Preconditioned Ghost Imaging Via Sparsity Constraint

Ghost imaging via sparsity constraint (GISC) can recover objects from the intensity fluctuation of light fields at a sampling rate far below the Nyquist rate. However, its imaging quality may degrade severely when the coherence of sampling matrices is large. To deal with this issue, we propose an efficient recovery algorithm for GISC called the preconditioned multiple orthogonal least squares (PmOLS). Our algorithm consists of two major parts: i) the pseudo-inverse preconditioning (PIP) method refining the coherence of sampling matrices and ii) the multiple orthogonal least squares (mOLS) algorithm recovering the objects. Theoretical analysis shows that PmOLS recovers any $n$-dimensional $K$-sparse signal from $m$ random linear samples of the signal with probability exceeding $1 - 3 n^2 e^{ - c m / K^2 }. $ Simulations and experiments demonstrate that PmOLS has competitive imaging quality compared to the state-of-the-art approaches.