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A half-quadratic block-coordinate descent method for spectral estimation

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(1)A half-quadratic block-coordinate descent method for spectral estimation Philippe Ciuciu, J. Idier. To cite this version: Philippe Ciuciu, J. Idier. A half-quadratic block-coordinate descent method for spectral estimation. Signal Processing, Elsevier, 2002, 82, pp.941-959. �cea-00333746�. HAL Id: cea-00333746 https://hal-cea.archives-ouvertes.fr/cea-00333746 Submitted on 24 Oct 2008. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(65)   ì ò#(  R(6nó*Óò#(B*gqò#2ÊX* ö . . .  ).  K;.  ' , . AŒ‚195%a-0JG<>= 4 ã ñ ò#*Ó4*g ¡ ° ‚µX” ¡Ï ö #ó n¨ûÈó%$' ö 2Ê #)(6ò , (tû4&ûì*ƒ""ÊJ   z@ò I*q ì* ö *  ó*g()q&* ø'&nò#4÷ : #o$'ò#4 ø: #   ¡. . . 0 '. s |. . Ï Gó.

(66) . mP<G/2=I9   8”  .  . . <G?M=<G5B=IZCJG35Ir ?%-•<G? ì38=I=I-5%bC<>/CQ¬;6-•ÔY5%-01-0?B<>;6<>-0/ ‡  r dq|PsjÓDdg| ÈjX5B9Á3b.   D. . °    µY”. ÜGÝ. ° KšCAµt”. .  G. ßà. ¿. ± . ¿. . ±.   Ã.  . A8Î •Ã. A«Î. . & °   µ@š Š   °   µ E š   ¡. Ï. Ï ã. CpihKAC9I/}rYQ<>O09/. ã.  . Y”. dq|8vj. . ±. . dq|8uj. W<>;%A A‘” ›  ¡ šÁÀÁÀÁÀš  ‡ê‰YŠKptm‚<G/C=9@3É=-07H1CJG9)ª¨3ZPªP<GJ><€35EŒ¬O835%<G3aCJG9  <G?=I-ZPD Š  ¢   1CJG9b;%-£3/Œ?%19I=;%563J37H1CJG<";6ZCb298 r D  bC9I19I/Cb2?^-0/É;ÓW<>=I97:-05B9o5B9Á3J3ZPªP<>JG<€385BŒ   O835%<G3aCJG9?z;6AC3/ D 

(67) p. 7ˆAC9I/. . . ). . . . | 0j^35%9H?63#;6<G?EÇ49Ib«r <>?†JG<G/29Á3538;<>/2Ç4/C<";ӌ0r};6A29I/‹dg | .0jƒ<>?o38ZPD ¡ ‡ è3/2b‹dq/ ;6-07:38;%<G=Á38JGJ>Œo9I/2?%ZC5B9Ib}pChKA29I5%9U\-05%98rCÔY5%-1-0?B<>;%<G-0/C?`v#DÓu3121CJ>Œ:3/Cb:a-8;6A£9/C9I5BQ0<G9? D  3/Cb ?  ”]Ì{ãHä D  r W<";6Aä ”—ä ´ _r#35%9`?B;%5%<G=;6J"Œ†=I-0/O9ªl38/Cb

(68)  p ÒÓ/14385B;6<>=IZCJG35Ir U\-05†;6AC9lAŒ‚195%a-0JG<>=l1-;%9I/;6<G3Jt- U iªC387:1CJ>9's~2r <>U  ¡ r ?  U\ZCJ>ÇCJGJG?Md 0aVjFDd 0=j)p ïXŒR=I-/È;%563?E;ÁryW<>;%A•;%AC9:J>-0Q8D+xT3ZC=nAŒR1-8;69I/;%<€3JYZC?B9IbL<>/ëdgm23==nAC<X9;{38Jqp"rYsu0u0vj)r /C=I-0/O9ªP<>;ӌ@5%9I?BZCJ>;z-> U ?  <>?z3ÁO83<>J€3aCJ>9r9O09I/Í<"U};6A29ƒU\ZC/C=;6<G-/ M<>?X=<G5B=IZCJG35Ir

(69) Ï 3/Cb ?B;%5%<G=;6J"Œ£=I-/ÈO9ª'U\-05  rV3==I-05BbC<G/CQM;%-Édg | 0j)p ¡Ï. . . . .. .  ö  . ‚!‚. 0 '. R,. 0 '. ‚ò#()* ö. E*. . R(nnó*Óò#(B*gqò#. #Áò#( ,. hKAC9ÍbC<"é«95%9I/;M?E;691C?l-U;6AC9 ?%19I=;6563H35B9/2- WðbC9;63<GJ>9Ib}p. . .m2f. d-5{ïKxTfkD+Ñ8:j{3JGQ-05%<";6AC7ôU\-05o=I-07H1CZ2;%<G/CQÉJG<G/29. . c45%-07ôdq|uj)rE?  3bC7H<>;%?z;6AC9†U\-0J>JG-W<G/2Q{9ªP1C5B9I?%?B<G-0/ ?. . . C 

