Continuous Optimization for Fields of Experts Denoising Works

March 25, 2014

Sameer Agarwal and I just uploaded a paper to arχiv.orgContinuous Optimization for Fields of Experts Denoising Works. We show that simple non-linear least-squares is better than sophisticated discrete optimization methods for certain image denoising problems.

I have used these denoising problems as a bechmark and motivation when developing generalized roof duality. But as it turns out, continuous optimization is much better. 🙂

Update: I should add that the source code used for the experiments in available in Ceres; see https://code.google.com/p/ceres-solver/ .

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Generalized Roof Duality: Experiments

August 17, 2011

This is a follow-up to the previous post about generalized roof duality and will contain some experimental results.

We have performed experiments with polynomials of degree 3 and 4. While these two cases are very similar in concept, implementing the degree 3 case is considerably easier.

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ICCV 2011: Generalized Roof Duality

August 7, 2011

Fredrik Kahl and I have a paper accepted to ICCV titled Generalized Roof Duality for Pseudo-Boolean Optimization.

Just as in the previous post, the problem of interest is to minimize degree-{m} polynomials {f: \mathbf{B}^n \rightarrow \bf \mathbf{R}} of the form:

\displaystyle  	f(\boldsymbol{x}) = \sum_i a_ix_i + \sum_{i<j} a_{ij}x_ix_j + \sum_{i<j<k} a_{ijk}x_ix_jx_k + \ldots.

The previous post showed that many different reductions to the quadratic case are possible. Our paper describes a generalization of roof duality which does not rely on reductions and is in a suitable sense optimal.

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Reductions in Pseudo-Boolean Optimization

May 21, 2011

This post is about reduction methods in pseudo-Boolean optimization and a recent paper to appear at CVPR 2011.

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