In a previous post we discussed how to find a common point in a family of convex sets by using the Bregman algorithm. Actually the algorithm is capable of more. We can use it to solve constrained optimization problems.

In the 1960s Lev Meerovich Bregman developed an optimization algorithm [1] which became rather popular beginning of 2000s. It’s not my intention to present the proofs for all the algorithmic finesse, but rather the general ideas why it is so appealing.

Let us consider a microphone array comprising $n$ microphones at known locations (see figure above). These microphones register the sound that is emitted by a number of sources with unknown locations.

Lossy image compression methods based on partial differential equations have received much attention in recent years. They may yield high-quality results but rely on the computationally expensive task of finding an optimal selection of data. For the …

We have investigated high performing optimization algorithms and matrix differential calculus technique in the context of Photometric Stereo and presented the results at the BMVC 2016
Source Code A github repository with the code is maintained by Yvain Quéau.

I’ve developed optimization algorithms for variational optical flow models based on the split Bregman algorithm in my Master thesis. A follow-up investigation on the necessity of certain intermediate filtering steps was published at the EMMCVPR 2011.

Oral presentation

Estimating shape and appearance of a three-dimensional object from a given set of images is a classic research topic that is still actively pursued. Among the various techniques available, photometric stereo is distinguished by the assumption that …

We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears similarities …

Poster presentation