Computing Nonnegative Tensor Factorizations, Arthur C. Clarke and Multi-Aperture Lenses

If you are lost because your data isn't 2-D, and you want a sparse decomposition of your dataset, Michael Friedlander and Kathrin Hatz just released Computing nonnegative tensor factorizations. The abstract reads:

Nonnegative tensor factorization (NTF) is a technique for computing a parts-based representation of high-dimensional data. NTF excels at exposing latent structures in datasets, and at finding good low-rank approximations to the data. We describe an approach for computing the NTF of a dataset that relies only on iterative linear-algebra techniques and that is comparable in cost to the nonnegative matrix factorization. (The better-known nonnegative matrix factorization is a special case of NTF and is also handled by our implementation.) Some important features of our implementation include mechanisms for encouraging sparse factors and for ensuring that they are equilibrated in norm. The complete Matlab software package is available under the GPL license.

The Matlab code is available here. This is a tool that enables one to build dictionaries from data not necessarily in dimension 2. It has its place in the sparse dictionaries section of the big picture on Compressive Sensing.



Arthur Clarke (who just passed away), the man publicizing the idea of geostationary satellites, once said, there are three phases to a great idea:

The first phase is when people tell you it’s a crazy idea, it will never work; the second phase is when people say, it might work, but it’s not worth doing; and the third phase is when people say, I told you that was a great idea all along!

Projecting on a few random bases and getting the full signal back from solving a linear programming step, that'll never work....

Following up on the evaluation of the current imaging systems that are tweaked to provide additional information, here is a multi-aperture system at Stanford using 12,616 lenses.

The 3-D information is extracted from the stereographic view projected in different parts of the CMOS. One should also note the statement that one now needs about 10 MP in order to provide a 3 MP spatial resolution. Much of that hardware engineering implementation is focused on not mixing different rays of light and one wonders if mixing them as done in Compressive Sensing would not be simpler. The difficulty of the Compressed Sensing approach resides in that most photographic customers do not want a "computational reconstruction" if that process requires a computer.

So the real question is: is there a customer base that is OK with the computational reconstruction step because it brings additional information (in hyperspectral mode or in a time mode) that they really care about?




Photo Credit: NASA/JPL, 36 locations found by the Mars Odyssey orbiter (named in Honor of Arthur Clarke and his book 2001: A Space Odyssey) and selected by NASA to be the first regions where humans (future Martians) will set foot on Mars when they go there.