Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovery of blocky images from noisy and blurred data
SIAM Journal on Applied Mathematics
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Fast Surface Interpolation using Multiresolution Wavelet Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Discontinuity-Adaptive Smoothness Priors in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF
IEEE Transactions on Image Processing
Markovian reconstruction using a GNC approach
IEEE Transactions on Image Processing
Simulated annealing, acceleration techniques, and image restoration
IEEE Transactions on Image Processing
Convex half-quadratic criteria and interacting auxiliary variables for image restoration
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
Optimization by Stochastic Continuation
SIAM Journal on Imaging Sciences
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The standard approach to image reconstruction is to stabilize the problem by including an edge-preserving roughness penalty in addition to faithfulness to the data. However, this methodology produces noisy object boundaries and creates a staircase effect. The existing attempts to favor the formation of smooth contour lines take the edge field explicitly into account; they either are computationally expensive or produce disappointing results. In this paper, we propose to incorporate the smoothness of the edge field in an implicit way by means of an additional penalty term defined in the wavelet domain. We also derive an efficient half-quadratic algorithm to solve the resulting optimization problem. Numerical experiments show that our technique preserves edge sharpness while smoothing contour lines; it produces visually pleasing reconstructions which are quantitatively better than the results obtained without wavelet domain constraints.