论文标题
ORKA：使用K-Approximation图的对象重建
ORKA: Object reconstruction using a K-approximation graph
论文作者
论文摘要
数据处理必须应对许多实际困难。数据通常会因工件或噪声而损坏，获取数据可能是昂贵且困难的。因此，给定的数据通常不完整且不准确。为了克服这些问题，通常假定某些域中的数据是稀疏或低维的。当进行多次测量时，这种稀疏性通常以结构化的方式出现。我们提出了一个新模型，该模型假设数据仅包含一些相关对象，即在某些对象域中它很少。我们将对象建模为一种结构，该结构只能以形式稍微变化，并且在不同的测量结果上不断地处于位置。这可以通过具有高度相关列的矩阵和我们在这项工作中介绍的列移动运算符进行建模。我们提出了一种有效的算法来基于k-approximation图解决对象重建问题。我们证明了最佳近似界限，并对该方法进行数值评估。将提供包括地球物理，视频处理等应用程序的示例。
Data processing has to deal with many practical difficulties. Data is often corrupted by artifacts or noise and acquiring data can be expensive and difficult. Thus, the given data is often incomplete and inaccurate. To overcome these problems, it is often assumed that the data is sparse or low-dimensional in some domain. When multiple measurements are taken, this sparsity often appears in a structured manner. We propose a new model that assumes the data only contains a few relevant objects, i.e., it is sparse in some object domain. We model an object as a structure that can only change slightly in form and continuously in position over different measurements. This can be modeled by a matrix with highly correlated columns and a column shift operator that we introduce in this work. We present an efficient algorithm to solve the object reconstruction problem based on a K-approximation graph. We prove optimal approximation bounds and perform a numerical evaluation of the method. Examples from applications including Geophysics, video processing, and others will be given.
