Abstract:
A method and system for imaging information comprising at least one processor for processing information; a light source for illuminating first and second locations; a spatial receiver located at the second location for receiving the illuminating light comprising an array of pixel locations for detecting high resolution spatial information concerning the illuminating light; the spatial receiver being operatively connected, to the at least one processor and operating to transmit high resolution spatial information correlated to specific intervals of time to the processor; the at least one receiver operatively connected to the processor(s) and operative to receive light reflected from a subject and operating to transmit low resolution spatial information to the processor correlated to specific intervals of time; the processor operating to correlate a response by the at least one receiver with spatial information derived from the spatial receiver at correlating time intervals to create a high resolution image.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation-In-part application of application Ser. No. 13/247,470 entitled “System and Method for Image Enhancement” (ARL 11-03) by R. Meyers &amp; K. Deacon, filed Sep. 28, 2011, and application Ser. No. 13/198,133 entitled “Method and System for Non-line-of-sight Imaging” (ARL 10-31) filed Aug. 4, 2011, and issued on Feb. 12, 2013 as U.S. Pat. No. 8,373,107, which in turn claims priority of U.S. patent application Ser. No. 12/819,602 entitled “Method and System for LIDAR Utilizing Quantum Properties,” filed Jun. 21, 2010 (ARL 09-35) and issued on Aug. 14, 2012 as U.S. Pat. No. 8,242,428, which in turn claims priority of U.S. application Ser. No. 12/330,401 (U.S. Pat. No. 7,812,303) (ARL07-33) entitled “Method and System for Creating an Image Using Quantum Properties of Light Based Upon Spatial Information From a Second Light Beam Which Does not Illuminate the Subject,” filed Dec. 8, 2008, which claims priority to U.S. Provisional Patent Application Ser. No. 60/993,792 filed Dec. 6, 2007. The present application, through U.S. patent application Ser. No. 13/198,133 (ARL 10-31) entitled “Method and System for Non-line-of-sight Imaging” and U.S. application Ser. No. 12/819,602 (ARL 09-35), entitled “Method and System for LIDAR Utilizing Quantum Properties,” filed Jun. 21, 2010, also claims priority of U.S. patent application Ser. No. 12/343,384 filed Dec. 23, 2008, entitled “Method and System for Quantum Imaging Using Entangled Photons Pairs,” now U.S. Pat. No. 7,847,234, issued Dec. 7, 2010 (ALR 09-15). The present application through application Ser. No. 13/198,133 claims the benefit of U.S. application Ser. No. 12/837,668 (ARL 07-33D) entitled “Method and System for Creating an Image Using the Quantum Properties of Sound or Quantum Particles, filed Jul. 16, 2010, now U.S. Pat. No. 8,053,715, which is a divisional application of U.S. Pat. No. 7,812,303. All of the patent applications and patents mentioned in this paragraph are hereby incorporated by reference. 
    
    
     STATEMENT OF GOVERNMENT INTEREST 
     The embodiments herein may be manufactured, used, and/or licensed by or for the United States Government without the payment of royalties thereon. 
    
