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Talk:Discrete wavelet transform

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Someone added {{dubious}} to the last section. That template expands to "see talk page" but it was empty when I got here. Someone with a knowledge of OCaml should confirm or deny the assertion that the OCaml code is not doing the right thing. Note that the OCaml code also appears as an example on
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According to Szeliski Book, chapter 3.5.4 wavelets produce one image that contains strong influence of vertical edges, and gradients, another in horizontal features and the last one in less frequent mixed derivatives, clearly the image has this three characteristics clearly splitted. I think that
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It would be helpful to have a simple diagram for IDWT, just like the existing diagrams for DWT. I came looking for hints on how to combine the different components back into the original image, but I was unable to find any. In the end, I found a nice diagram
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The university of bath has a selection of wavelet descriptions which I think would be interesting. Unfortunately, the use of them is not described well (at all). What do other people think about putting in a link?
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The OCaml code is pretty ugly and obscure, I reckon its causing more harm by being distracting than good, especially seeing as this is a math-based article, where pseudocode would be the
605: 573:"the second and third waves are translations of each other, corresponding to being 90° out of phase, like cosine and sine, of which these are discrete versions" 637:, a link to which already exists right next to the decomposition diagram. However, I think this is relevant enough that it should be included in this page. 676: 130: 671: 534:{\displaystyle {\frac {1}{2}}{\begin{bmatrix}1&1&1&1\\1&-i&-1&i\\1&-1&1&-1\\1&i&-1&-i\end{bmatrix}}.} 251:
The equations in this article are all discrete time, while the equations for discrete wavelets in the wavelet article are all continous time.
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and learned that I need to process each of the components with a filter, then sum the results together. This knowledge can also be found on
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Usually the opposite denotations are used (Mallat, Daubechies): G denotes high-pass filter and H stands for a low-pass one.
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appropriate form of representation. If you feel I am in error in deleting it, please give justification for reverting. --
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on the state of the wavelet articles. Nothing major has changed about this. -- This page as it is should be named „
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The following statement is correct for the removed matrix but not for the current. Or am I misstaken?
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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page, so if it (the OCaml code) turns out to be wrong, it should be changed there too. --
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It's either a mistake or a bad formulation, either cases need correction.
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http://fourier.eng.hmc.edu/e161/lectures/figures/wavelet_filterbank.gif
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http://www.bath.ac.uk/elec-eng/research/sipg/resource/warehouse.htm
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http://fourier.eng.hmc.edu/e161/lectures/wavelets/node7.html
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Lacking information about Inverse Discrete Wavelet Transform
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Wrong matrix in "Comparison with Fourier transform" section
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that photo description should include this information
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It's stated there that the basis of DFT in 4D-case is:
