A circuit design of a fiber endoscope is described that allows monitoring of hard-to-reach cavities and other partially transparent and/or reflective objects into which it is possible to pass a thin fiber bundle.
We describe a new method for the formation of optical ghost images, in which radiation in the object arm is detected by several detectors. The advantage of the proposed method is demonstrated, which is the smaller number of illumination patterns required for reconstructing the object image as compared to traditional schemes of ghost imaging. We propose variants of algorithms for measurement reduction to the form relevant to the imaging of the object of investigation, which are aimed at improvement of the performance of the computing component of the endoscope. The fiber-optic version of ghost imaging considered here is suitable for investigating hard-to-reach abdomens and organs of human organism, which permit the introduction of a thin fiber-optic bundle, thus extending its applicability as compared to traditional optic endoscopic methods.
We describe a new method for the formation of optical ghost images, in which radiation in the object arm is detected by several detectors. The advantage of the proposed method is demonstrated, which is the smaller number of illumination patterns required for reconstructing the object image as compared to traditional schemes of ghost imaging. We propose variants of algorithms for measurement reduction to the form relevant to the imaging of the object of investigation, which are aimed at improvement of the performance of the computing component of the endoscope. The fiber-optic version of ghost imaging considered here is suitable for investigating hard-to-reach abdomens and organs of human organism, which permit the introduction of a thin fiber-optic bundle, thus extending its applicability as compared to traditional optic endoscopic methods.
This article provides an overview of the fundamental research directions being pursued at the Faculty of Physics of Lomonosov Moscow State University under the guidance of Professor Yuri Petrovich Pyt’ev. These research directions can be categorized into three primary areas: methods of morphological analysis of images and signals, theory of computer-aided measuring systems, and methods related to the theory of possibilities and subjective mathematical modeling. The article elucidates the foundational ideas and concepts of these directions, contemplates alternative approaches to address similar challenges, and offers both model-based and application-driven examples utilizing the methods corresponding to these directions and their combinations.
We describe a new method for the formation of optical ghost images, in which radiation in the object arm is detected by several detectors. The advantage of the proposed method is demonstrated, which is the smaller number of illumination patterns required for reconstructing the object image as compared to traditional schemes of ghost imaging. We propose variants of algorithms for measurement reduction to the form relevant to the imaging of the object of investigation, which are aimed at improvement of the performance of the computing component of the endoscope. The fiber-optic version of ghost imaging considered here is suitable for investigating hard-to-reach abdomens and organs of human organism, which permit the introduction of a thin fiber-optic bundle, thus extending its applicability as compared to traditional optic endoscopic methods.
The importance of development of new methods for reconstruction of an object image given its sinogram and some additional information about the object stems from the possibility of artifact presence in the reconstructed image, or its insufficient sharpness when the used additional information does not hold. The problem of recovering artifact-free images of the studied object from tomography data is considered in the framework of the theory of computer-aided measuring systems. Methods for solving it are developed. They are based on narrowing the class of possible images using less artifact-inducing information. An example of such information is the natural condition of non-negativeness of the estimated brightnesses. The main problem that arises is the large dimensionality of the images, which prevents the use of direct algorithms. One proposed method is based on local approach, namely correction of the result of unfiltered backprojection by applying a locally (in the space of the output image) optimal linear transformation. Another method processes a sinogram directly, without using backprojection, using iterative implementation of the measurement reduction technique. Examples of use of the proposed methods for processing teeth sinograms are given.
We have applied the measurement reduction technique for the ghost imaging (GI) in fiber optics systems. Ghost images have been reconstructed by numerical simulation of the complete cycle of GI in the basic setup of a multimode fiber endoscope beginning from the propagation of randomly modulated light through a multimode fiber and ending by GI calculation using numerical methods of single-pixel visualization. We have used prior information on the investigated object to obtain high-quality reconstructed ghost images. It is shown that for the number of used patterns of illumination of the object that is much smaller than the number of pixels of the image being reconstructed, the object reconstruction error can be reduced despite the limitation imposed on the number of modes propagating through the optical fiber and forming incoherent radiation. For comparison, we have used several versions of the compressed sensing method and the traditional correlation method. It is demonstrated that the proposed version of the measurement reduction technique applied to multimode fibers shows comparable and often even better results than the traditional correlation method and the compressed sensing method.
Traditional quantum ghost imaging technique uses three-photon spontaneous parametric down-conversion for producing beams of entangled photons. Two main factors limiting the spatial resolution of ghost imaging techniques are the (usually small) angular range in which the phase-matching condition is satisfied and angular apertures of the optical elements. In this paper, we propose to use the spontaneous four-wave back-mixing process to obtain quantum ghost images due to its ability to weaken the requirements on the phase-matching condition. Thus, only angular apertures of the optical elements remain as the main limiting factor, in contrast to setups where three-photon processes are used. Therefore, the upper bound on spatial resolution is higher. As a result, an improvement in resolution can be expected, assuming that other factors remain the same. Two design options that provide these benefits are proposed.
