's predictions back to its training data. The gold standard for TDA relies on causal interventions, observing how a model changes when data is added or removed, but repeated retraining is computationally challenging for Large Language Models (LLMs). Consequently, most approaches approximate this effect in the parameter space using gradients. However, tracking gradients across billions of parameters is not only prohibitively expensive but relies on local approximations. In this work, we propose a shift: rather than estimating parameter changes, we model the functional effect of training data in the activation space. We introduce STRIDE (Steering-based Training Data Influence Decomposition), a framework that formulates TDA as a sparse recovery problem in the spirit of compressive sensing. STRIDE learns lightweight "steering operators" that mimic the behavioral shift caused by training on data subsets. By measuring how these operators perturb test predictions, we recover individual training example influences via sparse linear decomposition. STRIDE achieves state-of-the-art for LLM pre-training attribution while being an order of magnitude ($13\times$) faster than previous art. We further validate its practical utility through downstream applications including data selection, data contamination, and qualitative analysis.
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URL
https://arxiv.org/abs/2606.05165
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Beyond Single Solution: Multi-Hypothesis Collaborative Deep Unfolding Network for Image Compressive Sensing
2026-06-02 13:50:56Wenxue Cui, Hualin Li, Yuhang Qin, Yifu Xu, Xiaopeng Fan, Debin ZhaoAbstract
Recent deep unfolding networks (DUNs) have advanced Compressive Sensing (CS) by effectively integrating iterative optimization with deep learning architectures. However, most CS approaches predominantly confine their inference to a single solution space, neglecting the inherent ill-posedness of CS problems that intrinsically permits multiple plausible candidate hypotheses. In this paper, a novel Multi-Hypothesis Collaborative Deep Unfolding CS Network (MHC-DUN) is proposed, which explicitly models and leverages multiple hypotheses by jointly optimizing across diverse solution spaces. Specifically, following the Proximal Gradient Descent algorithm, MHC-DUN jointly performs gradient descent and proximal mapping within this multi-hypothesis paradigm. i) For gradient descent, a well-designed AlphaNet is introduced to dynamically predict spatially varying step sizes for all hypotheses, enabling collaborative gradient updates across multiple solutions. ii) For proximal operator, a sophisticated multi-hypothesis collaborative proximal mapping module is designed, which leverages both intra-hypothesis and inter-hypothesis correlation priors to jointly refine multiple solutions. To enable end-to-end training, a novel composite loss function is designed, which balances measurement fidelity, hypothesis diversity, and reconstruction accuracy, encouraging exploration of complementary solutions while maintaining reconstruction fidelity. Experimental results reveal that the proposed CS method outperforms existing CS networks.
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URL
https://arxiv.org/abs/2606.03666
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Deep Probabilistic Unfolding for Quantized Compressive Sensing
2026-05-12 03:44:03Gang Qu, Ping Wang, Siming Zheng, Xin YuanAbstract
We propose a deep probabilistic unfolding model to address the classical quantized compressive sensing problem that leverages an unfolding framework to enhance the reconstruction accuracy and efficiency. Unlike previous unfolding methods that apply L2 projection to measurements, we derive a closed-form, numerically stable likelihood gradient projection, which allows the model to respect the true quantization physics, turning the hard quantization constraint into a soft probabilistic guidance. Furthermore, an efficient, dual-domain Mamba module is specifically designed to dynamically capture and fuse the multi-scale local and global features, ensuring the interactions between the distant but correlated regions. Extensive experiments demonstrate the state-of-the-art performance of the proposed method over previous works, which is capable of promoting the application of quantized compressive sensing in real life.
