PMID- 18092598
OWN - NLM
STAT- MEDLINE
DCOM- 20080115
LR  - 20191027
IS  - 1057-7149 (Print)
IS  - 1057-7149 (Linking)
VI  - 16
IP  - 12
DP  - 2007 Dec
TI  - A new twIst: two-step iterative shrinkage/thresholding algorithms for image 
      restoration.
PG  - 2992-3004
AB  - Iterative shrinkage/thresholding (IST) algorithms have been recently proposed to 
      handle a class of convex unconstrained optimization problems arising in image 
      restoration and other linear inverse problems. This class of problems results 
      from combining a linear observation model with a nonquadratic regularizer (e.g., 
      total variation or wavelet-based regularization). It happens that the convergence 
      rate of these IST algorithms depends heavily on the linear observation operator, 
      becoming very slow when this operator is ill-conditioned or ill-posed. In this 
      paper, we introduce two-step IST (TwIST) algorithms, exhibiting much faster 
      convergence rate than IST for ill-conditioned problems. For a vast class of 
      nonquadratic convex regularizers (l(p) norms, some Besov norms, and total 
      variation), we show that TwIST converges to a minimizer of the objective 
      function, for a given range of values of its parameters. For noninvertible 
      observation operators, we introduce a monotonic version of TwIST (MTwIST); 
      although the convergence proof does not apply to this scenario, we give 
      experimental evidence that MTwIST exhibits similar speed gains over IST. The 
      effectiveness of the new methods are experimentally confirmed on problems of 
      image deconvolution and of restoration with missing samples.
FAU - Bioucas-Dias, Jose M
AU  - Bioucas-Dias JM
AD  - Instituto de Telecomunicacoes and the Instituto Superior Tecnico, Technical 
      University of Lisbon, 1049-001 Lisboa, Portugal. jose.bioucas@lx.it.pt
FAU - Figueiredo, Mario A T
AU  - Figueiredo MA
LA  - eng
PT  - Journal Article
PT  - Research Support, Non-U.S. Gov't
PL  - United States
TA  - IEEE Trans Image Process
JT  - IEEE transactions on image processing : a publication of the IEEE Signal 
      Processing Society
JID - 9886191
SB  - IM
MH  - *Algorithms
MH  - Image Enhancement/*methods
MH  - Image Interpretation, Computer-Assisted/*methods
MH  - Pattern Recognition, Automated/*methods
MH  - Reproducibility of Results
MH  - Sensitivity and Specificity
MH  - *Signal Processing, Computer-Assisted
EDAT- 2007/12/21 09:00
MHDA- 2008/01/16 09:00
CRDT- 2007/12/21 09:00
PHST- 2007/12/21 09:00 [pubmed]
PHST- 2008/01/16 09:00 [medline]
PHST- 2007/12/21 09:00 [entrez]
AID - 10.1109/tip.2007.909319 [doi]
PST - ppublish
SO  - IEEE Trans Image Process. 2007 Dec;16(12):2992-3004. doi: 
      10.1109/tip.2007.909319.