The applications of the eigenbasis of a measurement interpretation model in the problem of reducing the measured video data to the form typical of measurements of the studied object by an ideal measuring device when the object is translated in the field of view of the video sensors are studied in this work. The methods for selecting the components in the eigenbasis are considered that allow to obtain an estimate of the studied object that has an error lower than that of the linear reduction of measurements by means of nonrandom distortion; the distortion is defined by the subspace of the values of the studied-object characteristic interesting to the researcher that does not influence the result. In addition, the variants for refining the position of the object for subsequent measurement reduction that correspond to different information about the object and the mathematical model of its motion are considered and studied.
The development of new methods for reconstruction of an object image given its sinogram and some additional information about the object is important due to the possibility of artifact presence in the reconstructed image or its insufficient sharpness when the used additional information does not hold. A new method for processing tomographic images based on combining an assumptions-free image of the object and a dummy estimate followed by projection onto the set of images of possible objects is proposed and developed for the case when this set is the non-negative cone. This additional information corresponds to the natural condition of non-negativeness of the estimated brightnesses. The proposed method with different used iterative solving method and its parameters is illustrated by examples of processing teeth sinograms.
We consider the effect of diffraction due to the finite width of pump radiation illuminating a nonlinear crystal, in which spontaneous parametric down-conversion (SPDC) occurs, on the spatial resolution of ghost images. We propose the required formal relations and the computational algorithm and perform numerical simulation with account for the influence of this distorting factor on the quality of ghost images.
Quantum ghost imaging with the possibility of dynamic control by adaptive optics techniques is considered. The quality of ghost images at the spatial modulation of the pump has been analyzed. The variants of its improvement that provide new possibilities for increasing the informativeness of studies with the detection of ghost images have been presented.
We analyze the influence of diffraction caused by finite width of the pumping in quantum ghost imaging on the spatial resolution of produced ghost images. Following the necessary formal relations, we propose an algorithm for modeling and perform computer modeling. New variants of ghost imaging setups with spatial modulation of pumping phase are proposed. Their advantages are shown, and estimates of imaging resolution are provided.
The applications of the eigenbasis of the measurement interpretation model to the problem of reducing measured video data to a form typical for the measurements of the research object by an ideal measuring sensor are studied. In this case, video data are reduced as they are received and not after the recording is finished, and a researcher can stop the measurement at any time. Two methods are considered to estimate the research object image that could be obtained by an ideal measuring sensor, with an error smaller than the linear reduction error, but with a nonrandom distortion determined by the subspace of values of the research object features of interest that do not influence the result. In the first method, the research object image is estimated by selecting the components in the eigenbasis of the measurement interpretation model so that the noise component variance does not exceed a specified value and in the second method, by selecting the components of the linear reduction result by testing the hypothesis of equality of components to zero, and replacing by zero the components for which the hypothesis is not rejected. In some cases, the second method results in stronger noise suppression with less distortion.
We investigate the possibilities of increasing the measurement accuracy and creating the least-damaging regime of object illumination by mathematical simulation of the process of generating paired images, that is, a ghost image and a regular image, using a new scheme with quantum biphoton generation. It is shown that diffraction and non-unit quantum efficiency of the sensors in traditional ghost imaging cause missing some information carried by the object arm photons. Forming an image of the studied object in the object arm and registering it makes it possible to weaken the influence of these factors on the measurement result when using the developed version of the method of measurement reduction to the form that is typical for measuring the transparency distribution of the object for processing a pair of obtained images.
Experiments on the study of light-sensitive objects or rapidly evolving objects often employ a small number of photons that interact with the object. This leads to poor quality of the reconstructed image of the object. In this situation, mathematical techniques for processing measurements must not only provide a minimum error, but also use all information available to the researcher about the object to further reduce this error. The source of information used together with the measurement results to construct an estimate of the distribution of the optical characteristics of the object can be a researcher’s ideas about the possible form of the distribution of the optical characteristics of the object and about possible noise. A version of the mathematical method of measuring reduction is considered. It allows one to use such information, which is simulated by the mathematical formalism of subjective modeling, and to verify the agreement of subjective information proposed by the researcher with measurement data.
We consider the influence on the quantum ghost imaging of diffraction and non-unit quantum efficiency of the sensors for an original variant of ghost imaging setup. It is shown that acquisition of an additional image of the research object in the object arm allows to weaken the influence of these factors even if the quantum image in the object arm is additionally affected by noise photons that have not interacted with the object. This is achieved by measurement data processing using measurement reduction method to estimate the transparency distribution of the research object. We also propose an original computationally inexpensive technique for processing a pair of images formed by the CCD arrays in the object arm and by the coincidence circuit, in which only the photocounts made by sensors that correspond to each other are accepted. It allows to improve the resolution over the limit posed by diffraction.
This paper considers an application of the mathematical formalism of subjective modeling to improve the quality of the interpretation of measurement data given incomplete and unreliable subjective information about the research object. It is shown that the mathematical formalism of subjective modeling allows the researcher to use measurement data to test the adequacy of a subjective model to a particular research objective, correct the subjective model, combine the observation data and the researcher’s subjective notions about the research object (in order to optimize their conclusions about its features), and check the information about the research object for the presence of misinformation. The results are illustrated by computational experiments.
