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A Dual Algorithm For L1-Regularized Reconstruction Of Vector Fields

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti
2012
Conference paper
Abstract

Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these requirements in mind, we propose a computationally efficient algorithm for variational denoising and reconstruction of vector fields. Our variational objective combines rotation-and scale-invariant regularization functionals that permit one to tune the algorithm to the physical characteristics of the underlying phenomenon. In addition, these regularization terms involve L-1 norms in the spirit of total-variation (TV) regularization, which, as in the scalar case, leads to better preservation of discontinuities and superior SNR performance compared to its quadratic alternative. Some experimental results are provided to illustrate and verify the proposed scheme.

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Ontological neighbourhood
Mathematics
Related concepts (35)
Regularization (mathematics)
In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem.
Total variation denoising
In signal processing, particularly , total variation denoising, also known as total variation regularization or total variation filtering, is a noise removal process (filter). It is based on the principle that signals with excessive and possibly spurious detail have high total variation, that is, the integral of the absolute is high. According to this principle, reducing the total variation of the signal—subject to it being a close match to the original signal—removes unwanted detail whilst preserving important details such as .
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