Fast and Stable Bayesian Image Expansion Using Sparse Edge Priors

Raj, Ashish; Thakur, Keshav Kumar

doi:10.1109/tip.2006.891339

Cited by 4 publications

(2 citation statements)

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“…Periodic boundary conditions were applied whenever necessary. In all experiments, we set in (22) for NQR interpolation. The stopping criterion for Algorithms 2 and 3 is , where is the size of .…”

Section: Methodsmentioning

confidence: 99%

“…2) Nonquadratic Regularization: In this case, the problem (19) can be handled only in a numerical optimization framework. For the purpose of numerical tractability, we replace the integral in (20) by a Riemann sum which leads to the discrete nonquadratic regularization (22) where represents the discretized version of the differential operator . The use of for regularized interpolation distinguishes this work from those in [24]- [29] which primarily deal with quadratic regularization.…”

Section: ) Quadratic Regularization (Qr)mentioning

confidence: 99%

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Regularized Interpolation for Noisy Images

Ramani

Thévenaz

Unser

2010

IEEE Trans. Med. Imaging

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Abstract-Interpolation is the means by which a continuously defined model is fit to discrete data samples. When the data samples are exempt of noise, it seems desirable to build the model by fitting them exactly. In medical imaging, where quality is of paramount importance, this ideal situation unfortunately does not occur. In this paper, we propose a scheme that improves on the quality by specifying a tradeoff between fidelity to the data and robustness to the noise. We resort to variational principles, which allow us to impose smoothness constraints on the model for tackling noisy data. Based on shift-, rotation-, and scale-invariant requirements on the model, we show that the -norm of an appropriate vector derivative is the most suitable choice of regularization for this purpose. In addition to Tikhonov-like quadratic regularization, this includes edge-preserving total-variation-like (TV) regularization. We give algorithms to recover the continuously defined model from noisy samples and also provide a data-driven scheme to determine the optimal amount of regularization. We validate our method with numerical examples where we demonstrate its superiority over an exact fit as well as the benefit of TV-like nonquadratic regularization over Tikhonov-like quadratic regularization.

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Section: Methodsmentioning

confidence: 99%