    
     BACKGROUND OF THE INVENTION 
     Image processing is a form of signal processing for which the input is an image, such as, for example, a photograph or video frame, and the output is either an image (or series of images) or a set of characteristics or parameters related to the image (or series of images). Forms of image processing include, for example, face detection, feature detection, medical image processing, computer vision (extraction of information from an image by a computer), microscope image processing, etc. 
     Image resolution relates to the detail that an image possesses. For satellite images, the resolution generally correlates to the area represented by each pixel. Generally speaking, an image is considered to be more accurate and detailed as the area represented by each pixel is decreased. As used herein, the term images include digital or analog images, film images, and/or other types of images. When an image is captured by a monochrome camera, a single charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS) sensor is used to form an image via the light intensity projected onto the sensor. Cameras taking pictures from great distances, such as aerial photos, may not obtain detailed information about the subject matter. Also, the taking of photographs may be subject to motion of the camera and/or jitter. Consequently, subtle or detail information are not present in the images. 
     Quantum imaging is a relatively new science that is developing new technology such as Quantum Ghost Imaging (QGI) to exploit quantum optical information. The imaging is adaptable to adverse imaging situations and there is a benefit to exploiting quantum optical information to image objects through partially obscuring media, i.e., optical turbulence, obstructions, smoke, and fog. Imaging through obscuring media is difficult; such as the difficulty of driving in foggy weather. 
     Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more quantum particles are linked together such that the quantum state of one quantum particle appears to interact with its counterpart; even though the individual quantum particles may be spatially separated. This apparent interconnection leads to correlations between observable physical properties of remote systems, since the interaction of the remote system with quantum state of one of a pair can be observed though observation of the counterpart. For example, according to quantum mechanics, the spin of a quantum particle is indeterminate until such time as some physical intervention is made to measure the spin; which, in general, could equally be spin-up or spin-down. However, when two members of a spin entangled pair are measured, they will either be correlated or anti-correlated using spin measurements, regardless of the distance between the two particles. It is normally taught in quantum theory that no hidden variable theory can account for these results of quantum mechanics. The statistics of multiple measurements must generally relate to an inequality (called Bell&#39;s inequality), which is violated both by quantum mechanical theory and experimental results. 
     The non-classical two-photon interaction or quantum entanglement was described by Albert Einstein et al. (Einstein, Podolsky, Rosen (hereinafter Einstein, et al.) paradox), “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Physical Review, Volume 47, May 15, 1935, pgs. 777-800 The paradox of quantum entanglement, as described therein, relates to the concept that as a result of the process of measurement of a first system, using quantum mechanics, two different physical quantities are obtainable in the second system, despite the fact that at the time of the measurements, the two systems no longer interact and the second system is not disturbed in any way by the first. Einstein, et al, were unable to reconcile this quantum mechanical description of reality with the so-called classical physics determination that no “real” change can take place in the second system as a consequence of anything that may be done to the first system after the two systems no longer interact. 
     The theoretical work reported by Klyshko in “Combined EPR and Two-Slit Experiments: Interference of Advanced Waves”, Physics Letters A, Volume 132, number 6.7, pp. 299-304 (1988) see also, Soy. Phys. Usp. 31, 74 suggested a non-classical two-photon interaction could exist. 
     The first two-photon imaging experiment was reported by Pittman et al., in “Optical Imaging by Means of Two-photon Quantum Entanglement,” Physical Review, A, Vol. 52, No. 5, November 1995. According to the Pittman article, a two-photon optical imaging experiment was performed to test the two-particle entanglement as described by Albert Einstein et al., referenced above, to determine if there was a correlation in position and in momentum for an entangled two-photon system; using “test beam or path” and “reference beam or path” photon pairs. Specifically, an aperture placed in front of a fixed detector was illuminated by a signal beam through a convex lens. A sharp magnified image of the aperture was found in the coincidence counting rate when a mobile detector was scanned in the transverse plane of the reference beam at a specific distance in relation to the lens. The experiment was named “ghost imaging” due to its surprising nonlocal feature. 
     Additional experiments are reported in Pittman, et al. “Optical Imaging by Means of Two-Photon Entanglement,” Phys. Rev. A, Rapid Comm., Vol. 52, R3429 (1995) and ghost interference by Strekalov, et al, “Observation of Two-Photon ‘Ghost’ Interference and Diffraction,” Phys. Rev. Lett., Vol. 74, 3600 (1995), which together stimulated the foundation of quantum imaging in terms of multi-photon geometrical and physical optics. 
     The above publications are merely examples of the development and attempt to understand the science of quantum mechanics as it relates to photons. The present invention in effect uses similar principles and extensions thereof relating to quantum interactions. 
     SUMMARY OF THE INVENTION 
     An embodiment of the present invention enhances or increases the image quality of an object or scene as “seen” or recorded by a detector. When a low quality detector is aimed at an object, a high quality image is generated using the quantum properties of light. A low quality detector picks up quantum information on the object shape and its temporal relations to reference fields acting as a collection of bucket detectors that do not individually contain spatial information. The reference fields are recorded by a high resolution imager (CCD, camera, etc.) that images the source of light that illuminates the target object. 
     Current imaging methods are limited to the quality of the detector looking at the object being imaged. A preferred embodiment generates an improved quality image of the object without the object being imaged in high resolution directly. The preferred method may be used in connection with photographs taken during turbulent conditions. The current invention may be further directed towards overcoming a limitation that exists in current quantum ghost imaging embodiments wherein there exists a lack of a means to accurately direct the bucket detector or detectors to receive photons from a distant subject. 
     A preferred methodology comprises the following steps not necessarily in sequential order: providing a series of low resolution frames of a given region of interest and a series of high resolution images of a light source; determining the value of each pixel at each location within each high resolution frame and within each low resolution frame to form first and second arrays, respectively, of pixel values; determining the product of the first array of pixel values and the second array of pixel values; determining the sum of the products by adding together the products of first array of pixel values and second array of pixel values for a series of frames; determining the average of the sum of products by dividing the sum of products by the number of frames in the series of frames to form an average high resolution frame times low resolution pixel product; determining the average value of each pixel at each pixel location for the series of high resolution frames to form a third array of average pixel values; determining the average values at each pixel location for the series of low resolution frames to form a fourth array; and, for each pixel location in the low resolution frame:
         determining a fifth array of products of the low resolution pixel location times each pixel in each high resolution image for the series of frames;   summing the third arrays for the series of frames and dividing by the number of frames in the series to form a sixth array comprising the average product of the low resolution pixel location times the high resolution frames;   determining the product of the third array times the value at the low resolution pixel location of the fourth array to form a seventh array;   determining an intermediate image for the pixel location in the low resolution frame by subtracting the seventh array from the sixth array to form an eighth array;
 
summing together the eighth arrays to provide a final composite high resolution image.
       

