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Code L1-MAGIC is a collection of MATLAB routines for solving
the convex optimization programs central to compressive sampling. The
algorithms are based on standard interior-point methods, and are suitable
for large-scale problems. Download the User's Guide (pdf) top Papers A nonlinear sampling theorem The central result from this paper is that a sparse
vector can be recovered Fourier domain observations. More precisely, let f be a length-N discrete signal which has B nonzero components (we stress that the number and locations of the components are unknown a priori). We collect samples at K different frequencies which are randomly selected. Then for K on the order of B log N, we can recover f perfectly (with very high probability) through l1 minimization. Download
(pdf)
Near-optimal signal recovery and the Uniform Uncertainty
Principle
This paper derives precise conditions for when an
arbitrary sparse signal f can be recovered from a Download (pdf)
Stability This paper demonstrates that the recovery procedure
is stable. Given that the measurement matrix Download (pdf)
Statistical Estimation When the errors made in the measurement process are
Gaussian, much more can be said about the precision Download (pdf)
Linear Decoding This paper demonstrates that in addition to recovering
sparse signals, l1 minimization can be used to detect Download (pdf)
Finding Sparse Decompositions This paper revisits the now classical application
of l1 minimization to finding sparse representations in unions Download (pdf) top David Donoho's publications, including work on Compressed Sensing and Sparse Recovery (with Jared Tanner) The Rice University DSP group's Compressed Sensing resources page; see in particular the very recent work on building a CS camera Robert Nowak and Jarvis Haupt's paper on Signal Reconstruction from Noisy Random Projections. Terence Tao's summary of the current state of compressive sampling theory Joel Tropp's web page at the California Institute of Technology, see in particular his work on reconstruction using greedy algorithms (with Anna Gilbert). Martin Strauss and Anna Gilbert, at the University of Michigan, and their papers on fast algorithms for estimating sparse Fourier transforms Martin Vetterli and Irena Maravic's work on sampling signals with "finite rate of innovation" David Brady's Duke Integrated Sensing and Processing page top |