20:
49:. It replaces the intensity of each pixel with a weighted average of intensity values from nearby pixels. This weight can be based on a Gaussian distribution. Crucially, the weights depend not only on Euclidean distance of pixels, but also on the radiometric differences (e.g., range differences, such as color intensity, depth distance, etc.). This preserves sharp edges.
1097:
253:
437:
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1445:
increases, the bilateral filter gradually approaches
Gaussian convolution more closely because the range Gaussian widens and flattens, which means that it becomes nearly constant over the intensity interval of the
876:
1870:
Farbman, Zeev, Raanan Fattal, Dani
Lischinski, and Richard Szeliski. "Edge-preserving decompositions for multi-scale tone and detail manipulation." In ACM Transactions on Graphics, vol. 27, no. 3 (2008): 67.
1833:
R. Kimmel, R. Malladi, and N. Sochen. Images as
Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images. International Journal of Computer Vision, 39(2):111-129, Sept. 2000.
63:
1473:
There exist several extensions to the filter that deal with these artifacts, like the scaled bilateral filter that uses downscaled image for computing the weights. Alternative filters, like the
1821:
R. Kimmel, R. Malladi, and N. Sochen. Images as embedding maps and minimal surfaces: Movies, color, and volumetric medical images. IEEE CVPR'97, pp. 350-355, Puerto Rico, June 17–19, 1997.
470:
589:
1895:
Criminisi, Antonio, Toby Sharp, Carsten Rother, and
Patrick Pérez. "Geodesic image and video editing." In ACM Transactions on Graphphics (TOG), vol. 29, no. 5 (2010): 134.
1926:
Gastal, Eduardo S. L., and Manuel M. Oliveira. "Domain transform for edge-aware image and video processing." In ACM Transactions on
Graphics, vol. 30, no. 4 (2011): 69.
1858:
Durand, Frédo and Dorsey, Julie. "Fast
Bilateral Filtering for the Display of High-Dynamic-Range Images" In ACM Transactions on Graphics, Volume 21, Issue 3, pp 257–266.
536:
285:
1846:
N. Sochen, R. Kimmel, and A.M. Bruckstein. Diffusions and confusions in signal and image processing, Journal of
Mathematical Imaging and Vision, 14(3):195-209, 2001.
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2082:
1092:{\displaystyle w(i,j,k,l)=\exp \left(-{\frac {(i-k)^{2}+(j-l)^{2}}{2\sigma _{d}^{2}}}-{\frac {\|I(i,j)-I(k,l)\|^{2}}{2\sigma _{r}^{2}}}\right),}
2249:
1749:
1907:
He, Kaiming, Jian Sun, and Xiaoou Tang. "Guided image filtering." In
Computer Vision–ECCV 2010, pp. 1-14. Springer Berlin Heidelberg, 2010.
2586:
2443:
2325:
2239:
248:{\displaystyle I^{\text{filtered}}(x)={\frac {1}{W_{p}}}\sum _{x_{i}\in \Omega }I(x_{i})f_{r}(\|I(x_{i})-I(x)\|)g_{s}(\|x_{i}-x\|),}
1732:
Aswatha, Shashaank M.; Mukhopadhyay, Jayanta; Bhowmick, Partha (December 2011). "Image
Denoising by Scaled Bilateral Filtering".
1633:
2580:
2428:
2279:
1957:
1883:
Fattal, Raanan. "Edge-avoiding wavelets and their applications." In ACM Transactions on
Graphics vol. 28, no. 3 (2009): 22.
2113:
2489:
2396:
1700:
2244:
1966:
653:
is the spatial (or domain) kernel for smoothing differences in coordinates (this function can be a Gaussian function).
1911:
1774:
2169:
770:
that needs to be denoised in image using its neighbouring pixels and one of its neighbouring pixels is located at
2539:
2062:
1536:
36:
46:
1543:, weighted least squares, edge-avoiding wavelets, geodesic editing, guided filtering, and domain transforms.
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448:
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561:
2474:
1991:
1801:"G'MIC - GREYC's Magic for Image Computing: An Open and Full-Featured Framework for Image Processing"
1734:
2011 Third National Conference on Computer Vision, Pattern Recognition, Image Processing and Graphics
1532:
that was introduced as an edge preserving selective smoothing mechanism before the bilateral filter.