     A preferred embodiment is directed to a system of enhancing low resolution images by using high resolution images of the illuminating source that illuminates the low resolution images comprising: at least one processor; a high resolution spatial detector; an array of pixel locations; a light source which emits entangled photons pairs, the first photons of the photon pairs being reflected off a target to into an array of pixel locations to create a series of low resolution images; the second photons of the photon pairs being inputted into a high resolution spatial detector; the second photons not being reflected from or passing through the target; coincidence circuitry that transmits the measurements from the array of pixel locations and the high resolution spatial detector to the at least one processor at specific instances in time; whereby the at least one processor enhances the low resolution images recorded at the array of pixel locations using the first photons by combining the low resolution measurements with the high resolution measurements detected by the high resolution spatial detector using the second photons. 
     These and other aspects of the embodiments herein will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following descriptions, while indicating preferred embodiments and numerous specific details thereof, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the embodiments herein without departing from the spirit thereof, and the embodiments herein include all such modifications. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention can be better understood when reading the following detailed description with reference to the accompanying drawings, which are incorporated in and form a part of the specification, illustrate alternate embodiments of the present invention, and together with the description, serve to explain the principles of the invention. In the drawings: 
         FIG. 1  is an illustration a flow chart for performing a preferred method of practicing the present invention. 
         FIG. 2  is a partial schematic block diagram illustration of the steps for performing a preferred method of the present invention. 
         FIG. 3  is a partial schematic block diagram illustration of the steps for performing a preferred method of the present invention. Taken together,  FIGS. 1 ,  2 , and  3  outline the steps of a preferred methodology for the present invention. 
         FIG. 4  is schematic system block diagram of a preferred embodiment according to the principles of the present invention comprising, inter alia, a thermalizing element  17 . 
         FIG. 5  is a conceptual diagram of a preferred embodiment of the present invention, such as for example, that shown in  FIG. 4 . 
         FIG. 6  is a conceptual diagram of a preferred embodiment of the present invention, showing, inter alia, the summation of intermediate G (2)  images. 
         FIG. 7A  is an illustration of an image constructed using a bucket that consisted of all of the pixels of a simulated low-resolution multiple photo-sensor bucket array as the bucket measurement. 
         FIG. 7B  an illustration of an intermediate image constructed using a single bucket consisting of 2×2 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 8A  is an illustration of an intermediate image constructed using a single bucket consisting of 2×2 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 8B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets consisting of 2×2 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 9A  is an illustration of an average image measured by a multiple photo-sensor bucket array. 
         FIG. 9B  is an illustration of an average image measured by a low-resolution multiple photo-sensor bucket array simulated by 2×2 pixel spatial averaging. 
         FIG. 10A  is an illustration of an intermediate image constructed using a single bucket consisting of 4×4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 10B  is an illustration of an intermediate image constructed using a single bucket consisting of 4×4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 11A  is an illustration of an average image measured by a low-resolution multiple photo-sensor bucket array simulated by 4×4 pixel spatial averaging. 
         FIG. 11B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets consisting of 4×4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 12A  is an illustration of an intermediate image constructed using a single bucket consisting of 8×8 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 12B  is an illustration of an intermediate image constructed using a single bucket consisting of 8×8 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 13A  is an illustration of an average image measured by a low-resolution multiple photo-sensor bucket array simulated by 8×8 pixel spatial averaging. 
         FIG. 13B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets consisting of 8×8 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 14A  is an illustration of an intermediate image constructed using a single bucket consisting of 8×8 with overlap of 4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 14B  is an illustration of an intermediate image constructed using a single bucket consisting of 8×8 with overlap of 4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 15A  is an illustration of an average image measured by a low-resolution multiple photo-sensor bucket array simulated by 8×8 with overlap of 4 pixel spatial averaging. 
         FIG. 15B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets consisting of 8×8 overlap of 4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
         FIG. 16A  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 1 randomly spatially located pixel for 1400 shots. 
         FIG. 16B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 2 randomly spatially located pixels for 1400 shots. 
         FIG. 17A  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 2 randomly spatially located pixels for 500 shots. 
         FIG. 17B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 1000 randomly spatially located pixels for 10 shots. 
         FIG. 18A  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket, array that consisted of 20 randomly spatially located pixels for 150 shots. 
         FIG. 18B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 100 randomly spatially located pixels for 150 shots. 
         FIG. 19A  is an illustration of the final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 10 randomly spatially located pixels for 150 shots. 
         FIG. 19B  is an illustration of the final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 1000 randomly spatially located pixels for 150 shots. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The embodiments herein and the various features and advantageous details thereof are explained more fully with reference to the non-limiting embodiments that are illustrated in the accompanying drawings and detailed in the following description. Descriptions of well-known components and processing techniques are omitted so as to not unnecessarily obscure the embodiments herein. The examples used herein are intended merely to facilitate an understanding of ways in which the embodiments herein may be practiced and to further enable those of skill in the art to practice the embodiments herein. Accordingly, the examples should not be construed as limiting the scope of the embodiments herein. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the full scope of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     It will be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present. 
     It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. For example, when referring first and second photons in a photon pair, these terms are only used to distinguish one element, component, region, layer or section from another region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present invention. 
     Furthermore, relative terms, such as “lower” or “bottom” and “upper” or “top,” may be used herein to describe one element&#39;s relationship to other elements as illustrated in the Figures. It will be understood that relative terms are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. For example, if the device in the Figures is turned over, elements described as being on the “lower” side of other elements would then be oriented on “upper” sides of the other elements. The exemplary term “lower”, can therefore, encompass both an orientation of “lower” and “upper,” depending of the particular orientation of the figure. Similarly, if the device in one of the figures is turned over, elements described as “below” or “beneath” other elements would then be oriented “above” the other elements. The exemplary terms “below” or “beneath” can, therefore, encompass both an orientation of above and below. Furthermore, the term “outer” may be used to refer to a surface and/or layer that is farthest away from a substrate. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     It will also be appreciated by those of skill in the art that references to a structure or feature that is disposed “adjacent” another feature may have portions that overlap or underlie the adjacent feature. 
     A preferred embodiment system for image enhancement comprises at least one processor and at least one memory operatively associated with the at least one processor. As illustrated in  FIG. 1 , a preferred methodology for resolution improvement performed by the at least one processor comprises the following steps not necessarily in the order recited:
         A. Collect a set of N high resolution measurements of the illuminating source I(t) and low resolution measurements of the target object P(t).   B. Compute for each pixel or grouping of pixels in the low resolution set of measurements the product of the low resolution pixel with the measured illumination pixels I(t)*P i,j (t) individually for each i,j.   C. Obtain a sum of the I(t)*P i,j (t) individually for each i,j over the ensemble of measurements.   D. Divide the set of summed products by the number of measurements N to obtain &lt;I(t)*P i,j (t)&gt; where &lt; &gt; denotes the average over the ensemble of measurements.   E. Compute a sum of the ensemble of I(t) measurements and divide by the number of measurements N to obtain &lt;I(t)&gt;.   F. Compute for each low resolution pixel the sum of P i,j  over the ensemble of measurements N and divide by N to obtain &lt;P i,j &gt;.   G. Compute an intermediate G (2)  image for each i,j low resolution measurement using the following equation G i,j   (2) =&lt;I*P i,j &gt;−&lt;I&gt;&lt;P i,j .   H. Sum the intermediate G i,j   (2)  images into the final composite G (2)  image of the target object, Image final =ΣG i,j   (2)          

