On signal reconstruction in white noise using dictionaries
G. K. Golubev · Problems of Information Transmission · 2009
Assume that we observe a Gaussian vector Y = Xβ + σζ, where X is a known p × n matrix with p ≥ n, β ∈ ℝ n is an unknown vector, and ζ ∈ ℝ n is a standard Gaussian white noise. The problem is to reconstruct Xβ from observations Y, provided that β is a sparse vector.