(70) ) •Ã. ° KšCAµY”ð . A C  ° µ E ãO ° ȵ)š . ±. A. dgæ~j. A. WAC9I5B9. K”—–D˜2C ™ –R˜2™†ãÐä . ´± G Š š   ° µY”—–D˜2C ™ Žãíä . ´0± š Š   ° µY”—ä .  Î Î)Ï ´± ã   °   µ   < ¡ . A. dgæPs j. A. A. . A. À. 2^/L;6AC9£-/C9£A43/2b}r;%AC9Í3ZPªP<>JG<€385BŒ‘O835%<G3aCJ>9I?o35%9£Z21b43#;69IbüB-<G/;6J"Œ0ry?%<>/C=I9@;%AC9ŒìbC-. . /C-;l<>/È;%9I5%3=;IpihKA43/2Ղ?M;%-¨ÔY5B-01-?%<>;%<G-0/Læ2ri/C-R=JG-0?B9IbLU\-05B7 -U R<>?{/C9I=9I?B?635EŒN;6=Á3J>=IZCJG38;69.;6AC97:<>/C<G7H<GË9I5 ÖA ° `µz-K U ?  pVc45%-07 ;6AC9=IZ25%5%9/;ƒ9)ª2125%9I?B?%<>-0/-8U 2r49Á3=nA Ö =I-07H1-0/C9I/;  r2U\-05t¸‡¬· rC<G?KQ<>O09/aŒ“ Š  . . Ö. °    µY”. ,.°. .  . µ_” .  . Ã. .  .°. sæ. .  . µ`” .  . Ã. . ..  µ ¡ °   . ,.   ´. .  . À. dgæ0|0j.

(71) 2^/¬;6AC9{-8;6AC95ƒA43/2b}r«<";^<G?.?%AC-W/‘;6AC38;ƒ;%AC9{7H<G/C<>7:<>ËI9I5. . Ö ° Aȵ-U ?  =Á38/‘a9{=-07MD 1CZ2;%9Ib¬<>/Ž;%AC9c4-0Z25%<G95bC-07:3<G/Í;6AC3/CÕÈ?.;%-:=<G5%=ZCJ€385%<>;ӌ@-U  pVh -:;%AC<G?9I/2b}r5B9I7:35%Õ ;6A43#;  X<>?t<G/2bC9I19I/Cb29I/;`-U A2pÿŽ-05%9- O9I5r2– ˜2™ –R˜2™o<>?Y=I<>5%=IZ2J€3/;_3?Y?BAC-W/:<>/Ždqц<G-8D O83/C/C9JGJG<_38/CbLÒÓbC<>9I5Iri|~0~Ps jr}WAC<>=nAN3J>JG-W?;%-ÉbC9=I-07H1-0?%9:<>;o<G/R;6AC9@cV-ZC5%<>9I5a43?%<>? – ™#™ dq–R™8™‚– ™8™ ” – ™#™ –•™#™ê” § jpKÿŽ-05%9¬125%9I=<G?B9IJ>ŒrXWX9‘A43ÁO09•– ˜2™ –•˜P™ð” Š – ™#™ –•™#™VriWAC9I5B9Ž;%AC9'bC<€38Q0-0/43JX7@3#;65%<Sª <G?M-0/2J>ŒN=-07:1-0?B9Ibõ-Uk;ÓWz-¨bC<>é9I5B9I/; 9I<>Q09I/O83JGZ29I?Irs^38/CbÍ~2r‚-U 5B9I?%19I=;6<"O09†-05BbC9I5z¤ 3/Cb£§ÐѤ•p2hKAC95%9U\-5%9r  K<G?`=I<>5%=ZPD J€3/;Ir43/Cb'Wz9Q09;  K”Ø– ™#™ –R™8™ ´ §lr2W<>;%A.

(72) . . C. C. C. C. G. C.

(73) . C  . ” . . ?%-l;6A43#; Ö ° È A µz<>?KQ0<>O9I/ŽaŒ“. . Ö ° È A µ_” ”. H. G ’ ¾ ’ Š ’ ¾ ä . ´± G Š ’ ’ Š ’. . ° §ëãÐä ´0± µ. ƒ<G?K<>/O09I5E;6<>aCJG93/2b     . 6.9/C=I98r. C

(74) . À.

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