CS: Wishlist for Photography, Robust PCA code, Multiplicative noise removal, a Thesis, MRI, Sensor Networks, Bregman Methods, Template Matching

Today is Christmas eve, some of you are probably starting your gift finding journey, for others, it's time for writing a wishlist, for them here is an inspiring video of Ramesh Raskar's Wishlist for Photography.

By the way, on my wishlist, I have this LCD screen can recognise what happens in front of it. Am I gonna get it ?

It is pretty obvious that as Ramesh say, one wants more out of our photograpahic experience. Another proof of that is the ad-hoc datamining study performed on what people liked on Avatar [Thanks Aleks]. Can compressive sensing be part of that wave ?

[ By the way, the image shown here from Ramesh's presentation is from this publication: Fernald, R.D. (2006). "Casting a genetic light on the evolution of eyes." Science, 313: 1914-1918.PubMed and PDF ]

In case it was not obvious, the code for the Robust PCA paper mentioned earlier can be found here.

Jalal Fadili has a new toolbox out:

Multiplicative noise removal by L1-data fidelity on frame coefficients: Matlab toolbox

The Ph.D thesis of Wei Wang entitled Sparse signal recovery using sparse random projections is out. The abstract reads:

The problem of estimating a high-dimensional signal based on an incomplete set of noisy observations has broad applications. In remote sensing, network traffic measurement, and computational biology, the observation process makes it difficult or costly to obtain sample sizes larger than the ambient signal dimension. Signal recovery is in general intractable when the dimension of the signal is much larger than the number of observations. However, efficient recovery methods have been developed by imposing a sparsity constraint on the signal. There are different ways to impose sparsity, which has given rise to a diverse set of problems in sparse approximation, subset selection in regression, and graphical model selection.

This thesis makes several contributions. First, we examine the role of sparsity in the measurement matrix, representing the linear observation process through which we sample the signal. We develop a fast algorithm for approximation of compressible signals based on sparse random projections, where the signal is assumed to be well-approximated by a sparse vector in an orthonormal transform. We propose a novel distributed algorithm based on sparse random projections that enables refinable approximation in large-scale sensor networks. Furthermore, we analyze the information-theoretic limits of the sparse recovery problem, and study the effect of using dense versus sparse measurement matrices. Our analysis reveals that there is a fundamental limit on how sparse we can make the measurements before the number of observations required for recovery increases significantly. Finally, we develop a general framework for deriving information-theoretic lower bounds for sparse recovery. We use these methods to obtain sharp characterizations of the fundamental limits of sparse signal recovery and sparse graphical model selection.

Speeding up Magnetic Resonance Image Acquisition by Bayesian Multi-Slice Adaptive Compressed Sensing by Matthias Seeger. The abstract reads:

We show how to sequentially optimize magnetic resonance imaging measurement designs over stacks of neighbouring image slices, by performing convex variational inference on a large scale non-Gaussian linear dynamical system, tracking dominating directions of posterior covariance without imposing any factorization constraints. Our approach can be scaled up to high-resolution images by reductions to numerical mathematics primitives and parallelization on several levels. In a first study, designs are found that improve significantly on others chosen independently for each slice or drawn at random.

Energy efficient information collection in wireless sensor networks using adaptive compressive sensing by Rajib Kumar Rana, Chun Tung Chou, Salil Kanhere, Nirupama Bulusu, Wen Hu. The abstract reads:

We consider the problem of using Wireless Sensor Networks (WSNs) to measure the temporal-spatial field of some scalar physical quantities. Our goal is to obtain a sufficiently accurate approximation of the temporal-spatial field with as little energy as possible. We propose an adaptive algorithm, based on the recently developed theory of adaptive compressive sensing, to collect information from WSNs in an energy efficient manner. The key idea of the algorithm is to perform “projections” iteratively to maximise the amount of information gain per energy expenditure. We prove that this maximisation problem is NPhard and propose a number of heuristics to solve this problem. We evaluate the performance of our proposed algorithms using data from both simulation and an outdoor WSN testbed. The results show that our proposed algorithms are able to give a more accurate approximation of the temporal-spatial field for a given energy expenditure.

The Bregman Methods: Review and New Results by Wotao Yin. In the review, one can read the following at the very end:

More ... People use the words \Bregmanize" and \Bregmanized"

As for split Bregman, some people think it ought to have a different name (slide 41). From the Bregman website, we are told that:

The part below is two years old. A new page and software package is due middle of Feburary, 2010.

While we are on the subject of Split Bregman, we have the latest for UCLA in the form of Template Matching via L1 Minimization and Its Application to Hyperspectral Target Detection by Zhaohui Guo and Stanley Osher. The abstract reads:

Detecting and identifying targets or objects that are present in hyperspectral ground images are of great interest. Applications include land and environmental monitoring, mining, military, civil search-and-rescue operations, and so on. We propose and analyze an extremely simple and e±cient idea for template matching based on L1 minimization. The designed algorithm can be applied in hyperspectral target detection. Synthetic image data and real hyperspectral image (HSI) data are used to assess the performance. We demonstrate that this algorithm achieves excellent results with both high speed and accuracy by using Bregman iteration.

Happy Holidays y'all.