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Reconstruction of Irregularly Sampled Image Signals Using Sparse Representations

使用稀疏表示重建不规则采样图像信号

基本信息

批准号：
225074913
负责人：
Professor Dr.-Ing. André Kaup
金额：
--
依托单位：
Lehrstuhl für Multimediakommunikation und Signalverarbeitung
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/225074913?language=en
关键词：
Reconstruction Irregularly Sampled Image Signals

项目摘要

The sampling process is a fundamental element of digital signal processing. It is necessary to convert a continuous signal from the analog domain into the digital domain and it is the first step for further processing by methods and algorithms from digital signal processing. Commonly, a regular sampling is used where the sampling positions are regularly arranged on a corresponding grid. This kind of sampling is comprehensively investigated and documented and most methods from digital signal processing work with sampling positions on a regular grid. Due to some image acquisition systems or due to explicitly selecting the sampling positions in order to avoid artifacts from aliasing, the sampling positions may be distributed irregularly on the grid. For further processing, these sampling positions have to be reconstructed on a regular grid. During previous work on the reconstruction of irregularly sampled image data, it has been shown that this reconstruction can be done by identifying the dominant basis function and estimating its weight. Similar to Compressed Sensing, the property that most natural signals can be represented sparsely in certain domains is exploited. As a first objective, starting from the results for the reconstruction of irregularly sampled image data, a general method shall be developed to reconstruct irregularly sampled multidimensional signals. In doing so, detailed investigations are necessary to understand the effect of irregular sampling on multidimensional signals and to adapt the reconstruction process to this problem. By using these new insights, a method shall be developed to capture and reconstruct a video consisting of irregularly sampled frames with high quality. Existing sensors are either able to capture a video with high spatial but low temporal resolution or vice versa. By means of this new method a video with both high spatial and high temporal resolution can be acquired. Moreover, the relationship between irregular sampling followed by a sparsity-based reconstruction algorithm that has to be developed in this work and Compressed Sensing shall be theoretically investigated. Also the benefits of different reconstruction algorithms used in Compressed Sensing and the new sparsity-based reconstruction method shall be combined.

采样过程是数字信号处理的基本要素。需要将连续信号从模拟域转换到数字域，并且这是通过来自数字信号处理的方法和算法进行进一步处理的第一步。通常，使用规则采样，其中采样位置规则地布置在相应的网格上。这种采样被广泛研究和记录，并且来自数字信号处理的大多数方法都在规则网格上进行采样。由于某些图像采集系统或由于明确选择采样位置以避免来自混叠的伪影，采样位置可能不规则地分布在网格上。为了进一步处理，必须在规则网格上重建这些采样位置。在以前的工作不规则采样的图像数据的重建，它已被证明，这种重建可以通过识别的主导基函数和估计其权重。与压缩感知类似，大多数自然信号可以在某些域中稀疏表示的属性被利用。作为第一个目标，从不规则采样的图像数据的重建结果开始，将开发一种通用方法来重建不规则采样的多维信号。在这样做时，详细的调查是必要的，以了解不规则采样对多维信号的影响，并适应重建过程中这个问题。通过使用这些新的见解，将开发一种方法来捕获和重建由高质量的不规则采样帧组成的视频。现有的传感器能够捕获具有高空间分辨率但低时间分辨率的视频，反之亦然。通过这种新方法，可以获得具有高空间和高时间分辨率的视频。此外，不规则采样后，必须在这项工作中开发的基于稀疏性的重建算法和压缩感知之间的关系进行理论研究。此外，压缩感知中使用的不同重建算法和新的基于稀疏性的重建方法的益处将被组合。