2234:
2229:
2047:
1950:
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1896:
1592:"A Low-Memory, Straightforward and Fast Bilateral Filter Through Subsampling in Spatial Domain"
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2016:
2001:
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adds more control. A simple trick to efficiently implement a bilateral filter is to exploit
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2011:
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432:{\displaystyle W_{p}=\sum _{x_{i}\in \Omega }{f_{r}(\|I(x_{i})-I(x)\|)g_{s}(\|x_{i}-x\|)}}
40:
1935:
1528:
The bilateral filter has been shown to be an application of the short time kernel of the
1462:
The bilateral filter in its direct form can introduce several types of image artifacts:
1363:{\displaystyle I_{D}(i,j)={\frac {\sum _{k,l}I(k,l)w(i,j,k,l)}{\sum _{k,l}w(i,j,k,l)}},}
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1996:
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is the range kernel for smoothing differences in intensities (this function can be a
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2139:
1591:
1927:
1884:
1477:, have also been proposed as an efficient alternative without these limitations.
1466:
Staircase effect – intensity plateaus that lead to images appearing like cartoons
2591:
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2264:
2199:
2191:
2134:
2067:
2006:
1676:"Limitations? - A Gentle Introductionto Bilateral Filteringand its Applications"
1567:
1641:. Sixth International Conference on Computer Vision. Bombay. pp. 839–846.
19:
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1986:
32:
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43:
1908:
1860:
https://people.csail.mit.edu/fredo/PUBLI/Siggraph2002/DurandBilateral.pdf
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1505:
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684:
is assigned using the spatial closeness (using the spatial kernel
23:
Left: original image. Right: image processed with bilateral filter
1848:
https://www.cs.technion.ac.il/~ron/PAPERS/SocKimBru_JMIV2001.pdf
1836:
https://www.cs.technion.ac.il/~ron/PAPERS/KimMalSoc_IJCV2000.pdf
1513:
1493:
1939:
1897:
http://research.microsoft.com/apps/pubs/default.aspx?id=81528
1590:
Banterle, F.; Corsini, M.; Cignoni, P.; Scopigno, R. (2011).
1469:
Gradient reversal – introduction of false edges in the image.
1808:
516:
are the coordinates of the current pixel to be filtered;
711:) and the intensity difference (using the range kernel
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1379:
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1172:
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879:
844:
812:
802:. Then, assuming the range and spatial kernels to be
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https://www.cs.technion.ac.il/~ron/PAPERS/cvpr97.pdf
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1928:http://inf.ufrgs.br/~eslgastal/DomainTransform/
1885:http://www.cs.huji.ac.il/~raananf/projects/eaw/
1201:After calculating the weights, normalize them:
1453:increases, the larger features get smoothened.
1951:
1635:Bilateral filtering for gray and color images
8:
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1006:
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494:is the original input image to be filtered;
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18:
2434:Signal-to-interference-plus-noise ratio
1579:
2250:Equivalent pulse code modulation noise
1909:http://kaiminghe.com/eccv10/index.html
1699:He, Kaiming; Sun, Jian; Tang, Xiaoou.
1496:implements a bilateral filter in its
1488:implements a bilateral filter in its
7:
2373:(energy per symbol to noise density)
1873:http://www.cs.huji.ac.il/~danix/epd/
1400:is the denoised intensity of pixel
465:{\displaystyle I^{\text{filtered}}}
57:The bilateral filter is defined as
2444:Signal-to-quantization-noise ratio
578:
525:
328:
124:
14:
2358:(energy per bit to noise density)
2326:Carrier-to-receiver noise density
2240:Effective input noise temperature
2623:Image noise reduction techniques
1969:(physics and telecommunications)
1608:10.1111/j.1467-8659.2011.02078.x
806:, the weight assigned for pixel
584:{\displaystyle x_{i}\in \Omega }
2581:Block-matching and 3D filtering
2429:Signal-to-noise ratio (imaging)
2280:Noise, vibration, and harshness
1632:Tomasi, C; Manduchi, R (1998).
738:). Consider a pixel located at
1419:
1407:
1351:
1327:
1303:
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1273:
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1134:) are the intensity of pixels
1110:are smoothing parameters, and
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1:
2114:Additive white Gaussian noise
2490:Interference (communication)
2397:Signal-to-interference ratio
2387:Signal, noise and distortion
2245:Equivalent noise resistance
1674:Kornprobst, Pierre (2007).
