A Dual Algorithm For L1-Regularized Reconstruction Of Vector Fields

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.

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Emrah Bostan, Pouya Dehghani Tafti, Michaël Unser

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.

IEEE2012

An Efficient Numerical Method for General

Jean-Charles Baritaux, Kai Hassler, Michaël Unser

Reconstruction algorithms for fluorescence tomography have to address two crucial issues : 1) the ill-posedness of the reconstruction problem, 2) the large scale of numerical problems arising from imaging of 3-D samples. Our contribution is the design and implementation of a reconstruction algorithm that incorporates general Lp regularization (p ≥ 1). The originality of this work lies in the application of general Lp constraints to fluorescence tomography, combined with an efficient matrix-free strategy that enables the algorithm to deal with large reconstruction problems at reduced memory and computational costs. In the experimental part, we specialize the application of the algorithm to the case of sparsity promoting constraints (L1). We validate the adequacy of L1 regularization for the investigation of phenomena that are well described by a sparse model, using data acquired during phantom experiments.

IEEE2010

Graph-based regularization for spherical signal interpolation

Pascal Frossard, Tamara Tosic

This paper addresses the problem of the interpolation of 2-d spherical signals from non-uniformly sampled and noisy data. We propose a graph-based regularization algorithm to improve the signal reconstructed by local interpolation methods such as nearest neighbour or kernel-based interpolation algorithms. We represent the signal as a function on a graph where weights are adapted to the particular geometry of the sphere. We then solve a total variation (TV) minimization problem with a modified version of Chambolle's algorithm. Experimental results with noisy and uncomplete datasets show that the regularization algorithm is able to improve the result of local interpolation schemes in terms of reconstruction quality.

2010

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Emrah Bostan, Pouya Dehghani Tafti, Michaël Unser

L _{ 1 }

IEEE2012