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

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