Editing Super-resolution imaging

{{short description|Any technique to improve resolution of an imaging system beyond conventional limits}}
{{Essay-like|date=October 2019}}
'''Super-resolution imaging''' ('''SR''') is a class of techniques that improve the [[image resolution|resolution]] of an [[digital imaging|imaging]] system. In '''optical SR''' the [[diffraction-limited|diffraction limit]] of systems is transcended, while in '''geometrical SR''' the resolution of digital [[image sensor|imaging sensors]] is enhanced.

In some [[radar]] and [[sonar]] imaging applications (e.g. [[magnetic resonance imaging]] (MRI), [[high-resolution computed tomography]]), [[space (mathematics)|subspace]] decomposition-based methods (e.g. [[MUSIC (algorithm)|MUSIC]]<ref>Schmidt, R.O, "Multiple Emitter Location and Signal Parameter Estimation," IEEE Trans. Antennas Propagation, Vol. AP-34 (March 1986), pp.276-280.</ref>) and [[compressed sensing]]-based algorithms (e.g., [[SAMV (algorithm)|SAMV]]<ref name=AbeidaZhang>{{cite journal | last1=Abeida | first1=Habti | last2=Zhang | first2=Qilin | last3=Li | first3=Jian|author3-link=Jian Li (engineer) | last4=Merabtine | first4=Nadjim | title=Iterative Sparse Asymptotic Minimum Variance Based Approaches for Array Processing | journal=IEEE Transactions on Signal Processing | volume=61 | issue=4 | year=2013 | issn=1053-587X | doi=10.1109/tsp.2012.2231676 | pages=933–944 | url=https://qilin-zhang.github.io/_pages/pdfs/SAMVpaper.pdf | bibcode=2013ITSP...61..933A | arxiv=1802.03070 | s2cid=16276001 }}</ref>) are employed to achieve SR over standard [[periodogram]] algorithm.

Super-resolution imaging techniques are used in general [[image processing]] and in [[super-resolution microscopy]].

==Basic concepts==
Because some of the ideas surrounding super-resolution raise fundamental issues, there is need at the outset to examine the relevant physical and information-theoretical principles:

* [[Diffraction limit]]: The detail of a physical object that an optical instrument can reproduce in an image has limits that are mandated by laws of physics, whether formulated by the [[diffraction]] equations in the [[wave theory of light]]<ref>Born M,  Wolf E,  ''[[Principles of Optics]]'', Cambridge Univ. Press, any edition</ref> or equivalently the [[uncertainty principle]] for photons in [[quantum mechanics]].<ref>Fox M, 2007 '' Quantum Optics'' Oxford</ref>  Information transfer can never be increased beyond this boundary, but packets outside the limits can be cleverly swapped for (or multiplexed with) some inside it.<ref>Zalevsky Z,  Mendlovic D. 2003  '' Optical Superresolution'' Springer</ref>  One does not so much “break” as “run around” the diffraction limit. New procedures probing electro-magnetic disturbances at the molecular level (in the so-called near field)<ref name = "near-field">{{cite journal | last1 = Betzig | first1 = E | last2 = Trautman | first2 = JK | year = 1992 | title = Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit | journal = Science | volume = 257 | issue = 5067| pages = 189–195 | doi=10.1126/science.257.5067.189| pmid = 17794749 | bibcode = 1992Sci...257..189B | s2cid = 38041885 }}</ref> remain fully consistent with [[Maxwell's equations]].
** Spatial-frequency domain: A succinct expression of the diffraction limit is given in the spatial-frequency domain.  In [[Fourier optics]] light distributions are expressed as superpositions of a series of grating light patterns in a range of fringe widths, technically [[spatial frequencies]]. It is generally taught that diffraction theory stipulates an upper limit, the cut-off spatial-frequency, beyond which pattern elements fail to be transferred into the optical image, i.e., are not resolved.  But in fact what is set by diffraction theory is the width of the passband, not a fixed upper limit. No laws of physics are broken when a spatial frequency band beyond the cut-off spatial frequency is swapped for one inside it: this has long been implemented in [[dark-field microscopy]].  Nor are information-theoretical rules broken when superimposing several bands,<ref name = "Lukosz">Lukosz, W., 1966. Optical systems with resolving power exceeding the classical limit. J. opt. soc. Am. 56, 1463–1472.</ref><ref name="Guerra 3555–3557">{{Cite journal |last=Guerra |first=John M. |date=1995-06-26 |title=Super-resolution through illumination by diffraction-born evanescent waves |url=https://aip.scitation.org/doi/10.1063/1.113814 |journal=Applied Physics Letters |volume=66 |issue=26 |pages=3555–3557 |doi=10.1063/1.113814 |bibcode=1995ApPhL..66.3555G |issn=0003-6951}}</ref><ref name = "Gustaffson">Gustaffsson, M., 2000. Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy. J. Microscopy 198, 82–87.</ref>  disentangling them in the received image needs assumptions of object invariance during multiple exposures, i.e., the substitution of one kind of uncertainty for another.
* [[Information]]: When the term super-resolution is used in techniques of inferring object details from statistical treatment of the image within standard resolution limits, for example, averaging multiple exposures, it involves an exchange of one kind of information (extracting signal from noise) for another (the assumption that the target has remained invariant).
* Resolution and localization: True resolution involves the distinction of whether a target, e.g. a star or a spectral line, is single or double, ordinarily requiring separable peaks in the image. When a target is known to be single, its location can be determined with higher precision than the image width by finding the centroid (center of gravity) of its image light distribution. The word  ''ultra-resolution'' had been proposed for this process<ref>Cox, I.J., Sheppard, C.J.R., 1986. Information capacity and resolution in an optical system. J.opt. Soc. Am. A 3, 1152–1158</ref> but it did not catch on, and the high-precision localization procedure is typically referred to as super-resolution.

