Multidimensional Signal Processing in the Presence of Homeomorphic Deformations
同胚变形存在下的多维信号处理
基本信息
- 批准号:0633775
- 负责人:
- 金额:$ 9.69万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2006
- 资助国家:美国
- 起止时间:2006-10-01 至 2008-09-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The need to estimate signals from their deformed versions arises in a wide range of engineering problems. Such deformations may be due to inherent physical effects or due to the measurement process. As an example consider two images of a single object taken from different viewpoints and distances. These images are deformed versions of each other. Any attempt to compare these images requires transforming one or both so that corresponding elements in the images appear at the same coordinates. In the one-dimensional case consider the case of a signal measured in the presence of (possibly time-varying) delay and Doppler which causes a distortion of the time axis and a corresponding deformation of the signal shape. The difficulty of these problems is their non-linear and high-dimensional nature.This research provides a fundamental mathematical solution to a class of signal deformation problems. The solution involves a certain parametric model of the family of possible transformations (or rather, their inverses). Using this model the original problem is transformed into an equivalent problem expressed in the form of a linear system of equations in the low dimensional space. In other words, the method converts a computationally prohibitive estimation problem into a set of linear equations in the unknown parameters of the deformation model. In the case of affine transforms an exact closed form solution of the deformation parameters is obtained. In the more general case of homeomorphic deformations the solution is approximate, but high accuracy is achievable. The focus of the research is on evaluating the performance of this approach in the presence of noise and other uncertainties, and the optimal design of certain basis functions used by the algorithm. This research has applications to a wide range of image and video processing systems, in particular to medical imaging systems, and video/image based security systems.%%%%%%%%%%%%%%%%%%%%%%%%%% 3. A level of effort statement.At the recommended level of support, the PI will make every effort to address all of the issues related to the basic operation of the proposed technique as described in the proposal, with emphasis on its performance in the presence of noise and various uncertainties, and the optimal design of the basis functions. Because of the greatly reduced budget and period of performance the specific applications of the technique will not be addressed in any detail.
需要从它们的变形版本中估计信号,这在广泛的工程问题中出现。这种变形可能是由于固有的物理效应或由于测量过程。作为示例,考虑从不同视点和距离拍摄的单个对象的两个图像。这些图像是彼此的变形版本。任何试图比较这些图像的尝试都需要变换其中一个或两个,以便图像中的相应元素出现在相同的坐标处。在一维情况下,考虑在存在(可能时变的)延迟和多普勒的情况下测量的信号的情况,这导致时间轴的失真和信号形状的相应变形。这些问题的难点在于其非线性和高维性,本研究为一类信号变形问题提供了基本的数学解决方法。该解决方案涉及可能的变换(或者更确切地说,它们的逆变换)族的某种参数模型。利用这个模型,原问题转化为等价的问题,在低维空间中的线性方程组的形式表示。换句话说,该方法将计算上禁止的估计问题转换为变形模型的未知参数中的一组线性方程。 在仿射变换的情况下,得到变形参数的精确闭合形式解。在同胚变形的更一般的情况下,解是近似的,但可以达到高精度。研究的重点是评估这种方法在噪声和其他不确定性的存在下的性能,以及算法所使用的某些基函数的优化设计。这项研究应用于广泛的图像和视频处理系统,特别是医学成像系统,以及基于视频/图像的安全系统。 3.工作水平声明。在建议的支持水平下,PI将尽一切努力解决与提案中所述的拟议技术的基本操作相关的所有问题,重点是其在存在噪声和各种不确定性的情况下的性能,以及基函数的最佳设计。 由于预算和执行周期大大减少,将不详细讨论该技术的具体应用。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Benjamin Friedlander其他文献
Can Blood Flow Restricted Exercise Improve Ham:Quad Ratios Better Than Traditional Training?
血流受限运动能否比传统训练更好地改善腿肌与股四头肌的比例?
- DOI:
- 发表时间:
2019 - 期刊:
- 影响因子:0
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M. Bemben;Kirsten M Mitcheltree;R. Larson;David Ross;Charity Cavazos;Benjamin Friedlander;D. Bemben - 通讯作者:
D. Bemben
Parameter estimation of continuous-time stationary Gaussian processes with rational spectra
- DOI:
10.1007/bf01599009 - 发表时间:
1987-03-01 - 期刊:
- 影响因子:2.000
- 作者:
Boaz Porat;Benjamin Friedlander - 通讯作者:
Benjamin Friedlander
Recursive lattice forms for spectral estimation and adaptive control
- DOI:
10.1109/cdc.1980.271839 - 发表时间:
1980-12 - 期刊:
- 影响因子:0
- 作者:
Benjamin Friedlander - 通讯作者:
Benjamin Friedlander
Lattice filters for adaptive processing
- DOI:
10.1109/proc.1982.12407 - 发表时间:
1982-08 - 期刊:
- 影响因子:20.6
- 作者:
Benjamin Friedlander - 通讯作者:
Benjamin Friedlander
Benjamin Friedlander的其他文献
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{{ truncateString('Benjamin Friedlander', 18)}}的其他基金
Communications through time-varying subspace channels
通过时变子空间通道进行通信
- 批准号:
0725366 - 财政年份:2007
- 资助金额:
$ 9.69万 - 项目类别:
Standard Grant
ITR/SY+SI (C-CR) Collaborative Research: Signal Processing and Channel Modelling in Low-Dimensional Subspaces for Wireless Communication in Multi-Antenna Systems
ITR/SY SI (C-CR) 合作研究:多天线系统无线通信的低维子空间信号处理和信道建模
- 批准号:
0112508 - 财政年份:2001
- 资助金额:
$ 9.69万 - 项目类别:
Standard Grant
Adaptive Channel Equalization Based on High-Order Statistics
基于高阶统计的自适应信道均衡
- 批准号:
9017221 - 财政年份:1991
- 资助金额:
$ 9.69万 - 项目类别:
Continuing Grant
Adaptive Signal Processing Based on High-Order Statistics
基于高阶统计的自适应信号处理
- 批准号:
8760095 - 财政年份:1988
- 资助金额:
$ 9.69万 - 项目类别:
Standard Grant
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