Efficient Computational Methods for Robust Multispectral Multiframe Superresolution

所提出的研究考虑了多传感器、多帧超分辨率的计算模型。基本的数学模型是第一类Fredholm型积分方程。对于超分辨问题，不仅输入数据受到噪声的污染，而且由于传感器对准的不确定性，定义线性算子的参数也是不确定的。噪声输入使问题成为Tikhanov正则化最小二乘的候选者。算子中的不确定性使其成为正则化总体最小二乘的候选者。此外，由于构造了线性算子中的不确定性，因此构造的总体最小二乘模型是合适的，本课题考虑了这些最小二乘和总体最小二乘模型以及适当的正则化方法。根据美国国家科学基金会的标准，这项活动的优点如下。将空间变量正则化方法应用于最近提出的最小二乘和总体最小二乘模型。将总体最小二乘算法和空间变量正则化方法应用于多传感器阵列采集图像的盲反卷积问题。将结构化总体最小二乘算法推广到红绿蓝(RGB)彩色图像。将小波超分辨率算法应用于多传感器阵列获取的低分辨率退化图像。超分辨率问题影响到军事、商业和医疗保健等不同学科的应用，如生物工程、卫星成像以及电气和计算机工程。其他耐人寻味的可能性包括用更粗糙、更便宜的对应物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，将分辨率提高到更昂贵的设备所能获得的分辨率。除了在适当的参考期刊和会议上发表项目结果外，还将准备调查文章，以提供关于我们的计算方法的指导信息。PI和共同PI打算每年从宾夕法尼亚州立大学的大学学者方案中招聘4个REU。宾夕法尼亚州立大学的研究生将成为合作者，期望能发表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.