Image Segmentation for cDNA Microarray Data and Jump-Preserving Surface Estimation

本计画讨论两个不同但相关的研究问题：（1）分析基因微阵列影像的影像分割，以及（2）从杂讯资料中进行保跳曲面估计。基因表达数据广泛应用于医学和临床研究中，而基因表达数据的分割是基因表达数据生成的关键步骤。 在处理基因微阵列数据的一些软件包中已经包含了几种图像分割程序。在这个项目中，提出了一种新的基于局部线性核平滑的图像分割方法。预计该方法将具有良好的理论性质。 初步的数值研究表明，它优于一些现有的程序。为了去噪、改变图像分辨率、数据压缩等目的，通常需要重建图像。由于图像的边缘携带关于对象的关键信息，因此在重建图像时应该保留它们。因此，边缘保持图像重建是一个重要的研究课题。图像可以被视为图像强度函数的表面。本项目从曲面估计的角度研究图像重建问题。提出了一种新的基于局部线性核平滑的保跳曲面估计方法。与现有的一些方法相比，该方法使用方便，计算简单。在已有的局部线性核平滑理论基础上，为该方法发展更深层次的统计理论也是可能的。基因微阵列数据广泛应用于医药和临床研究。 通过比较正常和异常细胞中的基因表达，微阵列可以用于识别与特定疾病相关的基因，然后这些基因可以被治疗药物靶向。大多数基因表达数据是通过对微阵列图像进行分割而产生的。因此，图像分割技术直接关系到基因表达数据的质量。本计画提出一种新的影像分割技术。基于初步的数值研究，它可以改善目前的分割技术，从而提高基因表达数据的质量，并对涉及基因微阵列的药物和临床研究产生积极的影响。该项目还提出了一种新的跳跃保持表面估计方法，该方法可以直接用于从噪声版本中恢复真实图像。 与现有的一些方法相比，该方法使用方便，计算简单。它应该有助于使用这种技术的几个不同的科学和行业（例如，医学、气象学、海洋学、军事、空间通信等）。

This project discusses two different but related research problems: (1) image segmentation for analyzing cDNA microarray images, and (2) jump-preserving surface estimation from noisy data. Image segmentation of microarray images is a critical stage in generating gene expression data, which are widely used in pharmaceutical and clinical research for identifying particular diseases. Several image segmentation procedures have been included in some software packages for handling gene microarray data. In this project, a new image segmentation methodology is proposed based on local linear kernel smoothing. It is expected that this method would possess some good theoretical properties. Preliminary numerical studies show that it outperforms some existing procedures. For the purposes of de-noising, change of image resolution, data compression, etc., images often need to be reconstructed. Since edges of an image carry critical information about objects, they should be preserved when the image is reconstructed. So edge-preserving image reconstruction is an important research problem. An image can be regarded as a surface of the image intensity function. In this project, the image reconstruction problem is studied from the perspective of surface estimation. A new jump-preserving surface estimation methodology is proposed based on local linear kernel smoothing. Compared to some existing procedures, this method is easy to use and simple to compute. It is also possible to develop profound statistical theory for this method based on existing theory about local linear kernel smoothing.Gene microarray data are widely used in pharmaceutical and clinical research. By comparing gene expression in normal and abnormal cells, microarrays can be used for identifying genes involved in particular diseases, and then these genes can be targeted by therapeutic drugs. Most gene expression data are produced by segmentation of microarray images. So image segmentation techniques are related directly to the quality of gene expression data. This project proposes a new image segmentation technique. Based on preliminary numerical studies, it could improve the current segmentation techniques, and consequently, improve the quality of gene expression data and have a positive impact on pharmaceutical and clinical studies involving gene microarrays. This project also suggests a new jump-preserving surface estimation methodology, which can be used directly for restoring true images from their noisy versions. Compared to some existing procedures, this method is easy to use and simple to compute. It should be helpful for several different sciences and industries using such techniques (e.g., medical sciences, meteorology, oceanography, military, space communication, etc.).