Compressive Imaging has been an extensively researched area inoptical imaging, object tracking,satellite applications,etc. There are many signalrecovery methods and comparative analyses of different algorithms in the presence of Gaussian noise. However, certain applications such as optical imaging at low photon intensityhavecounts of discrete events, which cannot be modelled using a Gaussian noise model. Instead, anoise model that incorporates photon statistics is needed. Researchers haveworkedon the Poisson noise modeland a different compressive sensing reconstruction was found.In this thesis, weconsidered a more general scenario of Compressive Imaging using non-classical photon states as light sources. We assumed that the Compressive Imaging system that consists of digital micromirror device (DMD), lenses, and detectors are perfect so that all noises comes from photons. Fock states and squeezed light thatpossess non-Poissonian statistics plays animportant role in Quantum Imaging. The image reconstruction was performed using several common compressive sensing signal reconstruction algorithms assuming Gaussian noise. This thesis showedthe behavior of the root mean square error (RMSE)with respectto the signal-to-noise ratio (SNR)for different photon statistics. In particular, the study showedthat all the noises perform similarly for the different algorithms. Based on the performance results for the different light sources, this researchcan be helpful in designing ageneralized Compressive Sensing model incorporating the photon statistics thatareapplicable in the field of Quantum Optics.
Compressive Imaging has been an extensively researched area inoptical imaging, object tracking,satellite applications,etc. There are many signalrecovery methods and comparative analyses of different algorithms in the presence of Gaussian noise. However, certain applications such as optical imaging at low photon intensityhavecounts of discrete events, which cannot be modelled using a Gaussian noise model. Instead, anoise model that incorporates photon statistics is needed. Researchers haveworkedon the Poisson noise modeland a different compressive sensing reconstruction was found.In this thesis, weconsidered a more general scenario of Compressive Imaging using non-classical photon states as light sources. We assumed that the Compressive Imaging system that consists of digital micromirror device (DMD), lenses, and detectors are perfect so that all noises comes from photons. Fock states and squeezed light thatpossess non-Poissonian statistics plays animportant role in Quantum Imaging. The image reconstruction was performed using several common compressive sensing signal reconstruction algorithms assuming Gaussian noise. This thesis showedthe behavior of the root mean square error (RMSE)with respectto the signal-to-noise ratio (SNR)for different photon statistics. In particular, the study showedthat all the noises perform similarly for the different algorithms. Based on the performance results for the different light sources, this researchcan be helpful in designing ageneralized Compressive Sensing model incorporating the photon statistics thatareapplicable in the field of Quantum Optics.
This work experimentally demonstrates that the imaging quality of quantum ghost imaging (GI) with entangled photons can be significantly improved by properly handling the errors caused by the imperfection of optical devices. We also consider compressive GI to reduce the number of measurements and thereby the data acquisition time. The image reconstruction is formulated as a sparse total least square problem which is solved with an iterative algorithm. Our experiments show that, compared with existing methods, the new method can achieve a significant performance gain in terms of mean square error and peak signal⁻noise ratio.
Correlated imaging offers great potentiality, with respect to standard imaging, to obtain the imaging of objects located in optically harsh or noisy environment. It can solve the problems which are difficult to solve by conventional imaging techniques. Recently, it has become one of the hot topics in quantum optics. In this paper, we propose a new scheme of correlated imaging with differential correlated imaging based on compressive sensing, named differential compressive correlated imaging. The new scheme takes advantage of the high signal-to-noise ratio of the differential correlated imaging and low-imaging sampling frequency of the compressed sensing technique. In the scheme, we utilize the intensity of the thermal light, which is in line with the Gaussian distribution, as the measurement matrix of compressive sensing. We extract the differential object information as the image object information which could be recovered via orthogonal matching pursuit algorithm with high quality. By numerical simulations, we verify the proposed scheme. Here, we select the two gray-scale images, such as double-slit and NUPT, as well as the two multi-grayscale images (Lena and Boats) as the object. We take sampling 350 times in differential compressive correlated imaging for measurement. The numerical simulation results show that for the above image objects, the average mean-square error (MSE) over 10 times for the differential compressive correlated imaging scheme is reduced by 97.7%, 93.9%, 92.5% and 71.4% respectively with respect to that of the differential correlated imaging scheme. Moreover, compared with the compressive ghost imaging, the MSE value of the same double-slit in CDGI, as well as Lena and Boats under the same conditions, is reduced by 50.4%, 72.9% and 66.8% separately, which indicates that the compressive differential correlated imaging scheme can greatly improve the signal-to-noise ratio of the imaging, and significantly reduce the imaging time.
