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This paper considers a natural error correcting problem with real valued input/output. We wish to recover an input vector f/spl isin/R/sup n/ from corrupted measurements y=Af+e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y? We prove that under suitable conditions(More)
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as(More)
Suppose we wish to recover a vector x 0 ∈ R m (e.g. a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is a n by m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To recover x 0 , we consider the solution x to the 1-regularization(More)
Suppose we are given a vector f in a class FsubeRopf<sup>N </sup>, e.g., a class of digital signals or digital images. How many linear measurements do we need to make about f to be able to recover f to within precision epsi in the Euclidean (lscr<sub>2</sub>) metric? This paper shows that if the objects of interest are sparse in a fixed basis or(More)
We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension n 4) and the Schrr odinger equation (in dimension n 3). Three other applications are discussed: local existence for a nonlinear wave equation; and Strichartz-type estimates for more general dispersive equations and for(More)
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the <i>matrix completion</i> problem, and comes up in a great number of applications, including the famous <i>Netflix Prize</i> and other similar questions in collaborative filtering. In general, accurate recovery of a matrix from(More)
Let G be a finite abelian group, and let f : G → C be a complex function on G. The uncertainty principle asserts that the support supp(f) := {x ∈ G : f (x) = 0} is related to the support of the Fourier transformˆf : G → C by the formula |supp(f)||supp(ˆ f)| ≥ |G| where |X| denotes the cardinality of X. In this note we show that when G is the cyclic group(More)