BLIND SEPARATION OF SOURcES WITH SPARSE ... - Research

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IN A GIVEN SIGNAL DIcTIONARY. Michael Zibulevsky ... overcomplete dictionary and equal numbers of sources ... function (pdf) of an exponential type pi(. Ь.
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 ƒ òM OP O†ñˆP„†… „… … †…  † ôQR†ó ðñôPô ‡„RP„†…MQ„ôO ‰Y Xc`\^baYb a``WX_abX\Y[i bTU [UY[\^ [XfYaW[ cae TauU T]YZ^UZ[ \g _TaYYUW[ aYZ T]YZ^UZ[ \g bT\][aYZ[ \g [ac`WU[l STX[ cae cakU [U`a^abX\Y _\c`]babX\YaWWe ZX~ _]Wbl  U^U jU `^U[UYb aY a``^\a_T jTX_T _\c`^\h cX[U[ VUbjUUY [babX[bX_aW aYZ _\c`]babX\YaW U~ _XUY_el ‰Y \]^ Ud`U^XUY_U bTX[ a``^\a_T `^\uXZU[ TXfT ]aWXbe \g [U`a^abX\Y XY ^Ua[\YaVWU bXcUl }]``\[U bTab bTU ZX_bX\Ya^e X[ _\c`WUbUi rxwx Xb g\^c[ a Va[X[ XY bTU [`a_U \g ZX[_^UbU [XfYaW[l STX[ cUaY[ bTab bTU cab^Xd Ü X[ []a^U aYZ Y\Yh[XYf]Wa^l [ Udac`WU[ \g []_T a ZX_bX\Ya^e \YU _aY bTXYk \g bTU n\]^XU^ Va[X[i  aV\^ Va[X[i ua^X\][ jauUWUbh^UWabUZ Va[U[i wz{x mU _aY aW[\ \VbaXY aY \`bXcaW ZX_bX\Ya^e Ve WUa^YXYf g^\c fXuUY gacXWe \g [XfYaW[ ÍÏi Ði ÑÎl D Ub ][ ZUY\bU bTU Z]aW Va[X[ “ Ü =› vžÐ | aYZ []``\[U bTab _\U~ _XUYb[ \g ZU_\c`\[XbX\Y \g bTU [\]^_U[ “ Ù vžÑ | œ a^U [`a^[U aYZ [babX[bX_aWWe XYZU`UYZUYbl STX[ a[[]c`h bX\Y X[ ^Ua[\YaVWU g\^ `^\`U^We _T\[UY ZX_bX\Ya^XU[i aWh bT\]fT \g _\]^[U jU j\]WZ W\[U bTU aZuaYbafU[ \g \uU^h _\c`WUbUYU[[l D Ub VU bTU ZU_\c`\[XbX\Y \g bTU [UY[\^ [XfYaW[

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“ ‘ ” Ô vžø | œ jTU^U  X[ ZU_\c`\[XbX\Y \g bTU Y\X[U  “ ’ Õ vž |  U^U jU _\Y[XZU^ aY Ua[e [Xb]abX\Y i jTUY  X[ a jTXbU Y\X[Ui bTab ^U]X^U[ \^bT\f\YaWXbe \g l mU _aY [UU bTab aWW bTU \V 6 U_bXuU g]Y_bX\Y[ g^\c bTU `^UuX\][ [U_bX\Y[ ^UcaXY uaWXZ Xg jU ^Uc\uU g^\c bTUc Ü v[]V[bXb]bXYf XY[bUaZ bTU XZUYbXbe cab^Xd | aYZ ^U`Wa_U bTU [UY[\^ [Xfh YaW × Ve Xb[ ZU_\c`\[XbX\Y l n\^ Udac`WUi cadXc]c o p t  zwqr t qr \V 6 U_bXuU[ v•Ï | aYZ v• | a^U b^aY[g\^cUZ XYb\ cXY ž •  '‘ û '( ” ˜ üÚ ýv Ú ™ | vž # | ! ڙ œ œ aYZ cXY ž •  '‘ û '( ” ˜ ž * ™ œ Ú ™  vÏ | ! Ú ) Ý = › * ™ Ú™ œ œ

(57%)

(29%) (27%)

(0.2%)

Cardoso’s JADE

Fast ICA

BS Infomax

Equation 22

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vžÏ |

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4

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3000

6 2000

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0

2

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0 −1

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−0.4

−0.2

0

0.2

0.4

0.6

0.8

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x 10

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100 −4

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−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1 4

x 10

15 10

5

5

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2

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6

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−0.8

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−0.2

0

0.2

0.4

0.6

0.8

1

4

x 10

(8.8%)

(8.6%) (7.1%)

Cardoso’s JADE 

Fast ICA

BS Infomax

(0.9%)

(0.67%)

Spect− Infomax

Spect− BFGS

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185

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