     Note that the steps in  FIG. 1  are comparable to the numbered boxes in  FIGS. 2 and 3 , as denoted by the reference to “Box _” correlating to the Box number of  FIGS. 2 and 3 . 
     Referring now to  FIG. 2 , in accordance with a preferred methodology, in Box  1  a series or collection of high resolution measurements (or frames) of the illuminating light source (which may be, for example, the sun) are inputted into the memory or input of a processor or image processor. As used herein the terminology “processor” or “image processor” as used in the following claims includes a computer, multiprocessor, CPU, minicomputer, microprocessor or any machine similar to a computer or processor which is capable of processing algorithms. 
     In Box  2 , using the input from Box  1 , the frame data or value of each pixel at each pixel location is determined for each frame. In Box  3 , the pixel values in the low resolution set of measurements P i,j  is determined. The low resolution frames may comprise photographs of the same region of interest. The region of interest may be a scene, landscape, an object, a subject, person, or thing. Where the low resolution source is a low resolution camera, the value of a pixel correlates to a “bucket value” determination and correlates to the light intensity measured by the detector. In the case of an electronic display formed by pixels, the intensity of each pixel value at each pixel location P i,j  is determined. At Box  4 , the values in Box  2  are multiplied by the values determined in Box  3 . Box  5  represents the Frame Data×P i,j  Product. Inasmuch as the Boxes  2  and  3  are arrays of pixel values, the Box  5  Product is also an array of values. At Box  6 , the products of Box  5  are repeatedly calculated for each frame in a selected plurality of frames and summed together. As an example, one hundred frames may be selected. At Box  7 , the summation Box  6  (Products for the determined in Box  6 ) is divided by the number of frames (such as for example one hundred) to determine the Frame Data×P ij  Products Average for the plurality of frames. The Product Average in Box  7  is an array containing pixel values at each pixel location within the frame. 
       FIG. 3  is a continuation of  FIG. 2  and is a further description of a preferred methodology of the present invention. Note that Box  7  is carried over from  FIG. 2  into FIG.  3 . In Box  8 , the average frame data (or average value of each pixel at each pixel location) is determined for the plurality of frames (e.g. 100) by averaging the pixel values at each pixel location for the plurality of frames to determine an array of average pixel values. In Box  9 A the sum of P ij  over time N for each pixel is determined. P ij  represents the pixel location within each frame of the low resolution images (or bucket detector values). Prior to Box  9 B, the result of Box  9 A is divided by N. In Box  9 B, the average P ij  for the plurality of low resolution frames is determined. This correlates to the average of the light intensity of each pixel at each pixel location P ij  in the set of frames N. In the case of a picture, the correlates to the reflected illumination at each pixel location P ij . In the case of an electronic display formed by pixels, the average pixel intensity or pixel value at each pixel location is determined. 
     Box  10  represents the multiplication of Boxes  8  and  9 A to form the Average Frame Data×Average P ij  Product (Box  11 ), which is an array. As shown in the bottom portion of  FIG. 3 , the Average Frame Data×Average P ij  Product is subtracted from the Frame Data×P ij  Products Average to form the intermediate G (2) ij Image of Box  12 . In Box  13  the sum of the intermediate G (2) ij Images for the frames  1 -N is calculated to produce the final composite image. 
     A preferred embodiment of the present invention comprises multiple photo-sensor buckets scanned or in an array and high resolution images of the illuminating light source. Depending on the object and the light source that it is scattering and reflecting it is possible that light is scattering or reflecting from any location on the subject such that any or all of the photo-sensors in the array has a probability of measuring one or more photons of light. A low resolution camera can be used as the multiple photo-sensor bucket array. This invention demonstrates that a higher resolution G (2)  image of the target can be produced using high-resolution images of the illumination source coupled with information from the multiple photo-sensor bucket array. Use of the multiple photo-sensor bucket array can improve the convergence rate of the high resolution G (2)  image. Each photo-sensor in the multiple photo-sensor bucket array may measure light scattered and reflected from distinct portions of the target object with appropriate optics that images the subject onto the multiple photo-sensor bucket array. 
     A concept of the present invention is that if the nonspatial information resolving single-pixel “bucket” detector that measures light from the target object that is typically used for G (2)  imaging was replaced with a low resolution spatial information resolving device such as a Charge Coupled Device (CCD) camera and the detector that measures the light from the source of illumination is a high resolution spatial information resolving device, i.e., a high resolution CCD, then one could use the techniques of G (2)  imaging to generate an image that would be at the resolution and quality of the high-resolution device using the extra information measured by the low-resolution target object detector. This may be accomplished by treating each nonspatial information resolving pixel of the low-resolution detector as a separate “bucket” measurement to create a G (2)  image. The generation of G (2)  images is performed over the entire set of pixels of the low resolution camera and each low-resolution G (2)  image is accumulated into a composite G (2)  image that provides the final result. It should be noted that prior to generating a low-resolution pixel G (2)  image, the low-resolution pixel value can be tested to determine by some metric if a G (2)  image should be computed using that low-resolution pixel, i.e., an option includes not computing a G (2)  image if all the values at that low resolution pixel are 0 or below some threshold value. 
     Another preferred embodiment uses a single bucket detector to scan over different areas of a target. At each step of the scan a G (2)  image would be computed and accumulated into a composite G (2)  image for all positions that the detector scanned. 
