67 research outputs found
Convex recovery of a structured signal from independent random linear measurements
This chapter develops a theoretical analysis of the convex programming method
for recovering a structured signal from independent random linear measurements.
This technique delivers bounds for the sampling complexity that are similar
with recent results for standard Gaussian measurements, but the argument
applies to a much wider class of measurement ensembles. To demonstrate the
power of this approach, the paper presents a short analysis of phase retrieval
by trace-norm minimization. The key technical tool is a framework, due to
Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance."
v2: minor corrections. v3: updated citations and increased emphasis on
Mendelson's contribution
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