16:Smoothing filler for images
2639:
1449:As the spatial parameter σ
538:is the window centered in
2540:Total variation denoising
1537:edge-preserving smoothing
1775:"Guided Image Filtering"
1742:10.1109/NCVPRIPG.2011.33
1701:"Guided Image Filtering"
1647:10.1109/ICCV.1998.710815
1518:Poisson-disk subsampling
1500:tools; and it is called
1441:As the range parameter σ
258:and normalization term,
2454:Contrast-to-noise ratio
1596:Computer Graphics Forum
1502:Selective Gaussian Blur
531:{\displaystyle \Omega }
280:{\displaystyle {W_{p}}}
2377:Modulation error ratio
2312:Carrier-to-noise ratio
2275:Noise spectral density
1426:
1394:
1364:
1192:
1160:
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864:
832:
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678:
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614:
585:
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510:
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472:is the filtered image;
466:
433:
281:
249:
24:
2592:Denoising autoencoder
2566:Anisotropic diffusion
2411:Signal-to-noise ratio
2255:Impulse noise (audio)
2170:Johnson–Nyquist noise
2058:Government regulation
1541:anisotropic diffusion
1427:
1425:{\displaystyle (i,j)}
1395:
1393:{\displaystyle I_{D}}
1365:
1193:
1191:{\displaystyle (k,l)}
1161:
1159:{\displaystyle (i,j)}
1094:
865:
863:{\displaystyle (i,j)}
838:to denoise the pixel
833:
831:{\displaystyle (k,l)}
797:
795:{\displaystyle (k,l)}
765:
763:{\displaystyle (i,j)}
733:
731:{\displaystyle f_{r}}
706:
704:{\displaystyle g_{s}}
679:
677:{\displaystyle W_{p}}
648:
646:{\displaystyle g_{s}}
615:
613:{\displaystyle f_{r}}
586:
553:
533:
511:
489:
467:
434:
282:
250:
22:
2475:List of noise topics
1736:. pp. 122–125.
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294:
262:
64:
2235:Circuit noise level
2230:Channel noise level
1781:on 19 December 2017
1077:
996:
2291:Pseudorandom noise
2181:Quantization error
1992:Noise cancellation
1914:2017-12-19 at the
1713:on 9 December 2017
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484:
462:
429:
332:
277:
245:
128:
25:
2610:
2609:
2606:
2605:
2545:Wavelet denoising
2505:Thermal radiation
2500:Spectrum analyzer
2296:Statistical noise
2120:Atmospheric noise
2017:Noise temperature
2002:Noise measurement
1982:Acoustic quieting
1751:978-1-4577-2102-1
1558:Gaussian function
1539:filters include:
1355:
1308:
1242:
1079:
998:
622:Gaussian function
591:is another pixel;
551:{\displaystyle x}
509:{\displaystyle x}
487:{\displaystyle I}
459:
310:
106:
104:
74:
47:filter for images
2630:
2598:Deep Image Prior
2587:Shrinkage Fields
2571:Bilateral filter
2520:
2125:Background noise
2022:Phase distortion
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1807:. Archived from
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1777:. Archived from
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1706:. Archived from
1705:
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1680:
1671:
1665:
1664:
1662:
1661:
1655:
1649:. Archived from
1640:
1629:
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1587:
1510:Repair → Smooth
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804:Gaussian kernels
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29:bilateral filter
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2576:Non-local means
2549:
2530:Low-pass filter
2515:
2509:
2495:Noise generator
2485:Colors of noise
2463:
2370:
2366:
2355:
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2300:
2222:
2216:
2196:Coherent noise
2172:(thermal noise)
2102:
2026:
2012:Noise reduction
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1916:Wayback Machine
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1553:Gaussian filter
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1486:Adobe Photoshop
1483:
1481:Implementations
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37:edge-preserving
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2468:Related topics
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2205:Gradient noise
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2150:Gaussian noise
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2130:Brownian noise
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2107:Class of noise
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2093:Transportation
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1811:on 2014-12-27.
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1571:
1570:
1565:
1560:
1555:
1548:
1545:
1525:
1524:Related models
1522:
1498:Filters → Blur
1482:
1479:
1471:
1470:
1467:
1459:
1456:
1455:
1454:
1450:
1447:
1442:
1437:
1434:
1421:
1418:
1415:
1412:
1409:
1387:
1383:
1371:
1370:
1359:
1353:
1350:
1347:
1344:
1341:
1338:
1335:
1332:
1329:
1326:
1321:
1318:
1315:
1311:
1305:
1302:
1299:
1296:
1293:
1290:
1287:
1284:
1281:
1278:
1275:
1272:
1269:
1266:
1263:
1260:
1255:
1252:
1249:
1245:
1238:
1235:
1232:
1229:
1226:
1223:
1218:
1214:
1198:respectively.
