Python module for finite rate of innovation (FRI) sampling

Level: BS/MS semester project Description: Sampling signals with finite rate of innovation plays a key in the sucess of continuous domain sparse reconstructions [1], including the direction of arrival estimation (DOA) with a microphone array [2], point source reconstructions in radio astronomy, in-door localizations, etc. There are a few implementations (e.g., [1] and [2]) of a recently proposed robust FRI reconstruction algorithm [3]. Yet the implementations are still more research oriented — they are tailored to the specific sparse reconstruction problems considered there. It is difficult for an outsider to pick up the code and apply to thier sparse reconstruction problems directly. Python is one of the most popular programming languages, both in academia and industry. Its flexibility, open source implementation, and good quality of existing packages make it especially attractive for fast prototyping. We would like to build a modulized Python package so that potential users can easily specify the desired properties (e.g., real-valued, Hermitian symmetric, 1D, or 2D setups, etc.) in the reconstruction problem and apply the FRI technique with minimum efforts. Goals: Build a Python package that implements the robust reconstruction algorithm in [3] in a "modularized" manner for the ease of add/removing constraints on the reconstruction problem. We will focus on a few typical senarios in a sparse reconstruction problem. The code will be user-friendly, efficient, and robust. Your implementation will allow the package to be easily expandable by other contributors, so the code must be as readable as possible. The package will be made public at the LCAV Github page. Hence, a very important aspect is to write excellent documentations. See [4] for the expected outcome from a previous projection in a similar setup. References: [1] https://github.com/hanjiepan/FRI_pkg [2] https://github.com/LCAV/FRIDA [3] H. Pan, T. Blu and M. Vetterli. Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy, in IEEE Transactions on Signal Processing, vol. 65, num. 4, p. 821-835, 2017. [4] http://linvpy.readthedocs.io/ Prerequisites: Fluency in Python, strong background in linear algebra Type of work: 30% design, 70% development LCAV201709071