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Inverse Halftoning via Nonlocal Regularization. Xin Li West Virginia University. This work is partially supported by NSF CCF-0914353. What is Inverse Halftoning?. halftoning. X: continuous-tone original. inverse halftoning. Y: halftoned (B/W). ^. X: continuous-tone estimated. - PowerPoint PPT Presentation
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Inverse Halftoning via Nonlocal Regularization
Xin Li
West Virginia University
This work is partially supported by NSF CCF-0914353
What is Inverse Halftoning?
X: continuous-tone original
Y: halftoned (B/W)
halftoning
inversehalftoning
^X: continuous-tone estimated
Evolutionary Path of Inverse Halftoning
Inverse Halftoning
Inverse Problems
ImageRestoration
Regularizationtheory
ImagePrior
What is State-of-the-ArtMethod PSNR(dB)
Inverse halftoning and kernel estimation for error diffusion (PW Wong TIP’1996)
31dB (MMSE projection)32dB (MAP projection)
Inverse halftoning using wavelets (Xiong et al., TIP’1997)
31.67dB
Look-up table (LUT) method for inverse halftoning (Mese and Vaidyanathan TIP’2001)
31.50dB
A fast, high-quality inverse halftoning algorithm for error diffused halftones (Kite et al. TIP’2000)
31.30dB
Hybrid LMS-MMSE inverse halftoning technique(Chang et al. TIP’2001)
31.39dB
A Tantalizing Hypothesis
Wavelet-based(Xiong et al.)
LUT-based(Mese et al.)
Iterative filtering-based(Wong)
Hybrid LMS-MMSE(Chang et al.)
Gradient-based(Kite et al.)
Are they fundamentally equivalent? – all based on the local models (singularities in images are characterized by local intensity variations).
Hierarchy of Mathematical SpacesHilbert-space: a completeInner-product space
Quantum mechanics
Fourier/waveletanalysis
Learning theory
PDE(e.g., Total-Variation)
Mathematical formalism(Hilbert, Ackermann, Von Neumann …)
Metric space: a set witha notion of distance
General relativity
Fixed-point theorems
Game theory
Dynamic systems
Mathematical constructivism(Poincare, Brouwer, Weyl …)
Filtering as Projection
• Examples– Linear filtering (low-pass vs. high-pass)– Nonlinear filtering/diffusion – Bilateral filtering– Wavelet/DCT shrinkage– Nonlocal filtering (BM3D, nonlocal TV)
'')',';,(
'')','()',';,(
dydxyxyxw
dydxyxfyxyxwfNLFP
“Phase Space” of Image SignalsSA-DCT TV BM3D Nonlocal-TV
Local filters Nonlocal filters
Alternating Projections
X0
X1
X2
X∞
Projection-Onto-Convex-Set (POCS) Theorem: If C1,…,Ck areconvex sets, then alternating projection P1,…,Pk will convergeto the intersection of C1,…,Ck if it is not empty
C1
C2
C1 : observation constraint set
C2 : regularization constraint set
Graduated Nonconvexity (GNC)
temperature of deterministic annealing threshold or Lagrangian multiplier
Summary of Algorithm
Key messages:
1.From local to nonlocal regularization thanks to the fixed-point formulation in the metric space (PNLF depends on the clustering result or similarity matrix)2.From convex to nonconvex optimization: deterministic annealing (also-called graduated nonconvexity) is the ``black magic” behind
Experimental Results
MATLAB codes accompanying this work are availableFrom my homepage: http://www.csee.wvu.edu/~xinl/
“o” – lena“+” – peppers
Image Comparison Results (I)
This work(PSNR=32.90
dB)
wavelet-based (PSNR=31.95dB)
TV-based (PSNR=30.91dB)
This work(PSNR=32.64
dB)
wavelet-based (PSNR=31.03dB)
TV-based (PSNR=30.92dB)
Beyond Inverse Halftoning• Image denoising
– W. Dong, X. Li, L. Zhang and G. Shi, "Sparsity-based image denoising via dictionary learning and structural clustering" , CVPR'2011 (oral paper), June 2011
• Image deblurring– Xin Li , "Fine-Granularity and Spatially-Adaptive Regularization for Projection-based Image
Deblurring,"IEEE Trans. on Image Processing, Vol. 20, No. 4., pp. 971-983, Apr. 2011.– Weisheng Dong, Xin Li, Lei Zhang, and Guangming Shi, “Sparsity-based image deblurring with
locally adaptive and nonlocally robust regularization,” accept to Proc. IEEE International Conference on Image Processing (ICIP), 2011
• Image coding– X. Li, "Collective sensing: a fixed-point approach in the metric space," SPIE Conf. on Visual
Comm. and Image. Proc. (VCIP), Jul. 2010• Super-resolution
– Weisheng Dong, Guangming Shi, Lei Zhang, and Xiaolin Wu, “Super-resolution with nonlocal regularized sparse representation,” in Proc. SPIE Visual Communications and Image Processing (VCIP), July 2010
• Compressed sensing– X. Li, “The magic of nonloca Perona-Malik diffusion”, IEEE Signal Processing Letter, vol. 18, no.
9, pp. 533-534, Sep. 2011
Source code collection for reproducible research http://www.csee.wvu.edu/~xinl/source.html