     A third preferred embodiment utilizes the concept occurring when a set of random or pseudo-random pixels of the multiple photo-sensor bucket array measure light from the target subject. This random set of pixels may be different from one measurement time to another measurement time and these sets of random bucket pixels are used to compute sets of G (2)  images that are accumulated into a higher resolution and higher quality composite G (2)  image. 
     It should be noted that the calculation of the G (2)  image may be accomplished by using optimization methods such as Compressive Sensing techniques. 
       FIG. 4  is an illustration of a preferred embodiment system using entangled photon pairs in which a first part of entangled pair is sent towards a target  23  while a second part is sent along a reference path  12 B. If the first part of the entangled photon pair is absorbed or reflected by the target, it will affect a property (e.g., spin, polarization, transverse momentum, angular momentum, color) of the photon. The influence by the target is also reflected in the reference photons. In  FIG. 4  in a preferred embodiment, incoherent, partially coherent, chaotic or entangled light source is reflected from a subject target into a bucket detector which does not process spatial information and in effect, merely measures the “quantity” of light reflected from the subject into a plurality of bucket detectors  24 . A detector (CCD  29 ) is a spatial detector illuminated by the light source. Using spatial information from the second detector in conjunction with the light measurement from the first detector, an image is generated using coincidence circuitry. 
     Shown in  FIG. 4  is a laser  21  that sends light through a thermalizing element  27  which creates a light pattern. A beam splitter  28  is used to split the beam from the laser  21  into a target path  22 A and a reference path  22 B. The pattern of the beam is recorded by a charge coupled device (CCD)  29  or the like which records spatial information concerning the light pattern as discussed more fully in U.S. application Ser. No. 12/330,401, hereby incorporated by reference. In its simplest terms, CCD is a device for the movement of electrical charge from the detector area ( 29 ) to an area where the charge can be manipulated, for example conversion into a digital value. CCDs may be implemented as shift registers that move charge between capacitive bins in the device. The CCD device may be made up of semiconductors arranged in such a way that the electric charge output of one semiconductor charges an adjacent one. The CCD device may be integrated with an image sensor, such as a photoelectric device to produce the charge that is being read for digital imaging. The CCD device  29  may optionally be a camera, photodetector array or a photographic device capable of imaging the beam pattern  22 B. The beam pattern comprising the spatial information concerning the light beam  22 B is sent to computer  20 . Light Beam  22 A is directed to the target  23  and the returned and scattered light is collected by a first detector or sensor  24 . Detector  24  may be a plurality of bucket detectors, or any kind of detectors which have the capability of detecting a photon strike. Detectors  24  may be of a large variety of photo detectors well known to those of ordinary skill in the art. A feature of the preferred embodiments of  FIGS. 4 and 5  is that the detectors  24 , individually, need not record spatial information regarding the target  23 . However, cumulatively, spatial information is derived; although at low resolution. The spatial information derived by spatial detector  29  is transmitted to the computer  20  which combines and correlates this spatial information with the coincidence data received from detectors  24 . For example, the data recorded by detectors  24  may be transmitted to computer  20  in a form resembling that depicted in  FIG. 5 , for example, where roughly 16 “bucket” measurements are represented. 
     The spatial information from detector  29  is combined with the coincidence information from the detectors  14  in computer  20 . Computer  20  may be a microprocessor, processor, multiprocessor, CPU, mainframe, or any computing element capable of combining the spatial information from the detector  29  with the coincidence information from detectors  14 . Further description of the coincidence detection feature is found in U.S. Pat. No. 7,536,012 and U.S. patent application Ser. No. 12/330,401, both of which are hereby incorporated by reference. Since the photonic information detected by each particular detector  14  need not encompass spatial information, but simply indicate the occurrence of a photon returned from the target  23 , this capability facilitates the use of the preferred embodiment systems in environments in which the returned photons may be impacted by environmental conditions such as fog, smoke, atmospheric particles and the like. 
     A quantum photon mathematical equation will project the reference light intensity from the CCD  29 . This will be combined with “bucket” photon information (such as that exemplified in  FIGS. 4 and 5 ) for an ensemble of pulses to produce coincidence measurements needed for “ghost” imaging. The terminology “ghost” relates to the feature that the spatial information is not reflected from the target but is either derived from the modulation of the laser beam (not shown) or the spatial information obtained through the use of beam splitter  28  and detector  29  which records spatial information from a beam which has not “seen” or illuminated the target. 
       FIG. 5  is a conceptual diagram of a preferred embodiment of the present invention, such as for example, that shown in  FIG. 4 . Represented in  FIG. 5  is a light source  21 A which may be the sun (or a laser  21  as shown in  FIG. 4 ). The light source  21 A illuminates both the target  23  (which may be for example, the standard Air Force USAF resolution test chart). Light is reflected from the target into an array of “bucket” detectors as represented by an a 4×4 array  24  in  FIG. 5 . Photons from the light source  21 A are also measured by CCD  29 , in a manner as described in connection with  FIG. 4 . The high resolution array is represented by an 8 by 8 array, although any of a plurality of high resolution arrays may be used, such as in the form of a high resolution camera or the like. Note that light rays or photons reflected from the target  23  do not enter CCD  29 . CCD  29  derives spatial information from the light sources  21 A as opposed to target  23 . 
