Publication
Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomial or piecewise sinusoidal signals, and call the number of degrees of freedom per unit of time the rate of innovation. Classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited. In this paper, we show that many signals with finite rate of innovation can be sampled and perfectly reconstructed using kernels of compact support and a local reconstruction algorithm. The class of kernels that we can use is very rich and includes functions satisfying strang-fix conditions, exponential splines and functions with rational Fourier transforms. Extension of such results to the 2-dimensional case are also discussed and an application to image super-resolution is presented
Matthias Finger, Qian Wang, Yiming Li, Varun Sharma, Konstantin Androsov, Jan Steggemann, Xin Chen, Rakesh Chawla, Matteo Galli, Jian Wang, João Miguel das Neves Duarte, Tagir Aushev, Matthias Wolf, Yi Zhang, Tian Cheng, Yixing Chen, Werner Lustermann, Andromachi Tsirou, Alexis Kalogeropoulos, Andrea Rizzi, Ioannis Papadopoulos, Paolo Ronchese, Hua Zhang, Leonardo Cristella, Siyuan Wang, Tao Huang, David Vannerom, Michele Bianco, Sebastiana Gianì, Sun Hee Kim, Davide Di Croce, Kun Shi, Abhisek Datta, Jian Zhao, Federica Legger, Gabriele Grosso, Anna Mascellani, Ji Hyun Kim, Donghyun Kim, Zheng Wang, Sanjeev Kumar, Wei Li, Yong Yang, Ajay Kumar, Ashish Sharma, Georgios Anagnostou, Joao Varela, Csaba Hajdu, Muhammad Ahmad, Ekaterina Kuznetsova, Ioannis Evangelou, Milos Dordevic, Meng Xiao, Sourav Sen, Xiao Wang, Kai Yi, Jing Li, Rajat Gupta, Hui Wang, Seungkyu Ha, Pratyush Das, Anton Petrov, Xin Sun, Valérie Scheurer, Muhammad Ansar Iqbal, Lukas Layer