Preconditioned deconvolution method for high-resolution ghost imaging
Zhishen Tong, Zhentao Liu, Chenyu Hu, Jian Wang, Shensheng Han
Abstract
Ghost imaging (GI) can nonlocally image objects by exploiting the fluctuation characteristics of light fields, where the spatial resolution is determined by the normalized second-order correlation function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m1"> <mml:mrow> <mml:msup> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . However, the spatial shift-invariant property of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m2"> <mml:mrow> <mml:msup> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> is distorted when the number of samples is limited, which hinders the deconvolution methods from improving the spatial resolution of GI. In this paper, based on prior imaging systems, we propose a preconditioned deconvolution method to improve the imaging resolution of GI by refining the mutual coherence of a sampling matrix in GI. Our theoretical analysis shows that the preconditioned deconvolution method actually extends the deconvolution technique to GI and regresses into the classical deconvolution technique for the conventional imaging system. The imaging resolution of GI after preconditioning is restricted to the detection noise. Both simulation and experimental results show that the spatial resolution of the reconstructed image is obviously enhanced by using the preconditioned deconvolution method. In the experiment, 1.4-fold resolution enhancement over Rayleigh criterion is achieved via the preconditioned deconvolution. Our results extend the deconvolution technique that is only applicable to spatial shift-invariant imaging systems to all linear imaging systems, and will promote their applications in biological imaging and remote sensing for high-resolution imaging demands.