1187:
1184:
1181:
1178:
1175:
1155:
1152:
1149:
1146:
1143:
1107:
1103:
1100:
1099:
1088:
1084:
1075:
1070:
1066:
1062:
1055:
1051:
1047:
1044:
1041:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1011:
1008:
1002:
994:
989:
985:
981:
974:
970:
966:
963:
960:
957:
954:
949:
945:
941:
938:
935:
932:
926:
922:
918:
915:
912:
909:
906:
903:
900:
897:
894:
891:
888:
885:
882:
859:
856:
853:
850:
847:
827:
824:
821:
818:
815:
791:
788:
785:
782:
779:
759:
756:
753:
750:
747:
725:
721:
698:
694:
671:
667:
655:
654:
640:
636:
625:
607:
603:
592:
580:
577:
572:
568:
547:
527:
517:
505:
495:
483:
473:
455:
440:
439:
427:
424:
421:
418:
413:
409:
405:
402:
397:
393:
389:
386:
383:
380:
377:
374:
371:
368:
363:
359:
355:
352:
349:
346:
341:
337:
330:
327:
322:
318:
313:
309:
304:
300:
273:
269:
256:
255:
244:
241:
238:
235:
232:
227:
223:
219:
216:
211:
207:
203:
200:
197:
194:
191:
188:
185:
182:
177:
173:
169:
166:
163:
160:
155:
151:
147:
142:
138:
134:
131:
126:
123:
118:
114:
109:
101:
97:
93:
88:
85:
82:
79:
70:
54:
51:
41:noise-reducing
15:
13:
10:
9:
6:
4:
3:
2:
2635:
2624:
2621:
2620:
2618:
2599:
2596:
2593:
2590:
2588:
2585:
2582:
2579:
2577:
2574:
2572:
2569:
2567:
2564:
2562:
2561:Gaussian blur
2559:
2558:
2556:
2552:
2546:
2543:
2541:
2538:
2536:
2535:Median filter
2533:
2531:
2528:
2527:
2525:
2521:
2518:
2512:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2481:
2478:
2476:
2473:
2472:
2470:
2466:
2459:
2455:
2452:
2449:
2445:
2442:
2439:
2435:
2432:
2430:
2427:
2424:
2420:
2416:
2412:
2409:
2406:
2402:
2398:
2395:
2392:
2388:
2385:
2382:
2378:
2375:
2372:
2371:
2360:
2357:
2356:
2345:
2343:
2342:
2338:
2335:
2331:
2327:
2324:
2321:
2317:
2313:
2310:
2309:
2307:
2303:
2297:
2294:
2292:
2289:
2287:
2284:
2281:
2278:
2276:
2273:
2271:
2270:Noise shaping
2268:
2266:
2263:
2261:
2258:
2256:
2253:
2251:
2248:
2246:
2243:
2241:
2238:
2236:
2233:
2231:
2228:
2227:
2225:
2219:
2211:
2208:
2206:
2203:
2201:
2198:
2197:
2195:
2193:
2190:
2188:
2185:
2183:(or q. noise)
2182:
2179:
2177:
2174:
2171:
2168:
2166:
2163:
2161:
2158:
2156:
2153:
2151:
2148:
2146:
2145:Flicker noise
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2126:
2123:
2121:
2118:
2115:
2112:
2111:
2109:
2105:
2099:
2096:
2094:
2091:
2089:
2088:Sound masking
2086:
2084:
2081:
2079:
2076:
2074:
2071:
2069:
2066:
2064:
2061:
2059:
2056:
2054:
2051:
2049:
2046:
2044:
2041:
2039:
2036:
2035:
2033:
2029:
2023:
2020:
2018:
2015:
2013:
2010:
2008:
2005:
2003:
2000:
1998:
1997:Noise control
1995:
1993:
1990:
1988:
1985:
1983:
1980:
1979:
1977:
1973:
1968:
1961:
1956:
1954:
1949:
1947:
1942:
1941:
1938:
1929:
1923:
1920:
1917:
1913:
1910:
1904:
1901:
1898:
1892:
1889:
1886:
1880:
1877:
1874:
1867:
1864:
1861:
1855:
1852:
1849:
1843:
1840:
1837:
1830:
1827:
1824:
1818:
1815:
1810:
1806:
1802:
1796:
1793:
1780:
1776:
1773:He, Kaiming.