       FIG. 6  is a further conceptual diagram of a preferred embodiment of the present invention as a further example of an embodiment of the present invention. Represented in  FIG. 6  are the high resolution CCD  29  and the low resolution source  24 . The low resolution source may be any source of low resolution pixels. For example, it could be an analog photograph with reflected light correlating to the pixel values. In  FIG. 6 , the intermediate G (2)  images as represented by Box  12  in  FIG. 3 , are summed together to form the Final G (2)  images (designated as Box  13 ). Optionally, the intermediate G (2)  images may be weighted such that different values are assigned to different intermediate images. For this reason the image could be optimized, for example, for transmission or specific feature extraction. For example, if the background surrounding an object is of more importance than the object, this information would be weighted accordingly. 
     By way of example,  FIG. 7A  correlates to the image as produced using the methodology described in FIG. 5A of U.S. Pat. No. 7,812,303 (ARL 07-33) and  FIG. 7B  correlates to an image produced through to the processing stage as depicted at Box  12  of  FIG. 3 . 
     As further examples of image processing according to the methodology of the present invention,  FIG. 8A  is an image produced as represented at Box  12  and  FIG. 8B  correlates to the image produced when the process reaches Box  13 . 
     As further examples of image processing according to the methodology of the present invention,  FIG. 9B  is a low resolution image correlating to Box  9  of  FIG. 3  where blocks of 2×2 pixels are processed together.  FIG. 9A  is 1 by 1 a spatially averaged set of pixels of the target subject which correlates to an equivalent high resolution image. 
       FIGS. 10A and 10B  correlate to the image produced at the processing stage represented by Box  12  of  FIG. 3 .  FIG. 10A  is an illustration of an intermediate image constructed using a single bucket consisting of 4×4 pixels of a simulated low-resolution multiple photo-sensor bucket array.  FIG. 10B  is an illustration of an intermediate image constructed using a single bucket consisting of 4×4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
       FIGS. 11A and 11B  correlate to the images produced at the processing stages represented by Box  9  and Box  13  of  FIG. 3 , respectively.  FIG. 11A  is an illustration of an average image measured by a low-resolution multiple photo-sensor bucket array simulated by 4×4 pixel spatial averaging.  FIG. 11B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets consisting of 4×4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
       FIGS. 12  A and  12 B correlate to the images produced at the processing, stages represented by Box  12  of  FIG. 3 .  FIG. 12A  is an illustration of an intermediate image constructed using a single bucket consisting of 8×8 pixels of a simulated low-resolution multiple photo-sensor bucket array.  FIG. 12B  is an illustration of an intermediate image constructed using a single bucket consisting of 8×8 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
       FIGS. 13A and 13B  correlate to the images produced at the processing stages represented by Box  9  and Box  13  of  FIG. 3 , respectively.  FIG. 13A  is an illustration of an average image measured by a low-resolution multiple photo-sensor bucket array simulated by 8×8 pixel spatial averaging.  FIG. 13B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets consisting of 8×8 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
       FIGS. 14A and 14B  correlate to the images produced at the processing stages represented by Box  12  of  FIG. 3 .  FIG. 14A  is an illustration of an intermediate image constructed using a single bucket consisting of 8×8 with overlap of 4 pixels of a simulated low-resolution multiple photo-sensor bucket array.  FIG. 14B  is an illustration of an intermediate image constructed using a single bucket consisting of 8×8 with overlap of 4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
       FIGS. 15A and 15B  correlate to the images produced at the processing stages represented by Box  9  and Box  13  of  FIG. 3 , respectively.  FIG. 15A  is an illustration of an average image measured by a low-resolution multiple photo-sensor bucket array simulated by 8×8 with overlap of 4 pixel spatial averaging.  FIG. 15B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets consisting of 8×8 overlap of 4 pixels of a simulated low-resolution multiple photo-sensor bucket array. 
       FIGS. 16A and 16B  correlate to the images produced at the processing stages represented by Box  13  of  FIG. 3 .  FIG. 16A  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 1 randomly spatially located pixel for 1400 shots.  FIG. 16B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 2 randomly spatially located pixels for 1400 shots. 
       FIGS. 17 through 19  correlate to the images produced at the processing stages represented by Box  13  of  FIG. 3 . 
       FIG. 17A  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 2 randomly spatially located pixels for 500 shots. 
       FIG. 17B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 1000 randomly spatially located pixels for 10 shots. 
       FIG. 18A  is an illustration of a final composite image-produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 20 randomly spatially located pixels for 150 shots. 
       FIG. 18B  is an illustration of a final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 100 randomly spatially located pixels for 150 shots. 
       FIG. 19A  is an illustration of the final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 10 randomly spatially located pixels for 150 shots. 
       FIG. 19B  is an illustration of the final composite image produced by the sum of all the intermediate images using a set of buckets simulating a low resolution multiple photo-sensor bucket array that consisted of 1000 randomly spatially located pixels for 150 shots. 
     As described above, generally speaking, the progression of image stages in  FIG. 3  are represented in the presentation and comparison of images in  FIGS. 7 through 19  in order to demonstrate that high resolution images are producible from low resolution images using the principles of the present invention. 
     The preferred embodiments of the present invention described herein are based upon the calculation of a G (2)  “ghost” image for each bucket detector over the set of all bucket detectors that comprise the low resolution target object detector; however, the present invention is not limited to the specifics of the embodiments disclosed. Each of the intermediate G (2)  images are summed into a final composite image of the target object 
     A “ghost” or G (2)  image as used herein may be mathematically expressed as a result of a convolution between the aperture function (amplitude distribution function) of the object A(  r   o ) and a δ-function like second-order correlation function G (2) (  r   o ,  r   i )
 
