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We show here that for systems with “typical”/“random” Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a negligible residual. Starting with initial residual r ₀ = y , at the s -th stage it forms the “matched filter” Φ T _rs-1 , identifies all coordinates with amplitudes exceeding a specially chosen threshold, solves a least-squares problem using the selected coordinates, and subtracts the least-squares fit, producing a new residual. After a fixed number of stages (e.g., 10), it stops. In contrast to Orthogonal Matching Pursuit (OMP), many coefficients can enter the model at each stage in StOMP while only one enters per stage in OMP; and StOMP takes a fixed number of stages (e.g., 10), while OMP can take many (e.g., n ). 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Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit 论文

Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit · 相关技术

相关技术