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533:. 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.
351:
204:. 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
409:) 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
25:
189:. 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. 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) remain fully consistent with
440:
object. The classical example is
Toraldo di Francia's proposition 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?"
216:: 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).
393:
324:
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
219:
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
549:
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
439:
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
311:
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. The image now contains components resulting from the combination of the target and the
333:
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 which has superior resolution properties, see also
208:. Nor are information-theoretical rules broken when superimposing several bands, 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.
228:
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.
316:, 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).
536:
In practice, this frequency-based approach is not used for reconstruction, but even in the case of spatial approaches (e.g. shift-add fusion), the presence of aliasing is still a necessary condition for SR reconstruction.
558:. Originally, super-resolution methods worked well only on grayscale images, but researchers have found methods to adapt them to color camera images. Recently, the use of super-resolution for 3D data has also been shown.
297:. 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
301:
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
389:, 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.
358:
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.
550:
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:
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D. Poot, B. Jeurissen, Y. Bastiaensen, J. Veraart, W. Van Hecke, P. M. Parizel, and J. Sijbers, "Super-Resolution for
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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:
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image using it. 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
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173:: 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
35:
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should not be used in analytical applications with ambiguous inputs. These methods can hallucinate image features, which can make them unsafe for medical use.
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Substituting spatial-frequency bands: Though the bandwidth allowable by diffraction is fixed, it can be positioned anywhere in the spatial-frequency spectrum.
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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.
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had been proposed for this process but it did not catch on, and the high-precision localization procedure is typically referred to as super-resolution.
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Both features extend over 3 pixels but in different amounts, enabling them to be localized with precision superior to pixel dimension.
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light distributions are expressed as superpositions of a series of grating light patterns in a range of fringe widths, technically
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problems has been proposed and demonstrated to accelerate most of the existing
Bayesian super-resolution methods significantly.
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to perform super-resolution. In particular work has been demonstrated showing the transformation of a 20x
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are possible if and only if the input low resolution images have been under-sampled and therefore contain
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1769:"A Total Variation Regularization Based Super-Resolution Reconstruction Algorithm for Digital Video"
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There are many both single-frame and multiple-frame variants of SR. Multiple-frame SR uses the sub-
475:. More recently, a fast single image super-resolution algorithm based on a closed-form solution to
42:
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that states a
Knowledge editor's personal feelings or presents an original argument about a topic.
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Compared to a single image marred by noise during its acquisition or transmission (left), the
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width by finding the centroid (center of gravity) of its image light distribution. The word
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The location of a single source can be determined by computing the "center of gravity" (
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Please help update this article to reflect recent events or newly available information.
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Any technique to improve resolution of an imaging system beyond conventional limits
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The "structured illumination" technique of super-resolution is related to
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Ng, Michael K.; Shen, Huanfeng; Lam, Edmund Y.; Zhang, Liangpei (2007).
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Medical Image Computing and Computer Assisted Intervention – MICCAI 2018
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N. Zhao, Q. Wei, A. Basarab, N. Dobigeon, D. Kouamé and J-Y. Tourneret,
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A+: Adjusted Anchored Neighborhood Regression for Fast Super-Resolution
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the image in the frequency domain, by assuming that the object is an
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Mathematical Optics: Classical, Quantum, and Computational Methods
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distance information. It is also the mechanism underlying visual
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IEEE Transactions on Pattern Analysis and Machine Intelligence
417:(STORM), where fluorescent probes attached to molecules give
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Single Image Super-Resolution from Transformed Self-Exemplars
1053:"LidarBoost: Depth Superresolution for ToF 3D Shape Scanning"
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1397:"Statistics for optimal point prediction in natural images"
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Multiple parameter use within traditional diffraction limit
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personal reflection, personal essay, or argumentative essay
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IEEE Conference on Computer Vision and Pattern Recognition
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Timofte, R.; De Smet, V.; Van Gool, L. (November 2014).
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Cohen, Joseph Paul; Luck, Margaux; Honari, Sina (2018).
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Super-resolution imaging techniques are used in general
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International Journal of Imaging Systems and Technology
1088:"A neural lens for super-resolution biological imaging"
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P. Cheeseman, B. Kanefsky, R. Kraft, and J. Stutz, 1994
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Bayesian induction beyond traditional diffraction limit
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84:) is a class of techniques that enhance (increase) the
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Cheung, V.; Frey, B. J.; Jojic, N. (20–25 June 2005).
