CS: Inline hologram reconstruction with sparsity constraints, Reading the Book of Memory:

Responding to a request I made yesterday, one of the reader of this blog kindly sent me an invitation for Google Wave. However it looks like Google has a waiting list even for that so I have not received anything. Google, when a party sends an invitation, what is really important is not the sending, it is the receiving of that invitation by the second party that makes it an invitation. The process reminds me of the rental reservation process as experienced by Seinfeld.

In a recent entry, I mentioned the following paper A simple proof that random matrices are democratic but forgot to mention Mark Davenport from the list of authors. This has been fixed.

If you want to be added to the Compressive Sensing list of Twitter, please let me know.

Thanks to Andy for suggesting a replacement to Google Wave called ShowDocument and thanks to Laurent Jacques for mentioning different elements of response to Danny Bickson's question on Seeking CS data where the signal prior is not sparse or noise is non-gaussian. If you have answers to his question you are welcome to contribute.


In his blog, David Brady mentions this paper on compressive holography entitled: Inline hologram reconstruction with sparsity constraints by Loic Denis, Dirk Lorenz, Eric Thiebaut, Corinne Fournier, and Dennis Trede. The abstract reads:

Inline digital holograms are classically reconstructed using linear operators to model diraction. It has long been recognized that such reconstruction operators do not invert the hologram formation operator. Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin-images. When objects located at dierent depths are reconstructed from a hologram, in-focus and out-of-focus images of all objects superimpose upon each other. Additional processing, such as maximum-of-focus detection, is thus unavoidable for any successful use of the reconstructed volume. In this letter, we consider inverting the hologram formation model in Bayesian framework. We suggest the use of a sparsity-promoting prior, verified in many inline holography applications, and present a simple iterative algorithm for 3D object reconstruction under sparsity and positivity constraints. Preliminary results with both simulated and experimental holograms are highly promising.

Finally, on Twitter, Suresh Venkatasubramanian mentions two items of interest:

• a Junior Professorship (W1) „Bioinformatics for High Throughput Technologies“ and
• The Human Connectome Project

The first item related to the work in group testing and its relationship to compressive sensing while the second items connects to a paper I was reading at about the time I saw the tweet, namely Reading the Book of Memory: Sparse Sampling versus Dense Mapping of Connectomes by H. Sebastian Seung. It is an interesting paper as it brings to light the necessary methods to do a better job of understanding the brain connectivity. The abstract reads:

Many theories of neural networks assume rules of connection between pairs of neurons that are based on their cell types or functional properties. It is finally becoming feasible to test such pairwise models of connectivity, due to emerging advances in neuroanatomical techniques. One method will be to measure the functional properties of connected pairs of neurons, sparsely sampling pairs from many specimens. Another method will be to find a ‘‘connectome,’’ a dense map of all connections in a single specimen, and infer functional properties of neurons through computational analysis. For the latter method, the most exciting prospect would be to decode the memories that are hypothesized to be stored in connectomes.