1769:
1766:
1761:
1757:
1753:
1747:
1743:
1739:
1735:
1728:
1725:
1709:
1702:
1695:
1692:
1677:
1670:
1667:
1656:on 2008-08-29
1652:
1648:
1644:
1637:
1636:
1628:
1626:
1622:
1617:
1613:
1609:
1605:
1601:
1597:
1593:
1586:
1584:
1580:
1573:
1569:
1566:
1564:
1563:Gaussian blur
1561:
1559:
1556:
1554:
1551:
1550:
1546:
1544:
1542:
1538:
1533:
1531:
1530:Beltrami flow
1523:
1521:
1519:
1515:
1511:
1507:
1503:
1499:
1495:
1491:
1487:
1480:
1478:
1476:
1475:guided filter
1468:
1465:
1464:
1463:
1457:
1448:
1440:
1439:
1435:
1433:
1416:
1413:
1410:
1385:
1381:
1357:
1348:
1345:
1342:
1339:
1336:
1333:
1330:
1324:
1319:
1316:
1313:
1309:
1300:
1297:
1294:
1291:
1288:
1285:
1282:
1276:
1270:
1267:
1264:
1258:
1253:
1250:
1247:
1243:
1236:
1230:
1227:
1224:
1216:
1212:
1204:
1203:
1202:
1199:
1182:
1179:
1176:
1150:
1147:
1144:
1133:
1129:
1125:
1121:
1117:
1113:
1086:
1082:
1073:
1068:
1064:
1060:
1053:
1042:
1039:
1036:
1030:
1027:
1021:
1018:
1015:
1009:
1000:
992:
987:
983:
979:
972:
964:
961:
958:
952:
947:
939:
936:
933:
924:
920:
916:
913:
910:
904:
901:
898:
895:
892:
889:
886:
880:
873:
872:
871:
854:
851:
848:
822:
819:
816:
805:
786:
783:
780:
754:
751:
748:
723:
719:
696:
692:
669:
665:
638:
634:
626:
623:
605:
601:
593:
575:
570:
566:
545:
518:
503:
496:
481:
474:
453:
445:
444:
443:
419:
416:
411:
407:
395:
391:
378:
372:
369:
361:
357:
350:
339:
335:
325:
320:
316:
311:
307:
302:
298:
290:
289:
288:
271:
267:
242:
233:
230:
225:
221:
209:
205:
192:
186:
183:
175:
171:
164:
153:
149:
140:
136:
129:
121:
116:
112:
107:
99:
95:
91:
86:
80:
68:
60:
59:
58:
52:
50:
48:
45:
42:
38:
34:
30:
21:
2570:
2457:
2447:
2437:
2422:
2418:
2414:
2404:
2400:
2390:
2380:
2361:
2346:
2339:
2333:
2329:
2319:
2315:
2260:Noise figure
2221:Engineering
2210:Worley noise
2140:Cosmic noise
2063:Human health
1922:
1903:
1891:
1879:
1866:
1854:
1842:
1829:
1817:
1809:the original
1804:
1795:
1783:. Retrieved
1779:the original
1768:
1733:
1727:
1715:. Retrieved
1708:the original
1694:
1682:. Retrieved
1669:
1658:. Retrieved
1651:the original
1634:
1602:(1): 19–32.
1599:
1595:
1534:
1527:
1509:
1501:
1497:
1490:surface blur
1489:
1484:
1474:
1472:
1461:
1372:
1200:
1131:
1127:
1123:
1119:
1115:
1111:
1101:
870:is given by
656:
441:
257:
56:
28:
26:
2286:Phase noise
2265:Noise floor
2200:Value noise
2192:White noise
2135:Burst noise
2053:Environment
2048:Electronics
2031:Noise in...
2007:Noise power
1568:Convolution
1504:. The free
1458:Limitations
657:The weight
2554:2D (Image)
2187:Shot noise
2176:Pink noise
2160:Infrasound
2155:Grey noise
1987:Distortion
1660:2009-11-18
1574:References
1436:Parameters
53:Definition
33:non-linear
2480:Acoustics
2043:Buildings
1310:∑
1244:∑
1065:σ
1050:‖
1028:−
1007:‖
1001:−
984:σ
962:−
937:−
925:−
917:
579:Ω
576:∈
526:Ω
423:‖
417:−
404:‖
385:‖
370:−
348:‖
329:Ω
326:∈
312:∑
237:‖
231:−
218:‖
199:‖
184:−
162:‖
125:Ω
122:∈
108:∑
44:smoothing
2617:Category
2514:Denoise
1912:Archived
1760:25738863
1616:18288647
1547:See also
458:filtered
73:filtered
2523:General
2516:methods
2421:,
1975:General
1805:gmic.eu
1508:plugin
1102:where σ
2583:(BM3D)
2305:Ratios
2165:Jitter
2116:(AWGN)
2068:Images
1758:
1748:
1614:
1535:Other
1492:tool.