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Conference on Computer Vision and Pattern Recognition
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Known defects in a given imaging situation, such as
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1929:. 12th Asian Conference on Computer Vision (ACCV).
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1029:S. Farsiu, D. Robinson, M. Elad, and P. Milanfar,
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1051:S. Schuon, C. Theobalt, J. Davis, and S. Thrun,
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1773:EURASIP Journal on Advances in Signal Processing
1512:Super-resolution from image sequences — a review
889:"Optical superresolution and visual hyperacuity"
346:Geometrical or image-processing super-resolution
1941:Huang, J.-B; Singh, A.; Ahuja, N. (June 2015).
1940:
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1740:Multidimensional Systems and Signal Processing
1031:"Fast and Robust Multi-frame Super-resolution"
1002:, IEEE Trans. Image Process., 2016, to appear.
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329:Probing near-field electromagnetic disturbance
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1518:. Midwest Symposium on Circuits and Systems.
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415:stochastic optical reconstruction microscopy
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143:) are employed to achieve SR over standard
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65:Learn how and when to remove this message
1170:"The AI Tools Making Images Look Better"
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274:Optical or diffractive super-resolution
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1135:Blau, Yochai; Michaeli, Tomer (2018).
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653:IEEE Transactions on Signal Processing
282:in microscopy is an example. See also
2009:
1963:"Super-resolution Ultrasound Imaging"
1839:"Penrose Pixels for Super-Resolution"
1655:IEEE Transactions on Image Processing
1641:Super Resolution From Image Sequences
1592:IEEE Transactions on Image Processing
1455:(CVPR). Vol. 1. pp. 42–49.
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800:
566:There is promising research on using
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1815:Super-Resolution from a Single Image
1298:Zalevsky, Z.; Mendlovic, D. (2003).
717:, Cambridge Univ. Press, any edition
574:image of pollen grains into a 1500x
363:Multi-exposure image noise reduction
307:Multiplexing spatial-frequency bands
236:
100:of systems is transcended, while in
18:
1395:Geisler, W.S.; Perry, J.S. (2011).
992:{\displaystyle \ell _{2}-\ell _{2}}
509:{\displaystyle \ell _{2}-\ell _{2}}
451:, and that we can exactly know the
312:superimposed light structure, e.g.
125:high-resolution computed tomography
13:
1980:10.1016/j.ultrasmedbio.2019.11.013
1638:Irani, M.; Peleg, S. (June 1990).
1509:Borman, S.; Stevenson, R. (1998).
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1055:, In Proceedings of IEEE CVPR 2009
443:The approach can take the form of
131:decomposition-based methods (e.g.
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1092:Journal of Physics Communications
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906:10.1016/j.preteyeres.2012.05.001
739:Zalevsky Z, Mendlovic D. 2003
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1525:IEEE Signal Processing Magazine
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525:Geometrical SR reconstruction
1:
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640:Abeida, Habti; Zhang, Qilin;
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232:
1217:10.1007/978-3-030-00928-1_60
1168:Zeeberg, Amos (2023-08-23).
778:10.1126/science.257.5067.189
644:; Merabtine, Nadjim (2013).
580:deep convolutional upscalers
576:scanning electron microscope
401:Sub-pixel image localization
7:
1504:. University of Notre Dame.
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568:deep convolutional networks
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411:super-resolution microscopy
156:super-resolution microscopy
119:imaging applications (e.g.
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607:Single-particle trajectory
473:magnetic resonance imaging
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121:magnetic resonance imaging
104:the resolution of digital
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1905:10.1007/s11548-011-0545-9
1752:10.1007/s11045-007-0022-3
541:Technical implementations
250:This section needs to be
139:-based algorithms (e.g.,
2116:Super-resolution imaging
1545:10.1109/MSP.2003.1203207
1113:10.1088/2399-6528/ab267d
683:10.1109/tsp.2012.2231676
78:Super-resolution imaging
1676:10.1109/TIP.2007.903256
1300:Optical Superresolution
1155:10.1109/CVPR.2018.00652
825:Applied Physics Letters
741:Optical Superresolution
371:Single-frame deblurring
280:Dark-field illumination
1868:10.1109/TPAMI.2010.213
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887:Westheimer, G (2012).