Abstract (translated)
URL
https://arxiv.org/abs/2605.11475
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Dual-Path Hyperprior Informed Deep Unfolding Network for Image Compressive Sensing
2026-05-10 14:28:37Tianyi Lu, Wenxue Cui, Shaohui LiuAbstract
Recent Deep Unfolding Networks (DUNs) have significantly advanced Compressive Sensing (CS) by integrating iterative optimization with deep networks. However, existing DUNs still suffer from two challenges: 1) Reliance on a single measurement stream, which limits effective information interaction across distinct measurement subsets. 2) Uniform processing of all image regions, which overlooks varying reconstruction difficulties induced by diverse textures. To address these limitations, a novel Dual-Path Hyperprior Informed Deep Unfolding Network (DPH-DUN) is proposed, which partitions measurements into double subsets to enable hyperprior-guided reconstruction via a dual-path architecture. In the Deep Hyperprior Learning branch, a series of lightweight neural modules are designed to efficiently generate hyperprior knowledge of different domains, enabling collaborative guidance for the CS reconstruction. In the Hyperprior Informed Reconstruction branch, a deep unfolding framework with hyperprior guidance is constructed to iteratively refine reconstruction. Specifically, i) in the gradient descent step, a Hyperprior Informed Step Size Generation network is designed to dynamically generate spatially varying step maps, enabling adaptive fine-grained gradient updates. ii) In the proximal mapping step, two well-designed hyperprior informed attention mechanisms are introduced to dynamically focus on challenging regions via gradient-based hard and soft attentions, facilitating CS reconstruction accuracy. Extensive experiments demonstrate that the proposed DPH-DUN outperforms existing CS methods.
Abstract (translated)
URL
https://arxiv.org/abs/2605.09566
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Information Density as a Quantitative Measure for AI-enabled Virtual Sensing: Feasibility and Limits
2026-05-05 09:03:37Hrishikesh Dutta, Roberto Minerva, Reza Farahbakhsh, Noel CrespiAbstract
Modern IoT and sensor networks generate vast amounts of data, posing significant challenges for storage, transmission, and real-time processing. Traditional approaches, such as compressive sensing and machine learning-based compression, often suffer from computational inefficiencies and irreversible data loss. This paper introduces Information Density as a quantitative metric to support sensor deployment and enable AI-driven virtual sensing. We propose a framework that leverages spatial, temporal and inter-modal correlations among sensor signals to perform sensing tasks even in the absence of physical sensors. Two complementary measures: (i) Phase in Eigen Space and (ii) Mutual Information, are developed to quantify and assess information density, enabling the selection of optimal sensor configurations across both intra-modality and cross-modality scenarios. Validated using real-world data from Madrid's smart city infrastructure, this framework demonstrates the feasibility of replacing physical sensors with virtual ones under bounded error conditions (e.g., achieving $<3.21\%$ mean error with a single sensor). The results highlight the potential for scalable and energy-efficient sensing systems in smart environments.
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URL
https://arxiv.org/abs/2605.08180
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Compressive sensing inspired self-supervised single-pixel imaging
2026-03-31 13:31:43Jijun Lu, Yifan Chen, Libang Chen, Yiqiang Zhou, Ye Zheng, Mingliang Chen, Zhe Sun, Xuelong LiAbstract
Single-pixel imaging (SPI) is a promising imaging modality with distinctive advantages in strongly perturbed environments. Existing SPI methods lack physical sparsity constraints and overlook the integration of local and global features, leading to severe noise vulnerability, structural distortions and blurred details. To address these limitations, we propose SISTA-Net, a compressive sensing-inspired self-supervised method for single-pixel imaging. SISTA-Net unfolds the Iterative Shrinkage-Thresholding Algorithm (ISTA) into an interpretable network consisting of a data fidelity module and a proximal mapping module. The fidelity module adopts a hybrid CNN-Visual State Space Model (VSSM) architecture to integrate local and global feature modeling, enhancing reconstruction integrity and fidelity. We leverage deep nonlinear networks as adaptive sparse transforms combined with a learnable soft-thresholding operator to impose explicit physical sparsity in the latent domain, enabling noise suppression and robustness to interference even at extremely low sampling rates. Extensive experiments on multiple simulation scenarios demonstrate that SISTA-Net outperforms state-of-the-art methods by 2.6 dB in PSNR. Real-world far-field underwater tests yield a 3.4 dB average PSNR improvement, validating its robust anti-interference capability.
