Multiscale Methods for Signal Processing

信号处理的多尺度方法

• 批准号: 250241-2012
• 负责人: Saucier, Antoine
• 金额: $ 0.87万
• 依托单位: École Polytechnique de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570860
• 关键词: Multiscale; Methods; Signal; Processing

We propose a research program on multiscale methods for signal processing. My program is composed of the following two complementary components: Analysis: Adaptive Multiscale Orthogonal (AMO) bases for signal and image analysis. Synthesis: Patterns-based Simulation methods for signal and image synthesis. The success of wavelets in signal processing is based on the ability of wavelets to efficiently represent piecewise regular signals. For such signals, the discrete wavelet-transform representation is sparse in the sense that many transform coefficients are small enough to be neglected. We have been developing new AMO bases that provide exceptionally sparse representations for a signal, much sparser than wavelets for piecewise regular signals. We will develop and refine AMO bases so that they can be used effectively for a wide variety of signals and images, and revisit the main applications of wavelets with AMO bases. This work should have a major impact on a multitude of applications, e.g. medical imaging (diagnosis of disease, screening protocols), compression and denoising of medical images (MRI and ultrasound). Operational decisions made for the exploitation of natural resources (e.g, oil, water, ore) are guided by a stochastic modeling of the resource spatial distribution. In this context, the ability to characterize and model the complex spatial distribution of natural resources is essential for their assessment and exploitation. A correct description of multipoint statistics is particularly important to correctly simulate connected structures such as channels and fractures in oil reservoirs. We have been developing a simulation method that produces images that in many visual and quantitative aspects, i.e. morphology and connectivity, are superior to competing multipoint simulation approaches. Our method takes into account conditioning data, i.e. known geology at several locations, and multipoint statistics, i.e. complex patterns geometry. We propose to develop further our method to take into account constraints defined by geophysical measurements.

我们提出了一个关于信号处理多尺度方法的研究计划。我的程序由以下两个互补的组件组成： 分析：用于信号和图像分析的自适应多尺度正交 (AMO) 基础。 综合：用于信号和图像合成的基于模式的模拟方法。 小波在信号处理中的成功基于小波有效表示分段规则信号的能力。对于此类信号，离散小波变换表示是稀疏的，因为许多变换系数小到足以被忽略。我们一直在开发新的 AMO 基，为信号提供异常稀疏的表示，比分段规则信号的小波稀疏得多。我们将开发和完善 AMO 基，以便它们可以有效地用于各种信号和图像，并重新审视具有 AMO 基的小波的主要应用。这项工作应该对许多应用程序产生重大影响，例如医学成像（疾病诊断、筛查方案）、医学图像压缩和去噪（MRI 和超声）。 自然资源（例如石油、水、矿石）开发的运营决策以资源空间分布的随机模型为指导。在这种情况下，描述和模拟自然资源复杂空间分布的能力对于自然资源的评估和开发至关重要。多点统计的正确描述对于正确模拟油藏中的通道和裂缝等连通结构尤为重要。我们一直在开发一种模拟方法，该方法生成的图像在许多视觉和定量方面（即形态和连接性）都优于竞争的多点模拟方法。我们的方法考虑了条件数据（即多个位置的已知地质情况）和多点统计数据（即复杂的图案几何形状）。我们建议进一步开发我们的方法，以考虑地球物理测量定义的约束。