We describe an advanced image reconstruction algorithm for pseudothermal ghost imaging, reducing the number of measurements required for image recovery by an order of magnitude. The algorithm is based on compressed sensing, a technique that enables the reconstruction of an N -pixel image from much less than N measurements. We demonstrate the algorithm using experimental data from a pseudothermal ghost-imaging setup. The algorithm can be applied to data taken from past pseudothermal ghost-imaging experiments, improving the reconstruction's quality.Ghost imaging (GI) has emerged a decade ago as an imaging technique which exploits the quantum nature of light, and has been in the focus of many studies since [1, and references therin]. In GI an object is imaged even though the light which illuminates it is collected by a single-pixel detector which has no spatial resolution (a bucket detector). This is done by correlating the intensities measured by the bucket detector with an image of the eld which impinges upon the object. GI was originally performed using entangled photon pairs [2], and later on was realized with classical light sources [3,4,5,6]. The demonstrations of GI with classical light sources, and especially pseudothermal sources, triggered an ongoing e ort to implement GI for various sensing applications [4,7]. However, one of the main drawbacks of pseudothermal GI is the long acquisition times required for reconstructing images with a good signal-to-noise ratio (SNR) [1,8].In this work we propose an advanced reconstruction algorithm for pseudothermal GI, which reduces signicantly the required acquisition times. The algorithm is based on compressed sensing (or compressive sampling, CS) [9,10], an advanced sampling and reconstruction technique which has been recently implemented in several elds of imaging. Examples for such are magnetic resonance imaging [11], astronomy [12], THz imaging [13], and single-pixel cameras [14]. The main idea behind CS is to exploit the redundancy in the structure of most natural signals/objects to reduce the number of measurements required for faithful reconstruction. Here we show that applying a CS-based reconstruction algorithm to data taken from conventional pseudothermal GI measurements dramatically improves the SNR of the reconstructed images and thus allows for shorter acquisition times.In conventional pseudothermal GI, an object is illuminated by a speckle eld generated by passing a laser beam through a rotating di user [ Fig. 1(a)]. For each phase realization r of the di user, the speckle eld I r (x, y) which impinges on the object is imaged. This is done by splitting the beam before the object to an 'object arm' and a 'reference arm', and placing a CCD camera at the refer- * Electronic address: ori.katz@weizmann.ac.il Figure 1: (Color online) (a) Standard pseudothermal GI twodetectors setup. A copy of the speckle eld which impinges on the object is imaged with a CCD camera, and correlated with the intensity measured by a bucket detector. (b) The computational GI singl...