The EM Method in a Probabilistic Wavelet-Based MRI Denoising

<div>Comparative results for the different filtering methods in experiment 2 with number of averaged images NEX <svg height="11.4781pt" id="M263" style="vertical-align:-2.18977pt" version="1.1" viewbox="-0.0498162 -9.28833 56.7398 11.4781" width="56.7398pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M496 -1V52H376C259 52 161 132 147 236H496V289H147C162 392 259 473 376 473H496V526H374C213 526 83 408 83 262S213 -1 374 -1H496Z" id="g54-173"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="579" vert-adv-y="579"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.202,0)"><path d="M300 -169V-136C225 -126 216 -88 216 -42C216 19 230 84 230 152C230 207 206 255 147 268V272C206 286 230 333 230 388C230 453 216 523 216 586C216 630 225 667 300 677V710C239 710 151 696 151 579C152 514 160 438 160 373C160 338 157 293 68 287V253C157 247 160 202 160 168C159 106 151 32 151 -41C151 -157 239 -169 300 -169ZM181 710H180H181ZM181 -186H180H181Z" id="g50-124"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="360" vert-adv-y="360"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,15.882,0)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.214,0)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,27.5,0)"><path d="M253 635C142 635 71 555 71 471C71 401 113 353 178 316C144 294 106 267 91 252C70 231 46 202 46 157C46 51 132 -12 241 -12C328 -12 442 52 442 168C442 257 379 305 311 343C354 373 380 398 388 407C406 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 563 340 481C340 423 313 387 279 360C207 394 148 427 148 499C148 549 182 600 240 600ZM252 23C188 23 129 73 129 163C129 217 162 266 211 298C289 260 360 217 360 144C360 69 312 23 252 23Z" id="g50-57"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,33.831,0)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,39.117,0)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,45.448,0)"><path d="M141 347C171 480 264 541 327 570C364 587 403 599 436 605L429 641C389 634 339 622 300 609C191 570 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 380 397 272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z" id="g50-55"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,51.779,0)"><path d="M292 253V287C203 293 200 339 200 376C201 435 209 507 209 582C209 697 123 710 60 710V677C133 667 144 631 144 586C144 523 130 452 130 388C130 334 154 286 214 272V268C154 254 130 206 130 152C130 89 144 17 144 -45C144 -89 133 -126 60 -136V-169C121 -169 209 -154 209 -42C208 33 200 106 200 164C200 201 203 247 292 253Z" id="g50-126"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="360" vert-adv-y="360"></glyph.data></g></svg>.</div>

Computational and Mathematical Methods in Medicine

The EM Method in a Probabilistic Wavelet-Based MRI Denoising

Figure 8