Approximate Strang-Fix: Sparse Sampling with any acquisition device
Event details
| Date | 10.06.2013 |
| Hour | 11:15 › 12:15 |
| Speaker | Prof. Pier Luigi Dragotti, Imperial College London |
| Location | |
| Category | Conferences - Seminars |
The problem of reconstructing partially observed or sampled signals is an important one that finds application in many areas of signal processing. Traditional acquisition and reconstruction approaches are heavily influences by classical Shannon sampling theory which gives an exact sampling and interpolation formula for bandlimited signals. In the last few years, several new methods have been developed for the sampling and exact reconstruction of specific classes of sparse non-bandlimited signals known as signals with finite rate of innovation (FRI). This is achieved by using adequate acquisition devices (sampling kernels) and reconstruction schemes. Valid sampling kernels allow to connect the samples to some essential information of the original signal, typically, its Fourier or Laplace transform at specific frequencies. An example of valid kernel is given by the family of exponential reproducing functions. These satisfy the generalised Strang-Fix conditions, which ensure that proper linear combinations of the kernel with its shifted versions reproduce exponentials exactly.
In the first part of the talk, we discuss sampling and perfect reconstruction of parametric sparse signals such as piecewise sinusoidal signals or classes of 2-D signals using exponential reproducing kernels. We then show how to choose the exponential reproducing kernel that leads to the most stable reconstruction when estimating FRI signals from noisy samples. This analysis leads to the design of the e-MOMS family of kernels (Maximum order minimum support exponential reproducing kernels)
which we show includes all the compact support kernels used in FRI theory so far. Next we depart from the situation in which we can choose the sampling kernel and develop a new strategy that is universal in that it works with any kernel. We do so by noting that meeting the exact exponential reproduction condition is too stringent a constraint. We thus allow for a controlled error in the reproduction formula in order to use the exponential reproduction idea with arbitrary kernels and develop a universal reconstruction method which is also robust to noise.
To emphasize the relevance of these new theories, we conclude the talk by presenting applications in image super-resolution and in neuroscience. In particular, we will present a new fast algorithm for spike detection from two-photon calcium imaging and will show how to perform spike sorting at sub-Nyquist rates.
This is joint work with T. Blu (CUHK), H. Pan (CUHK) J. A. Uriguen (ICL), J. Onativia Bravo (ICL) and S. Schultz (ICL).
This work is supported by the European Research Council (ERC) starting investigator award Nr. 277800 (RecoSamp).
In the first part of the talk, we discuss sampling and perfect reconstruction of parametric sparse signals such as piecewise sinusoidal signals or classes of 2-D signals using exponential reproducing kernels. We then show how to choose the exponential reproducing kernel that leads to the most stable reconstruction when estimating FRI signals from noisy samples. This analysis leads to the design of the e-MOMS family of kernels (Maximum order minimum support exponential reproducing kernels)
which we show includes all the compact support kernels used in FRI theory so far. Next we depart from the situation in which we can choose the sampling kernel and develop a new strategy that is universal in that it works with any kernel. We do so by noting that meeting the exact exponential reproduction condition is too stringent a constraint. We thus allow for a controlled error in the reproduction formula in order to use the exponential reproduction idea with arbitrary kernels and develop a universal reconstruction method which is also robust to noise.
To emphasize the relevance of these new theories, we conclude the talk by presenting applications in image super-resolution and in neuroscience. In particular, we will present a new fast algorithm for spike detection from two-photon calcium imaging and will show how to perform spike sorting at sub-Nyquist rates.
This is joint work with T. Blu (CUHK), H. Pan (CUHK) J. A. Uriguen (ICL), J. Onativia Bravo (ICL) and S. Schultz (ICL).
This work is supported by the European Research Council (ERC) starting investigator award Nr. 277800 (RecoSamp).
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Practical information
- General public
- Free
Organizer
- SuRI 2013
Contact
- Simone Muller