602:Video super-resolution
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45:by rewriting it in an
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206:dark-field microscopy
183:uncertainty principle
1967:Ultrasound Med. Biol
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1341:10.1364/OL.29.001986
1283:10.1364/AO.31.006272
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714:Principles of Optics
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181:or equivalently the
179:wave theory of light
1785:2007EJASP2007..104N
1715:2011OptL...36..885C
1668:2007ITIP...16.2322S
1605:2001ITIP...10.1187E
1537:2003ISPM...20...21P
1372:2005ASAJ..118.3953C
1333:2004OptL...29.1986C
1275:1992ApOpt..31.6272M
1104:2019JPhCo...3f5004G
837:1995ApPhL..66.3555G
770:1992Sci...257..189B
675:2013ITSP...61..933A
202:spatial frequencies
191:Maxwell's equations
2089:Special processing
1794:10.1155/2007/74585
1502:(Technical report)
1253:Other related work
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893:Prog Retin Eye Res
711:Born M, Wolf E,
592:Optical resolution
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435:Bayesian inference
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284:aperture synthesis
137:compressed sensing
47:encyclopedic style
34:is written like a
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2131:Pixel art scaling
2096:Film colorization
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1574:10.1002/ima.20007
1402:Journal of Vision
1380:10.1121/1.2109167
1327:(17): 1986–1988.
1309:978-0-387-00591-1
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1226:978-3-030-00927-4
831:(26): 3555–3557.
764:(5067): 189–195.
449:analytic function
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187:quantum mechanics
177:equations in the
171:Diffraction limit
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1418:
1416:10.1167/11.12.14
1391:
1366:(6): 3953–3960.
1352:
1313:
1294:
1246:
1245:
1243:
1241:
1210:
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1183:
1181:
1180:
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908:
884:
878:
875:
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866:
857:
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845:10.1063/1.113814
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804:
798:
797:
753:
744:
737:
731:
724:
718:
709:
703:
702:
668:
650:
637:
631:
628:
612:Superoscillation
515:
513:
512:
507:
505:
504:
492:
491:
336:evanescent waves
266:
263:
257:
245:
244:
237:
222:ultra-resolution
152:image processing
70:
63:
59:
56:
50:
27:
26:
19:
2185:
2184:
2180:
2179:
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2150:
2149:
2147:
2145:
2140:
2084:
2045:Post-processing
2039:
2034:
1952:
1932:
1926:
1859:10.1.1.174.8804
1841:
1828:
1818:
1746:(2–3): 83–101.
1644:
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1448:
1310:
1255:
1250:
1249:
1239:
1237:
1227:
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1174:Quanta Magazine
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1080:
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1021:
1010:
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638:
634:
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496:
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483:
481:
478:
477:
455:values in some
437:
431:
403:
379:
373:
365:
348:
331:
322:
309:
276:
267:
261:
258:
255:
246:
242:
235:
185:for photons in
164:
106:imaging sensors
71:
60:
54:
51:
43:help improve it
40:
28:
24:
17:
12:
11:
5:
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2173:
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2141:
2139:
2138:
2133:
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2083:
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2072:
2067:
2066:
2065:
2055:
2049:
2047:
2041:
2040:
2033:
2032:
2025:
2018:
2010:
2004:
2003:
1973:(4): 865–891.
1958:
1954:"project page"
1938:
1917:
1899:(5): 663–673.
1888:
1834:
1809:
1764:
1735:
1709:(6): 885–887.
1702:Optics Letters
1696:
1649:
1635:
1614:10.1.1.11.2502
1586:
1557:
1520:
1506:
1494:
1465:
1445:Video epitomes
1439:
1392:
1353:
1320:Optics Letters
1314:
1308:
1295:
1262:Applied Optics
1254:
1251:
1248:
1247:
1225:
1185:
1160:
1127:
1078:
1057:
1044:
1035:
1019:
1004:
986:
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978:
973:
969:
949:
938:
929:
920:
879:
870:
858:
808:
799:
745:
732:
728:Quantum Optics
719:
704:
659:(4): 933–944.
