摘要翻译：
在这篇由两部分组成的论文中，我们提出了一种新的框架和方法来分析某些基于图像的生化检测数据，如ELISPOT和荧光斑点检测。在这第一部分，我们首先提出一个物理偏微分方程(PDE)模型，直到这些生化分析的图像采集。然后，我们使用偏微分方程的格林函数导出一个新的参数化的图像获取。这个参数化允许我们提出一个函数优化问题来解决逆扩散问题。特别地，我们提出了一个非负群稀疏正则化优化问题，目标是定位和表征所述分析中涉及的生物细胞。我们继续提出一个合适的离散化方案，使合成数据的产生和可实现的算法解决逆扩散。在第一部分的结尾，我们提供了一个初步的比较结果，我们的方法和一个专家人类标签的真实数据。第二部分致力于提供一个加速的近端梯度算法来解决所提出的问题，并对我们的方法进行实证验证。
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英文标题：
《Cell Detection by Functional Inverse Diffusion and Non-negative Group
  Sparsity$-$Part I: Modeling and Inverse Problems》
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作者：
Pol del Aguila Pla and Joakim Jald\'en
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs' Green function to derive a novel parametrization of the acquired images. This parametrization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a non-negative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology.
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PDF链接：
https://arxiv.org/pdf/1710.01604