Respiratory Motion Correction for Compressively Sampled Free Breathing Cardiac MRI Using Smooth <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.199599pt" id="M1" height="16.4602pt" version="1.1" viewBox="-0.0657574 -12.2606 10.8635 16.4602" width="10.8635pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-109" d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z"/></g><g transform="matrix(.012,0,0,-0.012,4.187,4.134)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g></svg>-Norm Approximation

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:10.12em"/><col style="width:9.17em"/><col style="width:9.13em"/><col style="width:8.96em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Technique</td><td class="align_center">Diastolic (frame #1)</td><td class="align_center">Systolic (frame #10)</td><td class="align_center">Middle (frame #13)</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">The proposed method</td><td class="align_center">0.001</td><td class="align_center"><span style="width: 59.5279ptpx;"><svg height="8.69875pt" id="M135" style="vertical-align:-0.3499298pt" version="1.1" viewbox="-0.0498162 -8.34882 59.5279 8.69875" width="59.5279pt" 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="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M447 623H65C61 580 56 530 47 475H76C100 541 106 550 172 550H388C308 376 196 170 91 -1L98 -12L172 -2C268 204 360 408 455 611L447 623Z" id="g113-56"></path></g><g transform="matrix(.013,0,0,-0.013,15.446,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" 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id="g113-49"></path></g><g transform="matrix(.013,0,0,-0.013,34.168,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z" id="g113-102"></path></g><g transform="matrix(.013,0,0,-0.013,42.456,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path></g><g transform="matrix(.013,0,0,-0.013,52.992,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path></g></svg></span></td></tr><tr><td class="align_left"><i>k-t</i> FOCUSS</td><td class="align_center">0.002</td><td class="align_center"><span style="width: 59.5279ptpx;"><svg height="8.69875pt" id="M137" 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class="tbody-hr"/></td></tr></table></td></tr></table>

<div>MSE comparison for the proposed method and <i>k-t</i> FOCUSS with MEMC.</div>

International Journal of Biomedical Imaging

tab3

Table 3

Table 3: Respiratory Motion Correction for Compressively Sampled Free Breathing Cardiac MRI Using Smooth <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.199599pt" id="M1" height="16.4602pt" version="1.1" viewBox="-0.0657574 -12.2606 10.8635 16.4602" width="10.8635pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-109" d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z"/></g><g transform="matrix(.012,0,0,-0.012,4.187,4.134)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g></svg>-Norm Approximation 

International Journal of Biomedical Imaging

Respiratory Motion Correction for Compressively Sampled Free Breathing Cardiac MRI Using Smooth -Norm Approximation

Table 3