HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="417486.fig.003a" src="https://static.hindawi.com/articles/tswj/volume-2014/417486/figures/417486.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Static interval wavelet (<svg height="11.175" id="M158" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 37.412498 11.175" width="37.412498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g><g transform="matrix(.017,-0,0,-.017,14.477,11.113)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,29.181,11.113)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>)</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="417486.fig.003b" src="https://static.hindawi.com/articles/tswj/volume-2014/417486/figures/417486.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Static interval wavelet (<svg height="11.175" id="M159" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 37.412498 11.175" width="37.412498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g><g transform="matrix(.017,-0,0,-.017,14.477,11.113)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,29.181,11.113)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>)</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="417486.fig.003c" src="https://static.hindawi.com/articles/tswj/volume-2014/417486/figures/417486.fig.003c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Static interval wavelet (<svg height="11.375" id="M160" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 37.412498 11.375" width="37.412498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g><g transform="matrix(.017,-0,0,-.017,14.477,11.112)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,29.181,11.112)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg>)</td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="417486.fig.003d" src="https://static.hindawi.com/articles/tswj/volume-2014/417486/figures/417486.fig.003d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>Dynamic interval wavelet</td></tr></table></td></tr></table>

<table>Comparison between the dynamic interval wavelet and the static interval wavelet.</table>

The Scientific World Journal

HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation

Figure 3