632:
622:
621:
619:
616:
615:
614:
609:
604:
599:
594:
587:
584:
563:
560:
542:
539:
522:
519:
503:
499:
495:
490:
486:
433:Main article:
430:
427:
402:
399:
375:Main article:
372:
369:
364:
361:
347:
344:
330:
327:
321:
318:
308:
305:
295:moiré patterns
275:
272:
269:
268:
249:
247:
240:
234:
231:
226:
225:
217:
211:
210:
209:
198:Fourier optics
163:
162:Basic concepts
160:
102:geometrical SR
73:
72:
31:
29:
22:
15:
9:
6:
4:
3:
2:
2182:
2171:
2168:
2166:
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2161:
2158:
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2134:
2132:
2129:
2127:
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2122:
2121:Video matting
2119:
2117:
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2112:
2109:
2107:
2106:Color grading
2104:
2101:
2097:
2094:
2093:
2091:
2087:
2081:
2078:
2076:
2073:
2071:
2070:Deinterlacing
2068:
2064:
2061:
2060:
2059:
2056:
2054:
2051:
2050:
2048:
2046:
2042:
2038:
2031:
2026:
2024:
2019:
2017:
2012:
2011:
2008:
2000:
1996:
1991:
1986:
1981:
1976:
1972:
1968:
1964:
1959:
1955:
1948:
1944:
1939:
1935:
1925:
1924:
1918:
1914:
1910:
1906:
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1898:
1894:
1889:
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1479:
1475:
1471:
1466:
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1458:
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1369:
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1276:
1272:
1268:
1264:
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1218:
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1200:
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1152:
1147:
1142:
1138:
1131:
1123:
1119:
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1101:
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1097:
1093:
1089:
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1073:
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1061:
1054:
1048:
1039:
1032:
1026:
1024:
1016:
1015:
1008:
1001:
999:
984:
980:
976:
971:
967:
953:
947:
942:
933:
924:
916:
912:
907:
902:
899:(5): 467–80.
898:
894:
890:
883:
874:
865:
863:
854:
850:
846:
842:
838:
834:
830:
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813:
803:
795:
791:
787:
783:
779:
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767:
763:
759:
752:
750:
742:
736:
729:
723:
716:
715:
708:
700:
696:
692:
688:
684:
680:
676:
672:
667:
662:
658:
654:
647:
643:
636:
627:
623:
613:
610:
608:
605:
603:
600:
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595:
593:
590:
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577:
573:
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559:
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553:
548:
538:
534:
532:
528:
518:
516:
501:
497:
493:
488:
484:
474:
470:
466:
462:
458:
454:
450:
446:
445:extrapolating
441:
436:
426:
424:
420:
416:
412:
408:
394:
390:
388:
384:
378:
368:
357:
352:
343:
341:
337:
326:
317:
315:
314:moiré fringes
300:
296:
291:
287:
285:
281:
265:
253:
248:
239:
238:
230:
223:
218:
215:
212:
207:
203:
199:
195:
194:
192:
188:
184:
180:
176:
172:
169:
168:
167:
159:
157:
153:
148:
146:
142:
138:
134:
130:
126:
122:
118:
114:
109:
108:is enhanced.
107:
103:
99:
95:
91:
87:
83:
79:
69:
66:
58:
48:
44:
38:
37:
32:This article
30:
21:
20:
2146:
2126:Uncompressed
2115:
1970:
1966:
1942:
1922:
1896:
1892:
1849:
1845:
1814:
1776:
1772:
1743:
1739:
1706:
1700:
1659:
1653:
1640:
1596:
1590:
1568:(2): 47–57.
1565:
1561:
1531:(3): 21–36.
1528:
1524:
1511:
1473:
1469:
1444:
1406:
1400:
1363:
1357:
1324:
1318:
1302:. Springer.
1299:
1266:
1260:
1238:. Retrieved
1198:
1188:
1177:. Retrieved
1173:
1163:
1136:
1130:
1095:
1091:
1081:
1060:
1047:
1038:
1013:
1007:
959:
952:
941:
932:
923:
896:
892:
882:
873:
828:
824:
802:
761:
757:
740:
735:
727:
726:Fox M, 2007
722:
712:
707:
656:
652:
635:
626:
597:Oversampling
565:
556:space domain
547:pixel shifts
544:
535:
524:
476:
442:
438:
404:
380:
366:
332:
323:
310:
277:
262:January 2023
259:
251:
227:
221:
165:
149:
110:
101:
93:
81:
77:
76:
61:
55:October 2019
52:
33:
1804:10722/73871
423:hyperacuity
387:aberrations
214:Information
175:diffraction
147:algorithm.
