This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

Random matrices now play a role in many areas of theoretical, applied, and computational
mathematics. Therefore, it is desirable to have tools for studying random matrices that are …

Recent research indicates that many convex optimization problems with random constraints
exhibit a phase transition as the number of constraints increases. For example, this …

As it becomes increasingly apparent that 4G will not be able to meet the emerging demands
of future mobile communication systems, the question what could make up a 5G system …

Dimension reduction is the process of embedding high-dimensional data into a lower
dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental …

We consider the problem of estimating an unknown but structured signal x 0 from its noisy
linear observations y= Ax 0+ z∈ ℝ m. To the structure of x 0 is associated a structure …

Consider the problem of estimating the mean of a Gaussian random vector when the mean
vector is assumed to be in a given convex set. The most natural solution is to take the …

We present a natural generalization of the recent low rank+ sparse matrix decomposition
and consider the decomposition of matrices into components of multiple scales. Such …

We study the question of extracting a sequence of functions from observing only the sum of
their convolutions, ie from. While convex optimization techniques are able to solve this joint …

We consider simultaneous blind deconvolution of r source signals from their noisy
superposition, a problem also referred to blind demixing and deconvolution. This signal …