415: 399: 190:, a collaborative effort to improve the coverage of 101:, a collaborative effort to improve the coverage of 273:This is right. See my comments on the talk page at 533: 593:Description from the castle image could be better 566:Error arising from correcting matrix but not text 387:1 1 1 1 1 0 –1 0 0 1 0 –1 1 –1 1 –1 8: 19: 638: 599: 152: 47: 410: 400: 398: 154: 49: 7: 281:“ to account for its main content.-- 184:This article is within the scope of 95:This article is within the scope of 38:It is of interest to the following 360:Strange use of denotations G and H 14: 677:Mid-priority mathematics articles 333:University of Bath sipg warehouse 247:Inconsistent with Wavelet Article 115:Knowledge:WikiProject Mathematics 672:Start-Class mathematics articles 279:fast wavelet transform algorithm 177: 156: 118:Template:WikiProject Mathematics 82: 72: 51: 20: 224:This article has been rated as 135:This article has been rated as 560:17:04, 27 September 2011 (UTC) 315:Objective Caml code irrelevant 292:No discussion for disputed tag 286:08:46, 13 September 2007 (UTC) 267:02:41, 13 September 2007 (UTC) 1: 198:and see a list of open tasks. 109:and see a list of open tasks. 687:Low-importance Java articles 657:23:23, 14 January 2020 (UTC) 614:13:34, 9 February 2018 (UTC) 328:16:48, 28 October 2006 (UTC) 708: 355:02:04, 22 March 2008 (UTC) 230:project's importance scale 204:Knowledge:WikiProject Java 692:WikiProject Java articles 682:Start-Class Java articles 606:2A01:388:474:150:0:0:1:B8 585:14:43, 7 April 2015 (UTC) 374:21:54, 22 June 2010 (UTC) 310:14:12, 20 June 2006 (UTC) 223: 207:Template:WikiProject Java 172: 134: 67: 46: 141:project's priority scale 98:WikiProject Mathematics 535: 28:This article is rated 536: 397: 121:mathematics articles 531: 522: 90:Mathematics portal 34:content assessment 659: 643:comment added by 616: 604:comment added by 550:comment added by 408: 269: 257:comment added by 244: 243: 240: 239: 236: 235: 151: 150: 147: 146: 699: 562: 540: 538: 537: 532: 527: 526: 409: 401: 376:Spellbound_mipt 252: 212: 211: 208: 205: 202: 187:WikiProject Java 181: 174: 173: 168: 160: 153: 123: 122: 119: 116: 113: 92: 87: 86: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 707: 706: 702: 701: 700: 698: 697: 696: 662: 661: 622: 595: 577:129.247.247.240 568: 545: 521: 520: 512: 504: 499: 493: 492: 484: 479: 471: 465: 464: 459: 451: 443: 437: 436: 431: 426: 421: 411: 395: 394: 388: 382: 366:Spellbound mipt 362: 335: 317: 294: 249: 209: 206: 203: 200: 199: 166: 120: 117: 114: 111: 110: 88: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 705: 703: 695: 694: 689: 684: 679: 674: 664: 663: 629:on this page: 621: 618: 594: 591: 589: 567: 564: 542: 541: 530: 525: 519: 516: 513: 511: 508: 505: 503: 500: 498: 495: 494: 491: 488: 485: 483: 480: 478: 475: 472: 470: 467: 466: 463: 460: 458: 455: 452: 450: 447: 444: 442: 439: 438: 435: 432: 430: 427: 425: 422: 420: 417: 416: 414: 407: 404: 386: 381: 378: 361: 358: 334: 331: 316: 313: 293: 290: 289: 288: 248: 245: 242: 241: 238: 237: 234: 233: 226:Low-importance 222: 216: 215: 213: 196:the discussion 182: 170: 169: 167:Low‑importance 161: 149: 148: 145: 144: 133: 127: 126: 124: 107:the discussion 94: 93: 77: 65: 64: 56: 44: 43: 37: 26: 13: 10: 9: 6: 4: 3: 2: 704: 693: 690: 688: 685: 683: 680: 678: 675: 673: 670: 669: 667: 660: 658: 654: 650: 646: 642: 636: 632: 628: 619: 617: 615: 611: 607: 603: 592: 590: 587: 586: 582: 578: 574: 571: 565: 563: 561: 557: 553: 549: 528: 523: 517: 514: 509: 506: 501: 496: 489: 486: 481: 476: 473: 468: 461: 456: 453: 448: 445: 440: 433: 428: 423: 418: 412: 405: 402: 393: 392: 391: 390:Wrong, it's: 385: 379: 377: 375: 371: 367: 359: 357: 356: 352: 348: 344: 343: 339: 332: 330: 329: 326: 322: 314: 312: 311: 308: 304: 300: 291: 287: 284: 280: 276: 272: 271: 270: 268: 264: 260: 259:70.225.81.131 256: 246: 231: 227: 221: 218: 217: 214: 210:Java articles 197: 193: 189: 188: 183: 180: 176: 175: 171: 165: 162: 159: 155: 142: 138: 132: 129: 128: 125: 108: 104: 100: 99: 91: 85: 80: 78: 75: 71: 70: 66: 60: 57: 54: 50: 45: 41: 35: 27: 23: 18: 17: 639:— Preceding 623: 600:— Preceding 596: 588: 575: 572: 569: 546:— Preceding 543: 389: 383: 363: 347:82.24.171.88 345: 340: 336: 320: 318: 295: 278: 250: 225: 185: 137:Mid-priority 136: 96: 62:Mid‑priority 40:WikiProjects 635:Filter_bank 552:91.79.31.66 303:Steve Pucci 253:—Preceding 112:Mathematics 103:mathematics 59:Mathematics 30:Start-class 666:Categories 653:contribs 641:unsigned 602:unsigned 548:unsigned 325:Dreddlox 255:unsigned 275:wavelet 228:on the 139:on the 645:Mraagh 36:scale. 299:OCaml 283:LutzL 649:talk 610:talk 581:talk 556:talk 370:talk 351:talk 321:most 307:talk 297:the 263:talk 201:Java 192:Java 164:Java 220:Low 131:Mid 668:: 655:) 651:• 612:) 583:) 558:) 515:− 507:− 487:− 474:− 454:− 446:− 372:) 353:) 305:| 265:) 647:( 608:( 579:( 554:( 529:. 524:] 518:i 510:1 502:i 497:1 490:1 482:1 477:1 469:1 462:i 457:1 449:i 441:1 434:1 429:1 424:1 419:1 413:[ 406:2 403:1 368:( 349:( 261:( 232:. 143:. 42::

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70.225.81.131
talk
02:41, 13 September 2007 (UTC)
wavelet
LutzL
08:46, 13 September 2007 (UTC)
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Steve Pucci

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