Abstract (translated)
URL
https://arxiv.org/abs/2603.29732
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Deep LoRA-Unfolding Networks for Image Restoration
2026-02-21 02:57:48Xiangming Wang, Haijin Zeng, Benteng Sun, Jiezhang Cao, Kai Zhang, Qiangqiang Shen, Yongyong ChenAbstract
Deep unfolding networks (DUNs), combining conventional iterative optimization algorithms and deep neural networks into a multi-stage framework, have achieved remarkable accomplishments in Image Restoration (IR), such as spectral imaging reconstruction, compressive sensing and this http URL unfolds the iterative optimization steps into a stack of sequentially linked this http URL block consists of a Gradient Descent Module (GDM) and a Proximal Mapping Module (PMM) which is equivalent to a denoiser from a Bayesian perspective, operating on Gaussian noise with a known this http URL, existing DUNs suffer from two critical limitations: (i) their PMMs share identical architectures and denoising objectives across stages, ignoring the need for stage-specific adaptation to varying noise levels; and (ii) their chain of structurally repetitive blocks results in severe parameter redundancy and high memory consumption, hindering deployment in large-scale or resource-constrained this http URL address these challenges, we introduce generalized Deep Low-rank Adaptation (LoRA) Unfolding Networks for image restoration, named LoRun, harmonizing denoising objectives and adapting different denoising levels between stages with compressed memory usage for more efficient this http URL introduces a novel paradigm where a single pretrained base denoiser is shared across all stages, while lightweight, stage-specific LoRA adapters are injected into the PMMs to dynamically modulate denoising behavior according to the noise level at each unfolding this http URL design decouples the core restoration capability from task-specific adaptation, enabling precise control over denoising intensity without duplicating full network parameters and achieving up to $N$ times parameter reduction for an $N$-stage DUN with on-par or better this http URL experiments conducted on three IR tasks validate the efficiency of our method.
Abstract (translated)
结合传统迭代优化算法和深度神经网络的深层展开网络（DUNs）在图像恢复领域，如光谱成像重建、压缩感知等任务中取得了显著成就。这类方法通过将迭代步骤拆解为一系列顺序连接的模块化块来工作，每个块包含一个梯度下降模块（GDM）和一个临近映射模块（PMM），后者从贝叶斯视角来看相当于一种去噪器，针对已知高斯噪声进行操作。然而，现有的DUNs面临两个关键限制：(i)它们的PMM在各阶段共享相同的架构及去噪目标，忽视了根据不同阶段所需的特定适应性调整；(ii)重复结构导致严重的参数冗余和高内存消耗，阻碍其在大规模或资源受限环境中的部署。 为解决这些问题，我们提出了广义深度低秩适配（LoRA）展开网络用于图像恢复，命名为LoRun。该方法通过压缩的内存使用量实现了不同阶段去噪目标之间的协调及适应不同的噪声水平，并且提高了效率。这种方法引入了一种新颖的方法：在整个过程中共享一个预训练的基本去噪器，同时在每个PMM中插入轻量级、阶段特定的LoRA适配器来根据展开步骤中的噪声级别动态调节去噪行为。 该设计解耦了核心恢复能力与任务特定适应性调整，从而能够在不复制完整网络参数的情况下实现对去噪强度的精确控制，并且最多可以将N个阶段DUN的参数减少到原来的1/N倍，在保持性能不变或更好的情况下。通过在三个图像恢复任务上的实验验证了我们方法的有效性。
URL
https://arxiv.org/abs/2602.18697
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MTS-CSNet: Multiscale Tensor Factorization for Deep Compressive Sensing on RGB Images
2026-02-04 20:38:04Mehmet Yamac, Lei Xu, Serkan Kiranyaz, Moncef GabboujAbstract
Deep learning based compressive sensing (CS) methods typically learn sampling operators using convolutional or block wise fully connected layers, which limit receptive fields and scale poorly for high dimensional data. We propose MTSCSNet, a CS framework based on Multiscale Tensor Summation (MTS) factorization, a structured operator for efficient multidimensional signal processing. MTS performs mode-wise linear transformations with multiscale summation, enabling large receptive fields and effective modeling of cross-dimensional correlations. In MTSCSNet, MTS is first used as a learnable CS operator that performs linear dimensionality reduction in tensor space, with its adjoint defining the initial back-projection, and is then applied in the reconstruction stage to directly refine this estimate. This results in a simple feed-forward architecture without iterative or proximal optimization, while remaining parameter and computation efficient. Experiments on standard CS benchmarks show that MTSCSNet achieves state-of-the-art reconstruction performance on RGB images, with notable PSNR gains and faster inference, even compared to recent diffusion-based CS methods, while using a significantly more compact feed-forward architecture.