 F (  ρ   i )=∫ obj   d  ρ     o   A (  ρ   o ) G   (2) (  ρ   o ,  ρ   i ),  (1)
 
where G (2) (  r   o ,  r   i ): d(  r   o −  r   i /m),  r   o  and  r   i  are 2D vectors of the transverse coordinate in the object plane and the image plane, respectively, and m is the magnification factor. The term δ function as used herein relates to the Dirac delta function which is a mathematical construct representing an infinitely sharp peak bounding unit area expressed as δ(x), that has the value zero everywhere except at x=0 where its value is infinitely large in such a way that its total integral is 1. The δ function characterizes the perfect point-to-point relationship between the object plane and the image plane. If the image comes with a constant background, as in this experiment, the second-order correlation function G (2) (  r   o ,  r   i ) in Eq. (1) must be composed of two parts
 
 G   (2) (  ρ   o ,  ρ   i )= G   0 +δ(  ρ   o −  ρ   i   /m )  (2)
 
where G 0  is a constant. The value of G 0  determines the visibility of the image. One may immediately connect Eq. (2) with the G (2)  function of thermal radiation
 
 G   (2)   =G   11   (1)   G   22   (1)   +|G   12   (1) | 2 ,  (3)
 
where G 11   (1) G 22   (1) ˜G 0  is a constant, and |G 12   (1) | 2 ˜d(  r   1 −  r   2 ) represents a nonlocal position-to-position correlation. Although the second-order correlation function G (2)  is formally written in terms of G (1) s as shown in equation (3), the physics are completely different. As we know, G 12   (1)  is usually measured by one photodetector representing the first-order coherence of the field, i.e., the ability of observing first-order interference. Here, in equation (3), G 12   (1)  may be measured by independent photodetectors at distant space-time points and represents a nonlocal EPR correlation.
 
     The present invention uses as its basis the calculation of a G (2)  ghost image for each bucket detector over the set of all bucket detectors that comprise the low resolution target object detector. Each of the intermediate G (2)  images are summed into a final composite image of the target object
 
Image final   =ΣG   i   (2)   (4)
 
where Σ indicates a summation operation. Similarly, when using Compressive Sensing (CS) techniques the R term of Eq. (9) is computed for each bucket for an intermediate image and these intermediate images are then summed as show in equation 4 to produce a final image of the target object.
 
     Typically ghost imaging uses two detectors, one to observe the light source and the other, single pixel or bucket detector, to observe the light scattering and reflecting from the target object.
 
 G   (2)   =               I ( x,y,t ) source   I ( t ) bucket           −           I ( x,y,t ) source                       I ( t ) bucket             (5)
 
where                     denotes an ensemble average. As used herein, and terminology “bucket” in general means a single pixel detector, a detector comprising a plurality or grouping of pixels, a low resolution imaging device, a low resolution scanning detector (or device) or the like. The terminology I(t) bucket  means the measurements taken from a single pixel detector, a detector comprising a plurality or grouping of pixels, a low resolution imaging device, a low resolution scanning detector (or device) or the like.