The technical achievements of enhancing the performance of imaging-forming and –sensing devices now classified as super-resolution use to the fullest but always stay within the bounds imposed by the laws of physics and information theory.

== Techniques ==
{{Update|section|date=January 2023|reason=We should update this to include progress in improving superresolution with machine learning and neural networks.}}

===Optical or diffractive super-resolution===
Substituting spatial-frequency bands: Though the bandwidth allowable by diffraction is fixed, it can be positioned anywhere in the spatial-frequency spectrum. [[Dark-field microscopy|Dark-field illumination]] in microscopy is an example. See also [[aperture synthesis]].

[[File:Structured Illumination Superresolution.png|thumb|left|220px|The "structured illumination" technique of super-resolution is related to [[moiré pattern]]s. The target, a band of fine fringes (top row), is beyond the diffraction limit. When a band of somewhat coarser resolvable fringes (second row) is artificially superimposed, the combination (third row) features [[Moiré pattern|moiré]] components that are within the diffraction limit and hence contained in the image (bottom row) allowing the presence of the fine fringes to be inferred even though they are not themselves represented in the image.]]

====Multiplexing spatial-frequency bands====
An image is formed using the normal passband of the optical device. Then some known light structure, for example a set of light fringes that need not even be within the passband, is superimposed on the target.<ref name="Guerra 3555–3557"/><ref name = "Gustaffson"/> The image now contains components resulting from the combination of the target and the superimposed light structure, e.g. [[Moiré pattern|moiré fringes]], and carries information about target detail which simple unstructured illumination does not. The “superresolved” components, however, need disentangling to be revealed. For an example, see structured illumination (figure to left).

====Multiple parameter use within traditional diffraction limit====
If a target has no special polarization or wavelength properties, two polarization states or non-overlapping wavelength regions can be used to encode target details, one in a spatial-frequency band inside the cut-off limit the other beyond it. Both would use normal passband transmission but are then separately decoded to reconstitute target structure with extended resolution.

====Probing near-field electromagnetic disturbance====
The usual discussion of super-resolution involved conventional imagery of an object by an optical system. But modern technology allows probing the electromagnetic disturbance within molecular distances of the source<ref name="near-field"/> which has superior resolution properties, see also [[evanescent waves]] and the development of the new [[super lens]].

===Geometrical or image-processing super-resolution===
[[File:Super-resolution example closeup.png|thumb|right|220px|Compared to a single image marred by noise during its acquisition or transmission (left), the [[Signal-to-noise ratio (imaging)|signal-to-noise ratio]] is improved by suitable combination of several separately-obtained images (right). This can be achieved only within the intrinsic resolution capability of the imaging process for revealing such detail.]]

====Multi-exposure image noise reduction====
When an image is degraded by noise, there can be more detail in the average of many exposures, even within the diffraction limit. See example on the right.

====Single-frame deblurring====
{{main|Deblurring}}
Known defects in a given imaging situation, such as [[defocus]] or [[optical aberration|aberration]]s, can sometimes be mitigated in whole or in part by suitable spatial-frequency filtering of even a single image. Such procedures all stay within the diffraction-mandated passband, and do not extend it.

[[File:Localization Resolution.png|thumb|left|220px|Both features extend over 3 pixels but in different amounts, enabling them to be localized with precision superior to pixel dimension.]]

