Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

Generalized linear models (GLMs) are used in high-dimensional machine learning,
statistics, communications, and signal processing. In this paper we analyze GLMs when the …

Is compressive sensing overrated? Or can it live up to our expectations? What will come
after compressive sensing and sparsity? And what has Galileo Galilei got to do with it …

A popular approach for estimating an unknown signal x 0∈ ℝ n from noisy, linear
measurements y= Ax 0+ z∈ ℝ m is via solving a so called regularized M-estimator: x̂:= arg …

When recovering a sparse signal from noisy compressive linear measurements, the
distribution of the signal's non-zero coefficients can have a profound effect on recovery …

Non-smooth regularized convex optimization procedures have emerged as a powerful tool
to recover structured signals (sparse, low-rank, etc.) from (possibly compressed) noisy linear …

Compressed sensing is a signal processing method that acquires data directly in a
compressed form. This allows one to make fewer measurements than were considered …

Compressed sensing has triggered a major evolution in signal acquisition. It consists of
sampling a sparse signal at low rate and later using computational power for the exact …

We consider linear regression in the high-dimensional regime where the number of
observations is smaller than the number of parameters. A very successful approach in this …

We characterize the measurement complexity of compressed sensing of signals drawn from
a known prior distribution, even when the support of the prior is the entire space (rather than …