     A relatively new mathematical field named Compressive Sensing (CS) or Compressive Imaging (CI) can be used to good effect within the context of G (2)  imaging. The use of compressive techniques in the context of Ghost Imaging was performed by the Katz group (see O. Katz, et al., “Compressive Ghost Imaging,” Appl Phys. Lett., 95, 131110 (2009)) (hereby incorporated by reference) who demonstrated a ghost like imaging proposal of Shapiro (see J. Shapiro, “Computational Ghost Imaging,” Phys. Rev. A 78 061802(R) (2008)) (hereby incorporated by reference). 
     The use of CS and Compressive Imaging (CI) herein is based on finding approximate solutions to the integral equations using the Gradient Projection for Sparse Reconstruction (GPSR) mathematical methodology where
 
 JR=B   (6)
 
and
 
 R=R ( x,y )  (7)
 
is the object reflectance. The term J is a matrix, where the rows are the illumination patterns at time k and the B vector:
 
 B=[B   k ]  (8)
 
represents the bucket values. In cases where the system is underdetermined (too few [B k ]), then L 1  constraints are applied to complete the system and sparseness is used:
 
     
       
         
           
             
               
                 
                   
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     The CS computational strategy takes advantage of the fact that it is normally true in images that not all pixels in an image contain new information and the system is said to be sparse on some basis since fewer degrees of freedom are needed to describe the system than the total number of pixels in the image. The parameter τ in equation (9) is often a constant. 
     The problem is then solvable using, for example, an L1 minimization as described further in “Compressed Sensing, IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 4, APRIL 2006” and “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems, IEEE J. Sel. Top. in Sig., Proc. 1, 586 2007.” (both of which are hereby incorporated by reference). 
     In an alternative preferred embodiment, when illuminating light source comprises entangled photons, in order to resolve the issue of multiple counts (i.e., counts originating from background photons), the following sequence is preformed: 
     providing a high speed time stamped series of low resolution frames of a given region of interest from the array of pixel locations; 
     providing a high speed time stamped series of high resolution images of a light source from the spatial detector; 
     the high speed time stamped frames being such that there is only one photon counted (or measured) on a pixel in both the low resolution frame and the high resolution frame per unit time (if more than one pixel is counted, the frame of pixels is discarded—This is to ensure proper discrimination of entangled photons from background light.) 
     determining the value of each pixel at each location per unit time within each high resolution frame to form first arrays of pixel values; 
     determining the value of each pixel at each location per unit time within each low resolution frame to form a second array of pixel values; 
     for each low resolution pixel location in the second array:
         determining a third array (which corresponds to the intermediate image) of time coincident values (i.e., when entangled photons are jointly measured) for the low resolution pixel location and each pixel in each high resolution image for the series of frames;
 
summing together the third arrays to provide a final composite high resolution image.
       

     Applications of the present invention improve the ability to image through obscuring media (e.g., smoke or clouds), which remains a problem in a variety of fields, such as satellite imaging analysts, firefighters, drivers, oceanographers, astronomers, military personnel, and medical personnel. The present invention improves the ability to improve resolution in each of these exemplary instances and represents an opportunity to derive more information from images and presumably the decisions made from such images. By way of example, improved resolution in x-ray or endoscopy medical imagery facilitates lower radiation dosing and diagnosis of abnormal morphologies earlier than currently possible with conventional imaging methodologies. Conventional imaging techniques have, to a large extent, arrived at the theoretical limits of image resolution owing to wavelength-limited resolution, optical element distortions, and the reflective interaction between photons and an object to be imaged. 
     As used herein the terminology G (2)  technique means where you have two measurements where the actual image is the convolution of the object function F(  ρ   i )=∫ obj d  ρ   o A(  ρ   o )G (2) (  ρ   o ,  ρ   i ), where the object function A is convolved with the correlations between two spatially distinct detections. 
     As used in the following, the terminology photon light source means or is defined to include, thermal photon light, partially coherent, and entangled photon light. As used in the following, the terminology media means or is defined to include vacuum, air, water, turbid fluids, turbulence fluids, soft tissues and partially transmissive solids. 
     As used herein, the terminology “subject” or “object” or “target” may include a photograph, a thing, a person, animate or inanimate subject, a plurality of objects, the ground, ground covering (e.g., grass), a localized piece or pieces of the environment, surface, physical entity (or entities) or anything that can be observed. 
     As used herein, the terminology “bucket” refers to a single-pixel (bucket) detector. 
     The invention is not restricted to the illustrative examples described above. Examples are not intended as limitations on the scope of the invention. Methods, apparatus, compositions, and the like described herein are exemplary and not intended as limitations on the scope of the invention. Changes therein and other uses will occur to those skilled in the art. The scope of the invention is defined by the scope of the claims. 
     Patents, patent applications, or publications mentioned in this specification are incorporated herein by object to the same extent as if each individual document was specifically and individually indicated to be incorporated by object. 
     The foregoing description of the specific embodiments are intended to reveal the general nature of the embodiments herein that others can, by applying current knowledge, readily modify and/or adapt for various applications such specific embodiments without departing from the generic concept, and, therefore, such adaptations and modifications should and are intended to be comprehended within the meaning and range of equivalents of the disclosed embodiments. It is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore, while the embodiments herein have been described in terms of preferred embodiments, those skilled in the art will recognize that the embodiments herein can be practiced with modification within the spirit and scope of the appended claims.