Reconstruction of Irregularly Sampled Image Signals Using Sparse Representations

• Applicant: Professor Dr.-Ing. André Kaup
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2012 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 225074913

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.

• DFG Programme: Research Grants