Abstract (translated)
基于深度学习的压缩感知（CS）方法通常使用卷积层或分块全连接层来学习采样算子，这些方法会限制感受野并导致在高维数据上的性能不佳。我们提出了MTSCSNet框架，该框架基于多尺度张量求和(MTS)分解，这是一种用于高效处理多维信号的结构化操作符。MTS通过模式级线性变换与多尺度求和实现大范围的感受野，并能有效建模跨维度的相关性。 在MTSCSNet中，首先使用MTS作为可学习的CS算子，在张量空间执行线性降维处理，其伴随算子定义了初始反投影。然后，在重建阶段应用MTS直接精炼该估计值。这一过程构建了一个简单的前馈架构，无需迭代或近似优化，并且保持参数和计算效率。 实验结果表明，基于标准CS基准测试的MTSCSNet在RGB图像重构性能上取得了当前最佳的结果，展示了显著的PSNR增益和更快的推理速度，即使与最近基于扩散的CS方法相比也表现出色。同时，它使用了一个更为紧凑的前馈架构。
URL
https://arxiv.org/abs/2602.07056
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DeMark: A Query-Free Black-Box Attack on Deepfake Watermarking Defenses
2026-01-23 06:04:43Wei Song, Zhenchang Xing, Liming Zhu, Yulei Sui, Jingling XueAbstract
The rapid proliferation of realistic deepfakes has raised urgent concerns over their misuse, motivating the use of defensive watermarks in synthetic images for reliable detection and provenance tracking. However, this defense paradigm assumes such watermarks are inherently resistant to removal. We challenge this assumption with DeMark, a query-free black-box attack framework that targets defensive image watermarking schemes for deepfakes. DeMark exploits latent-space vulnerabilities in encoder-decoder watermarking models through a compressive sensing based sparsification process, suppressing watermark signals while preserving perceptual and structural realism appropriate for deepfakes. Across eight state-of-the-art watermarking schemes, DeMark reduces watermark detection accuracy from 100% to 32.9% on average while maintaining natural visual quality, outperforming existing attacks. We further evaluate three defense strategies, including image super resolution, sparse watermarking, and adversarial training, and find them largely ineffective. These results demonstrate that current encoder decoder watermarking schemes remain vulnerable to latent-space manipulations, underscoring the need for more robust watermarking methods to safeguard against deepfakes.
Abstract (translated)
URL
https://arxiv.org/abs/2601.16473
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WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelope
2026-01-19 23:46:19Takanobu Furuhashi, Hidekata Hontani, Qibin Zhao, Tatsuya YokotaAbstract
Sparse regularization is fundamental in signal processing and feature extraction but often relies on non-differentiable penalties, conflicting with gradient-based optimizers. We propose WEEP (Weakly-convex Envelope of Piecewise Penalty), a novel differentiable regularizer derived from the weakly-convex envelope framework. WEEP provides tunable, unbiased sparsity and a simple closed-form proximal operator, while maintaining full differentiability and L-smoothness, ensuring compatibility with both gradient-based and proximal algorithms. This resolves the tradeoff between statistical performance and computational tractability. We demonstrate superior performance compared to established convex and non-convex sparse regularizers on challenging compressive sensing and image denoising tasks.
