Iteratively reweighted least squares minimization for sparse recovery

• Published in: Communications on pure and applied mathematics Vol. 63; no. 1; pp. 1 - 38
• Main Authors: Daubechies, Ingrid, DeVore, Ronald, Fornasier, Massimo, Güntürk, C. Si̇nan
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.01.2010; Wiley; John Wiley and Sons, Limited
• Subjects: Calculus of variations and optimal control; Convergence; Exact sciences and technology; Linear programming; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Optimization algorithms; Sciences and techniques of general use; Vector space; Least squares method; Optimization method; Linear programming; Iteration; Fast algorithm; Hyperplane; Method study

Under certain conditions (known as the restricted isometry property, or RIP) on the m × N matrix Φ (where m < N), vectors x ∈ ℝN that are sparse (i.e., have most of their entries equal to 0) can be recovered exactly from y := Φx even though Φ−1(y) is typically an (N − m)—dimensional hyperplane; i...