1446:image.
1373:where
1122:) and
442:where
39:, and
2594:(DAE)
2391:SINAD
2341:dBrnC
2282:(NVH)
2223:terms
2098:Video
2083:Ships
2078:Rooms
2073:Radio
2038:Audio
1967:Noise
1785:7 May
1756:S2CID
1717:7 May
1711:(PDF)
1704:(PDF)
1684:7 May
1679:(PDF)
1654:(PDF)
1639:(PDF)
1612:S2CID
1506:G'MIC
1106:and σ
558:, so
31:is a
2448:SQNR
2438:SINR
1787:2017
1746:ISBN
1719:2017
1686:2017
1514:GIMP
1512:for
1494:GIMP
1166:and
2458:CNR
2423:SNR
2381:MER
1738:doi
1643:doi
1604:doi
914:exp
2619::
2367:/N
2352:/N
2334:kT
1803:.
1754:.
1744:.
1624:^
1610:.
1600:31
1598:.
1594:.
1582:^
1520:.
1432:.
1130:,
1118:,
624:);
35:,
27:A
2460:)
2456:(
2450:)
2446:(
2440:)
2436:(
2425:)
2419:N
2417:/
2415:S
2413:(
2407:)
2405:I
2403:/
2401:S
2399:(
2393:)
2389:(
2383:)
2379:(
2369:0
2365:s
2363:E
2354:0
2350:b
2348:E
2336:)
2332:/
2330:C
2328:(
2322:)
2320:N
2318:/
2316:C
2314:(
1959:e
1952:t
1945:v
1789:.
1762:.
1740::
1721:.
1688:.
1663:.
1645::
1618:.
1606::
1451:d
1443:r
1420:)
1417:j
1414:,
1411:i
1408:(
1386:D
1382:I
1358:,
1352:)
1349:l
1346:,
1343:k
1340:,
1337:j
1334:,
1331:i
1328:(
1325:w
1320:l
1317:,
1314:k
1304:)
1301:l
1298:,
1295:k
1292:,
1289:j
1286:,
1283:i
1280:(
1277:w
1274:)
1271:l
1268:,
1265:k
1262:(
1259:I
1254:l
1251:,
1248:k
1237:=
1234:)
1231:j
1228:,
1225:i
1222:(
1217:D
1213:I
1186:)
1183:l
1180:,
1177:k
1174:(
1154:)
1151:j
1148:,
1145:i
1142:(
1132:l
1128:k
1126:(
1124:I
1120:j
1116:i
1114:(
1112:I
1108:r
1104:d
1087:,
1083:)
1074:2
1069:r
1061:2
1054:2
1046:)
1043:l
1040:,
1037:k
1034:(
1031:I
1025:)
1022:j
1019:,
1016:i
1013:(
1010:I
993:2
988:d
980:2
973:2
969:)
965:l
959:j
956:(
953:+
948:2
944:)
940:k
934:i
931:(
921:(
911:=
908:)
905:l
902:,
899:k
896:,
893:j
890:,
887:i
884:(
881:w
858:)
855:j
852:,
849:i
846:(
826:)
823:l
820:,
817:k
814:(
790:)
787:l
784:,
781:k
778:(
758:)
755:j
752:,
749:i
746:(
724:r
720:f
697:s
693:g
670:p
666:W
639:s
635:g
606:r
602:f
571:i
567:x
546:x
504:x
482:I
454:I
426:)
420:x
412:i
408:x
401:(
396:s
392:g
388:)
382:)
379:x
376:(
373:I
367:)
362:i
358:x
354:(
351:I
345:(
340:r
336:f
321:i
317:x
308:=
303:p
299:W
272:p
268:W
243:,
240:)
234:x
226:i
222:x
215:(
210:s
206:g
202:)
196:)
193:x
190:(
187:I
181:)
176:i
172:x
168:(
165:I
159:(
154:r
150:f
146:)
141:i
137:x
133:(
130:I
117:i
113:x
100:p
96:W
92:1
87:=
84:)
81:x
78:(
69:I
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