Preconditioned Multiple Orthogonal Least Squares and Applications in Ghost Imaging via Sparsity Constraint

Abstract

Ghost imaging via sparsity constraint (GISC) can recover objects from the intensity fluctuation of light fields even when the sampling rate is far below the Nyquist sampling rate. In this paper, we develop an efficient algorithm called the preconditioned multiple orthogonal least squares (PmOLS) for solving the GISC reconstruction problem. Our analysis shows that the PmOLS algorithm perfectly recovers any $n$-dimensional $K$-sparse signal from $m$ random linear samples of the signal with probability exceeding $1-3n^2{e}^{-cm/K^2}$. Simulations and experiments demonstrate that the proposed algorithm has very competitive imaging quality compared to the state-ofthe-art methods.

arXiv comment17 pages

References in corpus (8)

• Compressive ghost imaging
• Ghost imaging with a single detector
• Generalized Orthogonal Matching Pursuit
• Incoherent Coincidence Imaging and Its Applicability in X-ray Diffraction
• Nearly Optimal Bounds for Orthogonal Least Squares
• The effect of spatial transverse coherence property of a thermal source on Ghost imaging and Ghost imaging via compressive sampling
• Perturbation Analysis of Orthogonal Matching Pursuit
• The Generalized Wielandt Inequality in Inner Product Spaces