Abstract (translated)
稀疏正则化在信号处理和特征提取中至关重要，但通常依赖于非可微分的惩罚项，这与基于梯度的优化器相冲突。我们提出了WEEP（弱凸包络分段惩罚），这是一种新颖的可微正则化方法，源自弱凸包络框架。WEEP提供了一种可调、无偏的稀疏性，并具有简单的闭式形式近端操作符，同时保持完全可微性和L-光滑性，确保了与基于梯度和基于近端算法的兼容性。这解决了统计性能与计算可行性之间的权衡问题。我们在具有挑战性的压缩感知和图像去噪任务中展示了WEEP相较于现有的凸和非凸稀疏正则化方法的优越性能。
URL
https://arxiv.org/abs/2507.20447
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Efficient Hyperspectral Image Reconstruction Using Lightweight Separate Spectral Transformers
2026-01-03 04:19:14Jianan Li, Wangcai Zhao, Tingfa XuAbstract
Hyperspectral imaging (HSI) is essential across various disciplines for its capacity to capture rich spectral information. However, efficiently reconstructing hyperspectral images from compressive sensing measurements presents significant challenges. To tackle these, we adopt a divide-and-conquer strategy that capitalizes on the unique spectral and spatial characteristics of hyperspectral images. We introduce the Lightweight Separate Spectral Transformer (LSST), an innovative architecture tailored for efficient hyperspectral image reconstruction. This architecture consists of Separate Spectral Transformer Blocks (SSTB) for modeling spectral relationships and Lightweight Spatial Convolution Blocks (LSCB) for spatial processing. The SSTB employs Grouped Spectral Self-attention and a Spectrum Shuffle operation to effectively manage both local and non-local spectral relationships. Simultaneously, the LSCB utilizes depth-wise separable convolutions and strategic ordering to enhance spatial information processing. Furthermore, we implement the Focal Spectrum Loss, a novel loss weighting mechanism that dynamically adjusts during training to improve reconstruction across spectrally complex bands. Extensive testing demonstrates that our LSST achieves superior performance while requiring fewer FLOPs and parameters, underscoring its efficiency and effectiveness. The source code is available at: this https URL.
Abstract (translated)
高光谱成像（HSI）因其能够捕获丰富的光谱信息而在多个学科中至关重要。然而，从压缩感知测量高效重建高光谱图像面临重大挑战。为解决这些问题，我们采用了一种分而治之的策略，利用了高光谱图像独特的光谱和空间特性。为此，我们引入了轻量级独立光谱变压器（LSST），这是一种创新架构，专为高效的高光谱图像重建设计。 该架构包括用于建模光谱关系的独立光谱变换模块（SSTB）以及用于处理空间信息的轻量化空间卷积块（LSCB）。SSTB 采用分组光谱自注意力机制和光谱混洗操作，有效管理局部和非局部光谱关系。同时，LSCB 使用深度可分离卷积并采取战略性排列以增强空间信息处理。 此外，我们实施了焦点光谱损失（Focal Spectrum Loss），这是一种新颖的损失加权机制，在训练过程中动态调整，旨在改善复杂光谱带中的重建效果。广泛的测试表明，我们的 LSST 实现了卓越的性能，同时需要较少的浮点运算数（FLOPs）和参数，突显其高效性和有效性。源代码可在以下网址获取：[提供链接的地方，请根据实际情况插入正确的URL]。
URL
https://arxiv.org/abs/2601.01064
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Primal: A Unified Deterministic Framework for Quasi-Orthogonal Hashing and Manifold Learning
Abstract
We present Primal, a deterministic feature mapping framework that harnesses the number-theoretic independence of prime square roots to construct robust, tunable vector representations. Diverging from standard stochastic projections (e.g., Random Fourier Features), our method exploits the Besicovitch property to create irrational frequency modulations that guarantee infinite non-repeating phase trajectories. We formalize two distinct algorithmic variants: (1) StaticPrime, a sequence generation method that produces temporal position encodings empirically approaching the theoretical Welch bound for quasi-orthogonality; and (2) DynamicPrime, a tunable projection layer for input-dependent feature mapping. A central novelty of the dynamic framework is its ability to unify two disparate mathematical utility classes through a single scaling parameter {\sigma}. In the low-frequency regime, the method acts as an isometric kernel map, effectively linearizing non-convex geometries (e.g., spirals) to enable high-fidelity signal reconstruction and compressive sensing. Conversely, the high-frequency regime induces chaotic phase wrapping, transforming the projection into a maximum-entropy one-way hash suitable for Hyperdimensional Computing and privacy-preserving Split Learning. Empirical evaluations demonstrate that our framework yields superior orthogonality retention and distribution tightness compared to normalized Gaussian baselines, establishing it as a computationally efficient, mathematically rigorous alternative to random matrix projections. The code is available at this https URL
Abstract (translated)
URL
https://arxiv.org/abs/2511.20839
