Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothed <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.67648pt;width:17.487499px;" id="M1" height="20.4375" version="1.1" viewBox="0 0 17.487499 20.4375" width="17.487499">
	
		
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			<g transform="matrix(.016,-0,0,-.016,9.275,20.187)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg> Norm

<table>Comparison of the four approximate <svg height="15.5375" id="M95" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 13.45 15.5375" width="13.45" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.25)"><path d="M363 114l21 -20q-62 -106 -161 -106q-61 0 -94 40t-33 138v56l-54 -40l-14 27l68 57v89q0 112 15.5 166t49.5 91q43 46 96 46q44 0 71 -32.5t27 -88.5q0 -41 -17.5 -81.5t-49.5 -76t-55.5 -57t-55.5 -46.5v-87q0 -138 81 -138q60 0 105 63zM177 421v-101q117 105 117 217
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<g transform="matrix(.012,-0,0,-.012,7.05,15.325)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg> norm functions with <svg height="11.125" id="M96" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 49.349998 11.125" width="49.349998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109
q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" id="x1D70E"></path></g><g transform="matrix(.017,-0,0,-.017,14.375,10.862)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,29.079,10.862)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,37.239,10.862)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,41.114,10.862)"><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>.</table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothed <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.67648pt;width:17.487499px;" id="M1" height="20.4375" version="1.1" viewBox="0 0 17.487499 20.4375" width="17.487499">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,14.812)"><path id="xF0A93" d="M442 569q0 -34 -17 -69.5t-41 -64.5t-61.5 -61t-66.5 -53l-67 -47l-19 -87q-30 -138 45 -138q31 0 71.5 25t67.5 55l15 -23q-40 -53 -93.5 -85.5t-106.5 -32.5t-74 31q-13 19 -15.5 59t7.5 88l13 56q-27 -19 -70 -46l-7 26q53 36 83 62l17 70q30 125 59 184.5t73 97.5
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</svg> Norm 

Mathematical Problems in Engineering

Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothed Norm

Figure 1