Efficient Computational Methods for Robust Multispectral Multiframe Superresolution

本研究考虑了多传感器、多帧超分辨率的计算模型。其基础数学模型是第一类Fredholm积分方程。对于超分辨率问题，不仅输入数据受噪声污染，而且由于传感器对准的不确定性，定义线性算子的参数是不确定的。噪声输入使该问题成为Tikhanov正则化最小二乘的候选问题。算子的不确定性使其成为正则化总最小二乘的候选。此外，线性算子的不确定性是结构化的，因此结构化的总最小二乘模型是合适的。本文研究了这些最小二乘和总最小二乘模型，并给出了正则化它们的适当方法。根据美国国家科学基金会的标准，这项活动的优点如下。知识Merit1。空间变量正则化在最近提出的最小二乘和总最小二乘模型中的应用。总最小二乘算法和空间变异正则化在多传感器阵列图像盲反卷积问题中的应用。结构化总最小二乘算法在RGB彩色成像中的推广。小波超分辨率算法在多传感器阵列低分辨率退化成像中的应用。更广泛的Impact1。超分辨率问题已经影响到军事、商业和医疗保健在不同学科的应用，如生物工程、卫星成像、电子和计算机工程。其他有趣的可能性包括用更粗糙、更便宜的同类产品取代昂贵的高分辨率仪器，如扫描电子显微镜，然后应用技术方法，用更昂贵的设备提高分辨率。将准备调查文章，提供关于我们的计算方法的教程信息。除此之外，还将在适当的期刊和会议上发表该项目的结果。PI和联合PI计划每年从宾夕法尼亚州立大学学者计划中招募4名reu。宾夕法尼亚州立大学的研究生将成为合作者，并有望撰写与该项目相关的博士论文。

The proposed research considers computational models for multisensor, multiframe superresolution.The underlying mathematical model is a Fredholm integral equation of the first kind. For thesuperresolution problem, not only is the input data contaminated by noise, but the parameters defining the linear operator are uncertain because of uncertainty in sensor alignment. The noisy input makes the problem a candidate for Tikhanov regularized least squares. The uncertainty in the operator make it a candidate for regularized total least squares. Moreover, the uncertainty in the linear operator is structured, thus structured total least squares models are appropriate.This project considers these least squares and total least squares models and appropriate methods forregularizing them. The merits of this activity according to NSF criteria are given below.Intellectual Merit1. The deployment of space variant regularization to the recently proposed least squares and total least squares models.2. The application of total least squares algorithms and space variant regularization to the solutionof blind deconvolution problems using images acquired by multisensor arrays.3. The extension of structured total least squares algorithms to red--green--blue (RGB) color imaging.4. The application of wavelet superresolution algorithms to multisensor array acquired low resolutiondegraded imaging.Broader Impact1. The superresolution problem has impact upon military, commercial, and health careapplications in diverse disciplines such as bioengineering,satellite imaging, and electrical and computer engineering. Other intriguing possibilities include substituting expensive high resolution instruments such asscanning electron microscopes by their cruder, cheaper counterparts and then applying technical methods for increasing the resolution to that derivable with much more costly equipment.2. Survey articles will be prepared to provided tutorial information on our computational methods.This is in addition to publishing the project's results in appropriate refereed journals and conferences.3. The PI and co-PI intend to recruit 4 REUs per year from Penn State's University Scholars program.4. Penn State graduate students will be collaborators with the expectation of producing Ph.D. theses related to the project.