A New Smoothed L0 Regularization Approach for Sparse Signal Recovery

<table class="fixed-width table-group" id="tab5"><tr><td><table class="table"><colgroup><col style="width:9.29em"/><col style="width:4.36em"/><col style="width:4.38em"/><col style="width:4.34em"/><col style="width:4.44em"/><col style="width:4.31em"/></colgroup><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Noise intensity (<span class="nowrap"><svg height="12.5794pt" id="M428" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 14.8 12.5794" width="14.8pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.396,3.132)"><path d="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z"></path></g></svg>)</span></td><td class="align_center" colspan="5">PSNR of Barbara image recovery</td></tr><tr class="thead"><td class="align_center">BPDN </td><td class="align_center">SL0 </td><td class="align_center">L2-SL0 </td><td class="align_center"><span class="nowrap"><svg height="14.1101pt" id="M429" style="vertical-align:-5.4742pt" version="1.1" viewbox="-0.0498162 -8.6359 14.3759 14.1101" width="14.3759pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 415C194 400 159 383 126 359L131 330C159 344 187 357 222 368L109 -147C96 -204 80 -214 18 -223L13 -255L256 -244L259 -212L236 -210C184 -205 180 -195 191 -141L219 -1C240 -10 268 -12 284 -12C352 4 431 48 484 104C543 166 573 240 573 302ZM481 290C481 165 381 37 305 37C280 37 249 56 235 71L302 395C328 399 353 402 372 402C427 402 481 378 481 290Z"></path></g></svg>-</span>RLS </td><td class="align_center">RRSL0 </td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">0</td><td class="align_center"> 28.6613</td><td class="align_center"> 29.5761</td><td class="align_center"> 31.7921</td><td class="align_center"> 32.3566</td><td class="align_center"> 33.4074</td></tr><tr><td class="align_left">0.01</td><td class="align_center"> 27.7887</td><td class="align_center"> 30.4746</td><td class="align_center"> 30.9875</td><td class="align_center"> 31.7365</td><td class="align_center"> 32.6767</td></tr><tr><td class="align_left">0.05</td><td class="align_center"> 26.0316</td><td class="align_center"> 26.1561</td><td class="align_center"> 26.3147</td><td class="align_center"> 27.3533</td><td class="align_center"> 29.8613</td></tr><tr><td class="align_left">0.1</td><td class="align_center"> 20.7076</td><td class="align_center"> 21.6914</td><td class="align_center"> 23.8343</td><td class="align_center"> 26.9408</td><td class="align_center"> 27.5167</td></tr><tr><td class="align_left">0.2</td><td class="align_center"> 16.6564</td><td class="align_center"> 16.6721</td><td class="align_center"> 19.1297</td><td class="align_center"> 19.2624</td><td class="align_center"> 19.7801</td></tr><tr><td class="align_left">0.5</td><td class="align_center"> 9.1316</td><td class="align_center"> 9.3525</td><td class="align_center"> 13.1838</td><td class="align_center"> 15.7972</td><td class="align_center"> 16.9070</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>PSNR analysis of recovered Barbara image by BPDN, SL0, L2-SL0, <span class="nowrap"><svg height="14.1101pt" id="M426" style="vertical-align:-5.4742pt" version="1.1" viewbox="-0.0498162 -8.6359 14.3759 14.1101" width="14.3759pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 415C194 400 159 383 126 359L131 330C159 344 187 357 222 368L109 -147C96 -204 80 -214 18 -223L13 -255L256 -244L259 -212L236 -210C184 -205 180 -195 191 -141L219 -1C240 -10 268 -12 284 -12C352 4 431 48 484 104C543 166 573 240 573 302ZM481 290C481 165 381 37 305 37C280 37 249 56 235 71L302 395C328 399 353 402 372 402C427 402 481 378 481 290Z"></path></g></svg>-</span>RLS, and RRSL0 with noise intensity changes according to sequence <span class="nowrap"><svg height="12.5794pt" id="M427" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 160.798 12.5794" width="160.798pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.396,3.132)"><path 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Mathematical Problems in Engineering

A New Smoothed L0 Regularization Approach for Sparse Signal Recovery

Table 5