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A Plug-and-Play Framework for Volumetric Light-Sheet Image Reconstruction
2025-11-05 00:49:00Yi Gong, Xinyuan Zhang, Jichen Chai, Yichen Ding, Yifei LouAbstract
Cardiac contraction is a rapid, coordinated process that unfolds across three-dimensional tissue on millisecond timescales. Traditional optical imaging is often inadequate for capturing dynamic cellular structure in the beating heart because of a fundamental trade-off between spatial and temporal resolution. To overcome these limitations, we propose a high-performance computational imaging framework that integrates Compressive Sensing (CS) with Light-Sheet Microscopy (LSM) for efficient, low-phototoxic cardiac imaging. The system performs compressed acquisition of fluorescence signals via random binary mask coding using a Digital Micromirror Device (DMD). We propose a Plug-and-Play (PnP) framework, solved using the alternating direction method of multipliers (ADMM), which flexibly incorporates advanced denoisers, including Tikhonov, Total Variation (TV), and BM3D. To preserve structural continuity in dynamic imaging, we further introduce temporal regularization enforcing smoothness between adjacent z-slices. Experimental results on zebrafish heart imaging under high compression ratios demonstrate that the proposed method successfully reconstructs cellular structures with excellent denoising performance and image clarity, validating the effectiveness and robustness of our algorithm in real-world high-speed, low-light biological imaging scenarios.
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URL
https://arxiv.org/abs/2511.03093
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A Statistical Method for Attack-Agnostic Adversarial Attack Detection with Compressive Sensing Comparison
2025-10-03 04:05:20Chinthana Wimalasuriya, Spyros TragoudasAbstract
Adversarial attacks present a significant threat to modern machine learning systems. Yet, existing detection methods often lack the ability to detect unseen attacks or detect different attack types with a high level of accuracy. In this work, we propose a statistical approach that establishes a detection baseline before a neural network's deployment, enabling effective real-time adversarial detection. We generate a metric of adversarial presence by comparing the behavior of a compressed/uncompressed neural network pair. Our method has been tested against state-of-the-art techniques, and it achieves near-perfect detection across a wide range of attack types. Moreover, it significantly reduces false positives, making it both reliable and practical for real-world applications.
Abstract (translated)
对抗性攻击对现代机器学习系统构成了重大威胁。然而，现有的检测方法通常缺乏检测未见过的攻击或以高精度检测不同类型的攻击的能力。在这项工作中，我们提出了一种统计方法，在神经网络部署之前建立一个检测基线，从而能够进行有效的实时对抗性检测。通过比较压缩和未压缩的一对神经网络的行为，我们生成了一个衡量对抗性存在的指标。我们的方法已经经过最先进的技术测试，并在广泛的攻击类型中实现了近乎完美的检测率。此外，它大大减少了误报，使其既可靠又实用，适合实际应用。
URL
https://arxiv.org/abs/2510.02707
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Flow-Matching Guided Deep Unfolding for Hyperspectral Image Reconstruction
2025-10-02 11:32:00Yi Ai, Yuanhao Cai, Yulun Zhang, Xiaokang YangAbstract
Hyperspectral imaging (HSI) provides rich spatial-spectral information but remains costly to acquire due to hardware limitations and the difficulty of reconstructing three-dimensional data from compressed measurements. Although compressive sensing systems such as CASSI improve efficiency, accurate reconstruction is still challenged by severe degradation and loss of fine spectral details. We propose the Flow-Matching-guided Unfolding network (FMU), which, to our knowledge, is the first to integrate flow matching into HSI reconstruction by embedding its generative prior within a deep unfolding framework. To further strengthen the learned dynamics, we introduce a mean velocity loss that enforces global consistency of the flow, leading to a more robust and accurate reconstruction. This hybrid design leverages the interpretability of optimization-based methods and the generative capacity of flow matching. Extensive experiments on both simulated and real datasets show that FMU significantly outperforms existing approaches in reconstruction quality. Code and models will be available at this https URL.