Imaging is the estimation of the spatial distribution of a physical object by measuring the optical radiation it emits, or by making use of an optical wave that interacts with the object, via reflection or transmission, for example, before being measured by a detector. The resolution of an imaging system is limited by the inability to localize the optical field at points of the object. Under otherwise ideal conditions, resolution is limited by diffraction. The sensitivity of an imaging system is limited by the uncertainty in the measurement. Under ideal conditions, this is determined by photon noise, which depends on the statistical fluctuations of the light. In conventional imaging systems, an extended detector, such as a CCD camera or an array detector, measures the spatial distribution of the optical intensity, which is proportional to the photon flux density. In interferometric systems, the spatial distribution of the optical field is inferred from measurements of the optical intensity. With the emergence of coherence theory, imaging systems based on measurements of the second-order coherence function at pairs of points in the detection plane were developed. An example is the imaging of an incoherent object based on the van Cittert-Zernike theorem. Imaging systems based on measurement of intensity correlation, or the photon coincidence rate, at pairs of points, were developed in the 1960s. A classic example of the photon-correlation imaging of an object emitting thermal light is stellar imaging using a Hanbury-Brown-Twiss intensity-correlation interferometer. More recently, two-photon light, which may be generated via spontaneous parametric downconversion in a second-order nonlinear optical crystal, has been used for imaging. This type of two-photon (or biphoton) imaging, which has come to be called quantum imaging, is also based on the measurement of photon coincidence by the use of photon-counting array detectors or by scanning two photon-counting detectors at pairs of points. To compare the resolution and sensitivity of imaging systems based on the aforementioned types of measurements, it is necessary to derive expressions for the measured quantities in terms of the object distribution. The point-spread functions based on such expressions can be used to assess the resolution. One measure of the sensitivity of the imaging process is the signal-to-noise ratio (SNR) of the measured variables. The statistical nature of the light source must be known in order to determine the SNR. The purpose of this chapter is to compare the resolution and sensitivity of photon-correlation imaging systems that make use of thermal light and two-photon light. We will henceforth refer to these two imaging modalities as classical and quantum photon-correlation imaging, or simply classical and quantum imaging, respectively. Clearly, light in other quantum states can also be used for imaging.
Nonlocal point-to-point correlations between two photons have been used to produce ``ghost'' images without placing the camera towards the object. Here we theoretically demonstrate and analyze the advantage of non-Gaussian quantum light in improving the image quality of a ghost imaging system over a traditional Gaussian light source. For any squeezing degree, the signal-to-noise ratio (SNR) of the ghost image can be enhanced by the non-Gaussian operations of photon addition and subtraction on a two-mode squeezed light source. We find striking evidence that using non-Gaussian coherent operations, the SNR can be promoted to a high level even within the extremely weak squeezing regime. The resulting insight provides experimental recipes of quantum imaging using non-Gaussian light for illumination.
Compressive sensing utilizes sparsity to realize efficient image reconstruction. It is a valuable processing technique when cost, power, technology or computational overhead are limited or high. In the quantum domain technology usually limits efficient acquisition of weak or fragile signals. I will discuss the basics of information theory, compression, and compressive sensing. I will then discuss our recent work in compressive sensing. The topics of discussion include low-flux laser Radar, photonic phase transitions, high resolution biphoton ghost imaging, Ghost object tracking, 3D object tracking and high dimensional entanglement characterization. I will touch lightly on our current work of rapid wavefunction reconstruction and wavefront sensing. As an example (shown below), we were able efficiently and rapidly reconstruct high dimensional joint probability functions of biphotons in momentum and position. With conventional raster scanning this process would take approximately a year, but using double-pixel compressive sensing, the pictures were acquired in a few hours with modest flux.