This software package contains a collection of tools for implementing fast alorithms for working with the Slepian basis, also known as discrete prolate spheroidal sequences. For more information, see "The Fast Slepian Transform," by S. Karnik, Z. Zhu, M. B. Wakin, J. Romberg, and M. A. Davenport.
The code can be downloaded here; see the included readme file for a detailed description of the contents and for usage instructions.
This software package contains a collection of functions that can be useful in modeling event-based data as Hawkes processes. For more information, see "Analysis of wireless networks using Hawkes processes," and "A Hawkes' eye view of network information flow" by M. G. Moore and M. A. Davenport.
The code can be downloaded here; see the included readme file for a detailed description of the contents and for usage instructions.
This software package contains code that can be used to select an optimal set of measurements for sensing a sparse vector in the constrained setting. For further details, see the paper "Constrained adaptive sensing," by M. A. Davenport, A. K. Massimino, D. Needell, and T. Woolf.
The code can be downloaded here; see the included readme file for a detailed description of the contents and for usage instructions.
This software package contains code used to simulate an idealized TOFMS system with random pulse times. For further details, see the paper "Randomized Multi-Pulse Time-of-Flight Mass Spectrometry," by M. G. Moore, A. K. Massimino, and M. A. Davenport.
The code can be downloaded here; see the included readme file for a detailed description of the contents and for usage instructions.
This software package implements a penalized maximum-likelihood optimization approach to the problem of matrix completion for the extreme case of noisy 1-bit observations, where instead of observing a subset of the real-valued entries of a matrix M, we obtain a small number of binary (1-bit) measurements generated according to a probability distribution determined by the real-valued entries of M. For further details, see the paper "1-Bit Matrix Completion," by M.A. Davenport, Y. Plan, E. van den Berg, and M. Wootters.
The code can be downloaded here; the Matlab file entitled "demo.m" provides an example of how to use the software package. Please e-mail mdav-at-gatech-dot-edu if you find any bugs or have any questions.
The bulk of the Compressive sensing (CS) literature has focused on the case where the acquired signal has a sparse or compressible representation in an orthonormal basis. In practice, however, there are many signals that cannot be sparsely represented or approximated using an orthonormal basis, but that do have sparse representations in a redundant dictionary. Standard results in CS can sometimes be extended to handle this case provided that the dictionary is sufficiently incoherent or well-conditioned, but these approaches fail to address the case of a truly redundant or overcomplete dictionary.
This software package implements a variant of the iterative reconstruction algorithm CoSaMP for this more challenging setting. In contrast to prior approaches, the method is "signal-focused"; that is, it is oriented around recovering the signal rather than its dictionary coefficients.
For further details, see the paper "Signal Space CoSaMP for Sparse Recovery with Redundant Dictionaries," by M.A. Davenport, D. Needell, and M.B. Wakin.
Signal Space CoSaMP can be downloaded here; the Matlab files entitled "demo_*.m" provide several examples of how to invoke Signal Space CoSaMP and compare the results to traditional CS algorithms. The Matlab data (.mat) files necessary to reproduce the figures presented in the paper can be downloaded here. Please e-mail mdav-at-gatech-dot-edu if you find any bugs or have any questions.
Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal.
This software package provides a set of tools for bridging this gap through the use of Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that offers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework.
For further details, see the paper "Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences," by M.A. Davenport and M.B. Wakin.
DART contains all of the software necessary to reproduce the results presented in this paper. It can be downloaded here. Please e-mail mdav-at-gatech-dot-edu if you find any bugs or have any questions.