145:periodogram
92:system. In
2154:Categories
2080:Deflicking
2063:Comparison
2053:Deblocking
1779:: 074585.
1409:(12): 14.
1208:1805.08841
1179:2023-08-28
1146:1711.06077
1072:1603.08155
666:1802.03070
618:References
572:microscope
527:algorithms
469:microscopy
377:Deblurring
340:super lens
233:Techniques
94:optical SR
86:resolution
2111:Film look
2075:Denoising
1854:CiteSeerX
1609:CiteSeerX
1122:2399-6528
1000:problems"
981:ℓ
977:−
968:ℓ
853:0003-6951
691:1053-587X
552:frequency
498:ℓ
494:−
485:ℓ
465:astronomy
419:nanoscale
2136:Telecine
2058:Resizing
1999:31973952
1913:21298404
1876:21135446
1760:16452552
1731:21403717
1684:17784605
1631:18255535
1582:12351561
1553:12320918
1490:12932769
1435:22011382
1388:16419839
1349:15455755
1291:20733840
1235:43919703
915:22634484
794:38041885
786:17794749
743:Springer
699:16276001
642:Li, Jian
586:See also
562:Research
531:aliasing
521:Aliasing
457:interval
453:function
407:centroid
129:subspace
111:In some
2170:Imaging
2100:tinting
2098: (
1990:8388823
1825:(ICCV).
1781:Bibcode
1711:Bibcode
1692:6367149
1664:Bibcode
1601:Bibcode
1533:Bibcode
1426:5144165
1368:Bibcode
1329:Bibcode
1271:Bibcode
1100:Bibcode
833:Bibcode
766:Bibcode
758:Science
671:Bibcode
413:, e.g.
383:defocus
252:updated
154:and in
123:(MRI),
90:imaging
41:Please
1997:
1987:
1911:
1884:184868
1882:
1874:
1856:
1758:
1729:
1690:
1682:
1629:
1611:
1580:
1551:
1488:
1470:Micron
1433:
1423:
1386:
1347:
1306:
1289:
1233:
1223:
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913:
851:
792:
784:
730:Oxford
697:
689:
302:image.
135:) and
88:of an
1927:(PDF)
1880:S2CID
1842:(PDF)
1819:(PDF)
1756:S2CID
1688:S2CID
1645:(PDF)
1578:S2CID
1549:S2CID
1516:(PDF)
1449:(PDF)
1240:1 May
1231:S2CID
1203:arXiv
1141:arXiv
1067:arXiv
790:S2CID
695:S2CID
661:arXiv
649:(PDF)
461:radar
299:moiré
133:MUSIC
117:sonar
113:radar
1995:PMID
1909:PMID
1872:PMID
1777:2007
1727:PMID
1680:PMID
1627:PMID
1486:PMID
1431:PMID
1384:PMID
1345:PMID
1304:ISBN
1287:PMID
1242:2022
1221:ISBN
1118:ISSN
911:PMID
849:ISSN
782:PMID
687:ISSN
141:SAMV
115:and
96:the
1985:PMC
1975:doi
1901:doi
1864:doi
1799:hdl
1789:doi
1748:doi
1719:doi
1672:doi
1619:doi
1570:doi
1541:doi
1478:doi
1457:doi
1421:PMC
1411:doi
1376:doi
1364:118
1337:doi
1279:doi
1213:doi
1151:doi
1108:doi
901:doi
841:doi
774:doi
762:257
679:doi
554:or
471:or
467:,
385:or
127:),
2156::
1993:.
1983:.
1971:46
1969:.
1965:.
1951:;
1945:.
1931:;
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1878:.
1870:.
1862:.
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1775:.
1771:.
1754:.
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1405:.
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1343:.
1335:.
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1172:.
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1116:.
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1090:.
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909:.
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861:^
847:.
839:.
829:66
827:.
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780:.
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748:^
693:.
685:.
677:.
669:.
657:61
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463:,
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342:.
286:.
193:.
158:.
82:SR
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2029:e
2022:t
2015:v
2001:.
1977::
1956:.
1949:.
1936:.
1915:.
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1886:.
1866::
1832:.
1807:.
1801::
1791::
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1762:.
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1733:.
1721::
1713::
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776::
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49:.
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