Abstract (translated)
高光谱成像（HSI）提供了丰富的空间-光谱信息，但由于硬件限制和从压缩测量中重构三维数据的难度，其获取成本仍然较高。尽管诸如CASSI之类的压缩感知系统提高了效率，但准确重建仍受到严重退化和精细光谱细节丢失的挑战。我们提出了Flow-Matching指导下的展层网络（FMU），据我们所知，这是首次将流匹配集成到HSI重构中，在深度解卷积框架内嵌入其生成先验的方法。为了进一步增强学习的动力学，我们引入了平均速度损失，以强制执行流的全局一致性，从而实现更稳健和准确的重建。这种混合设计利用了基于优化方法的可解释性和流匹配的生成能力。在仿真数据集和真实数据集上的广泛实验表明，FMU在重构质量上显著优于现有方法。代码和模型将在以下网址提供：[此链接]（请将方括号内的文本替换为实际提供的URL）。
URL
https://arxiv.org/abs/2510.01912
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NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problems
2025-10-02 02:45:06Roman Jacome, Romario Gualdr\'on-Hurtado, Leon Suarez, Henry ArguelloAbstract
Imaging inverse problems aims to recover high-dimensional signals from undersampled, noisy measurements, a fundamentally ill-posed task with infinite solutions in the null-space of the sensing operator. To resolve this ambiguity, prior information is typically incorporated through handcrafted regularizers or learned models that constrain the solution space. However, these priors typically ignore the task-specific structure of that null-space. In this work, we propose \textit{Non-Linear Projections of the Null-Space} (NPN), a novel class of regularization that, instead of enforcing structural constraints in the image domain, promotes solutions that lie in a low-dimensional projection of the sensing matrix's null-space with a neural network. Our approach has two key advantages: (1) Interpretability: by focusing on the structure of the null-space, we design sensing-matrix-specific priors that capture information orthogonal to the signal components that are fundamentally blind to the sensing process. (2) Flexibility: NPN is adaptable to various inverse problems, compatible with existing reconstruction frameworks, and complementary to conventional image-domain priors. We provide theoretical guarantees on convergence and reconstruction accuracy when used within plug-and-play methods. Empirical results across diverse sensing matrices demonstrate that NPN priors consistently enhance reconstruction fidelity in various imaging inverse problems, such as compressive sensing, deblurring, super-resolution, computed tomography, and magnetic resonance imaging, with plug-and-play methods, unrolling networks, deep image prior, and diffusion models.
Abstract (translated)
图像逆问题的目标是从欠采样且含有噪声的测量中恢复高维信号，这是一个本质上无法确定的问题，在感知算子的零空间中有无限多个解。为了消除这种不确定性，通常通过手工设计的正则化器或学习模型来整合先验信息以约束解的空间范围。然而，这些先验信息往往忽略了该零空间中的任务特定结构。在本文中，我们提出了“非线性零空间投影”（NPN），这是一种新的正则化方法，它不通过图像域施加结构性限制，而是利用神经网络来促进那些位于感知矩阵的低维零空间投影上的解。我们的方法有两大优势： 1. **可解释性**：通过关注零空间结构，我们设计了与感知过程本质盲目的信号成分正交的信息特异于感知矩阵的先验。 2. **灵活性**：NPN能够适应各种逆问题，可以与现有的重建框架兼容，并且是对传统图像域先验的一种补充。我们在插件式方法中提供了关于收敛性和重构准确性的理论保证。 实验结果表明，在多种不同的感知矩阵下，NPN在压缩感知、去模糊化、超分辨率、计算机断层扫描和磁共振成像等各类成像逆问题中的重构保真度上始终有所提升。这些改进适用于插件式方法、展卷网络、深度图像先验以及扩散模型等多种技术框架内。
URL
https://arxiv.org/abs/2510.01608
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