====Sub-pixel image localization====
The location of a single source can be determined by computing the "center of gravity" ([[centroid]]) of the light distribution extending over several adjacent pixels (see figure on the left). Provided that there is enough light, this can be achieved with arbitrary precision, very much better than pixel width of the detecting apparatus and the resolution limit for the decision of whether the source is single or double.  This technique, which requires the presupposition that all the light comes from a single source, is at the basis of what has become known as [[super-resolution microscopy]], e.g. [[stochastic optical reconstruction microscopy]] (STORM),  where fluorescent probes attached to molecules give [[Nanoscopic scale|nanoscale]] distance information.  It is also the mechanism underlying visual [[hyperacuity]].<ref>{{cite journal | last1 = Westheimer | first1 = G | year = 2012 | title = Optical superresolution and visual hyperacuity | journal = Prog Retin Eye Res | volume = 31 | issue = 5| pages = 467–80 | doi=10.1016/j.preteyeres.2012.05.001| pmid = 22634484 | doi-access = free }}</ref>

====Bayesian induction beyond traditional diffraction limit====
{{Main|Bayesian inference}}
Some object features, though beyond the diffraction limit, may be known to be associated with other object features that are within the limits and hence contained in the image.  Then conclusions can be drawn, using statistical methods, from the available image data about the presence of the full object.<ref>Harris, J.L., 1964. Resolving power and decision making. J. opt. soc. Am. 54, 606–611.</ref>  The classical example is Toraldo di Francia's proposition<ref>Toraldo di Francia, G., 1955. Resolving power and information. J. opt. soc. Am. 45, 497–501.</ref> of judging whether an image is that of a single or double star by determining whether its width exceeds the spread from a single star.  This can be achieved at separations well below the classical resolution bounds, and requires the prior limitation to the choice "single or double?"

The approach can take the form of [[extrapolation|extrapolating]] the image in the frequency domain, by assuming that the object is an [[analytic function]], and that we can exactly know the [[Function (mathematics)|function]] values in some [[Interval (mathematics)|interval]]. This method is severely limited by the ever-present noise in digital imaging systems, but it can work for [[radar]], [[astronomy]],  [[microscope|microscopy]] or [[magnetic resonance imaging]].<ref>[[#refPoot12|D. Poot, B. Jeurissen, Y. Bastiaensen, J. Veraart, W. Van Hecke, P. M. Parizel, and J. Sijbers, "Super-Resolution for Multislice Diffusion Tensor Imaging", Magnetic Resonance in Medicine, (2012)]]</ref> More recently, a fast single image super-resolution algorithm based on a closed-form solution to ''<math>\ell_2-\ell_2</math>'' problems has been proposed and demonstrated to accelerate most of the existing Bayesian super-resolution methods significantly.<ref>N. Zhao, Q. Wei, A. Basarab, N. Dobigeon, D. Kouamé and J-Y. Tourneret, [https://arxiv.org/abs/1510.00143 "Fast single image super-resolution using a new analytical solution for ''<math>\ell_2-\ell_2</math>'' problems"], IEEE Trans. Image Process., 2016, to appear.</ref>

==Aliasing==
Geometrical SR reconstruction [[algorithm]]s are possible if and only if the input low resolution images have been under-sampled and therefore contain [[aliasing]]. Because of this aliasing, the high-frequency content of the desired reconstruction image is embedded in the low-frequency content of each of the observed images. Given a sufficient number of observation images, and if the set of observations vary in their phase (i.e. if the images of the scene are shifted by a sub-pixel amount), then the phase information can be used to separate the aliased high-frequency content from the true low-frequency content, and the full-resolution image can be accurately reconstructed.<ref>J. Simpkins, R.L. Stevenson, "An Introduction to Super-Resolution Imaging."[http://www.crcpress.com/product/isbn/9781439869604 '' Mathematical Optics: Classical, Quantum, and Computational Methods''], Ed. V. Lakshminarayanan, M. Calvo, and T. Alieva. CRC Press, 2012. 539-564.</ref>

In practice, this frequency-based approach is not used for reconstruction, but even in the case of spatial approaches (e.g. shift-add fusion<ref name="users.soe.ucsc.edu">S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, [http://users.soe.ucsc.edu/~milanfar/publications/journal/SRfinal.pdf "Fast and Robust Multi-frame Super-resolution"], IEEE Transactions on Image Processing, vol. 13, no. 10, pp. 1327–1344, October 2004.</ref>), the presence of aliasing is still a necessary condition for SR reconstruction.

