6533b85ffe1ef96bd12c1b56
RESEARCH PRODUCT
CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration
Samuel VaiterJoseph SalmonCharles-alban DeledalleNicolas Papadakissubject
FOS: Computer and information sciencesInverse problemsMathematical optimization[ INFO.INFO-TS ] Computer Science [cs]/Signal and Image ProcessingComputer Vision and Pattern Recognition (cs.CV)General MathematicsComputer Science - Computer Vision and Pattern RecognitionMachine Learning (stat.ML)Mathematics - Statistics TheoryImage processingStatistics Theory (math.ST)02 engineering and technologyDebiasing[ INFO.INFO-CV ] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]01 natural sciencesRegularization (mathematics)Boosting010104 statistics & probabilitysymbols.namesake[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing[STAT.ML]Statistics [stat]/Machine Learning [stat.ML]Variational methods[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]Statistics - Machine LearningRefittingMSC: 49N45 65K10 68U10[ INFO.INFO-TI ] Computer Science [cs]/Image ProcessingFOS: Mathematics0202 electrical engineering electronic engineering information engineeringCovariant transformation[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]0101 mathematicsImage restoration[ STAT.ML ] Statistics [stat]/Machine Learning [stat.ML]MathematicsApplied Mathematics[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]EstimatorInverse problem[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]Jacobian matrix and determinantsymbolsTwicing020201 artificial intelligence & image processingAffine transformationAlgorithmdescription
International audience; In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a ``twicing'' flavor and allows re-fitting the restored signal by adding back a local affine transformation of the residual term. We illustrate the benefits of our method on numerical simulations for image restoration tasks.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-01-01 |