Algorithms for Data Simplicity

数据简单化算法

• 批准号: EP/J020567/2
• 负责人: Jared Tanner
• 金额: $ 3.96万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ020567%2F2
• 关键词: Algorithms; Data; Simplicity

Most of the information we encounter on a day to day basis has some inherent simplicity, from music having a limited number of dominant frequencies at any given time and natural images being composed of smooth regions separated by relatively few abrupt edges. This inherent simplicity can be leveraged to allow extraction of meaningful information from the vast data and for more efficient information acquisition. For example, consider consumer grade mega-pixel digital cameras. The camera has a carefully constructed array of millions of photodiodes, but as soon as the image is taken the camera compresses the data to a much smaller JPG format. This compression is crucial to allow for efficient storage and transmission of the image, but it is wasteful to have acquired millions of pixels and then to immediately compress and remove the measured image. Compressed sensing and matrix completion are techniques by which the camera can measure the image at a rate proportional to the size of the final compressed image, dramatically increasing the efficiency of the camera. Taking advantage of this technology requires the design of computationally efficient algorithms for the recovery of the image from the compressed measurements. This proposal concerns the design, analysis, and application of fast algorithms able to act on large data sets.

我们每天遇到的大多数信息都有一些固有的简单性，例如音乐在任何给定时间都具有有限数量的主频率，而自然图像则由由相对较少的陡峭边缘分隔的平滑区域组成。可以利用这种固有的简单性来从大量数据中提取有意义的信息，并更有效地获取信息。例如，考虑消费级百万像素数码相机。该相机具有精心构建的数百万个光电二极管阵列，但一旦拍摄图像，相机就会将数据压缩为小得多的 JPG 格式。这种压缩对于图像的有效存储和传输至关重要，但是获取数百万像素然后立即压缩和删除测量的图像是一种浪费。压缩感知和矩阵补全是相机能够以与最终压缩图像的大小成比例的速率测量图像的技术，从而显着提高相机的效率。利用这项技术需要设计计算效率高的算法，用于从压缩测量中恢复图像。该提案涉及能够作用于大型数据集的快速算法的设计、分析和应用。

项目成果

CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion

• DOI: 10.1093/imaiai/iav011
• 发表时间: 2015-12-01
• 期刊: INFORMATION AND INFERENCE-A JOURNAL OF THE IMA
• 影响因子: 1.6
• 作者: Blanchard, Jeffrey D.;Tanner, Jared;Wei, Ke
• 通讯作者: Wei, Ke

Parallel coordinate descent methods for big data optimization

• DOI: 10.1007/s10107-015-0901-6
• 发表时间: 2016-03-01
• 期刊: MATHEMATICAL PROGRAMMING
• 影响因子: 2.7
• 作者: Richtarik, Peter;Takac, Martin
• 通讯作者: Takac, Martin

Matrix Rigidity and the Ill-Posedness of Robust PCA and Matrix Completion

矩阵刚性以及鲁棒 PCA 和矩阵补全的不适定性

• DOI: 10.1137/18m1227846
• 发表时间: 2019
• 期刊: SIAM Journal on Mathematics of Data Science
• 影响因子: 3.6
• 作者: Tanner J

NORMALIZED ITERATIVE HARD THRESHOLDING FOR MATRIX COMPLETION

• DOI: 10.1137/120876459
• 发表时间: 2013-01-01
• 期刊: SIAM JOURNAL ON SCIENTIFIC COMPUTING
• 影响因子: 3.1
• 作者: Tanner, Jared;Wei, Ke
• 通讯作者: Wei, Ke

Multispectral Snapshot Demosaicing Via Non-Convex Matrix Completion

通过非凸矩阵补全进行多光谱快照去马赛克

• DOI: 10.1109/dsw.2019.8755561
• 发表时间: 2019
• 作者: Antonucci G