==Technical implementations==
There are many both single-frame and multiple-frame variants of SR. Multiple-frame SR uses the sub-[[pixel shift]]s between multiple low resolution images of the same scene. It creates an improved resolution image fusing information from all low resolution images, and the created higher resolution images are better descriptions of the scene. Single-frame SR methods attempt to magnify the image without producing blur. These methods use other parts of the low resolution images, or other unrelated images, to guess what the high-resolution image should look like. Algorithms can also be divided by their domain: [[frequency domain|frequency]] or [[Digital signal processing#Time and space domains|space domain]]. Originally, super-resolution methods worked well only on grayscale images,<ref>P. Cheeseman, B. Kanefsky, R. Kraft, and J. Stutz, 1994</ref> but researchers have found methods to adapt them to color camera images.<ref name="users.soe.ucsc.edu"/> Recently, the use of super-resolution for 3D data has also been shown.<ref>S. Schuon, C. Theobalt, J. Davis, and S. Thrun,  [https://ai.stanford.edu/~schuon/2009/04/superresolution-of-3d-lidarboost.html "LidarBoost: Depth Superresolution for ToF 3D Shape Scanning"], In Proceedings of IEEE CVPR 2009</ref>

==Research==
There is promising research on using [[convolutional neural network|deep convolutional networks]] to perform super-resolution.<ref>{{Cite arXiv|last1=Johnson|first1=Justin|last2=Alahi|first2=Alexandre|last3=Fei-Fei|first3=Li|date=2016-03-26|title=Perceptual Losses for Real-Time Style Transfer and Super-Resolution|eprint=1603.08155|class=cs.CV}}</ref> In particular work has been demonstrated showing the transformation of a 20x [[microscope]] image of pollen grains into a 1500x [[scanning electron microscope]] image using it.<ref>{{Cite journal|last1=Grant-Jacob|first1=James A|last2=Mackay|first2=Benita S|last3=Baker|first3=James A G|last4=Xie|first4=Yunhui|last5=Heath|first5=Daniel J|last6=Loxham|first6=Matthew|last7=Eason|first7=Robert W|last8=Mills|first8=Ben|date=2019-06-18|title=A neural lens for super-resolution biological imaging|journal=Journal of Physics Communications|volume=3|issue=6|pages=065004|doi=10.1088/2399-6528/ab267d|issn=2399-6528|bibcode=2019JPhCo...3f5004G|doi-access=free}}</ref> While this technique can increase the information content of an image, there is no guarantee that the upscaled features exist in the original image and [[Image scaling#Deep convolutional neural networks|deep convolutional upscalers]] should not be used in analytical applications with ambiguous inputs.<ref>{{Cite conference |author=Blau |first1=Yochai |last2=Michaeli |first2=Tomer |year=2018 |title=The perception-distortion tradeoff |conference=IEEE Conference on Computer Vision and Pattern Recognition |pages=6228–6237 |doi=10.1109/CVPR.2018.00652|arxiv=1711.06077 }}</ref><ref>{{Cite web |last=Zeeberg |first=Amos |date=2023-08-23 |title=The AI Tools Making Images Look Better |url=https://www.quantamagazine.org/the-ai-tools-making-images-look-better-20230823/ |access-date=2023-08-28 |website=Quanta Magazine |language=en}}</ref> These methods can [[Hallucination (artificial intelligence)|hallucinate]] image features, which can make them unsafe for medical use.<ref name="cohen-miccai-2018">{{cite conference <!-- Citation bot no --> |conference=21st International Conference, Granada, Spain, September 16–20, 2018, Proceedings, Part I |last1=Cohen |first1=Joseph Paul |chapter=Distribution Matching Losses Can Hallucinate Features in Medical Image Translation |title=Medical Image Computing and Computer Assisted Intervention – MICCAI 2018 |series=Lecture Notes in Computer Science |date=2018 |volume=11070 |pages=529–536 |doi=10.1007/978-3-030-00928-1_60 |arxiv=1805.08841 |isbn=978-3-030-00927-4 |s2cid=43919703 |chapter-url=https://www.springerprofessional.de/en/en/distribution-matching-losses-can-hallucinate-features-in-medical/16122390 |access-date=1 May 2022 | first2=Margaux |last2=Luck |first3= Sina |last3=Honari |editor1= Alejandro F. Frangi |editor2= Julia A. Schnabel |editor3= Christos Davatzikos |editor4= Carlos Alberola-López |editor5= Gabor Fichtinger }}</ref>

==See also==
*[[Optical resolution]]
*[[Oversampling]]
*[[Video super-resolution]]
*[[Single-particle trajectory]]
*[[Superoscillation]]

==References==
{{Reflist}}

===Other related work===
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{{Video processing}}<br />

[[Category:Image processing]]
[[Category:Signal processing]]
[[Category:Imaging]]