Compressive ghost imaging

Abstract

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...

Single-pixel digital ghost holography

“…This hybrid digital-optical scheme enables three-dimensional sectioning while simply using a point detector [12]. The computation comes at the expense of storing and processing thousands of speckle patterns to achieve an image with a suitable signal-to-noise ratio (SNR), a problem that can be partly alleviated by using compressive sensing algorithms [22].…”

Single-pixel imaging by means of Fourier spectrum acquisition

“…Later single-pixel imaging techniques that use a classical light source to exploit Helmholtz reciprocity 3 have been proposed. These techniques include GI [4][5][6][7] , computational imaging [8][9][10][11] and dual photography 1,12,13 . These single-pixel techniques can potentially capture a scene with indirect measurement where detectors sample the indirect light only.…”

Compressive microscopic imaging with “positive–negative” light modulation

“…However, we think that the only difference between single-pixel compressive imaging [20] and computational GI [15] was that the spatial modulator was placed behind the object instead of in front. Furthermore, the GI community has already employed CS to obtain compressed ghost images (see in [22,23,25,26], Opt. Lett.…”

“…For example, in Hadamard-multiplexed illumination, about half of the light sources operate simultaneously, creating brighter, clearer captured images. In fact, the mathematical models of single-pixel compressive imaging, computational GI or multiplexed illumination are the same [22], only with the change of reconstruction algorithms, which will in turn result in the difference of the number of measurements. Although GI, single-pixel compressive imaging and multiplexed illumination were historically independent and developed in parallel with each other, these techniques promise a resource-efficient alternative to array detectors, permitting us to reduce operational problems involved in systems based on raster scanning.…”

“…The application of CS in the field of imaging allows one to retrieve high resolution images from many fewer measurements than those established by the Nyquist-Shannon criterion. Recently, the GI community has employed CS to obtain compressed ghost images [22], greatly reducing both the acquisition time and the number of frames required. These improvements have motivated an ongoing effort to implement technologies based on GI such as multispectral imaging [23], optical encryption [24,25], and most recently, adaptive compressive GI [26].…”