Detecting defects in solar cells using compressive sensing

You probably remember this Accidental Single Pixel Camera that was unwittingly imaging the Sun ?  Well, the same concept that can be used to test PV cells. 

 

 

The actual poster is here.

From the press release:

Detecting defects in solar cells

Scientists at the National Physical Laboratory (NPL) have developed a new method for detecting defects in solar cells using a technique called 'compressed sensing'.

Patterns of light are projected onto PV cells to
measure their response

Solar panels, or photovoltaic (PV) modules, are being rapidly deployed across the world as costs fall and the need for sustainable, low-carbon energy grows. Being able to effectively characterise PV cells is a key factor in quality control during manufacturing and understanding their long-term behaviour.
NPL researchers, Simon Hall, Matt Cashmore and John Blackburn, have developed a new technique for efficiently detecting malfunctioning areas of a PV module.
Conventional testing involves scanning the PV cells, row by row, with a laser beam and measuring the current generated in response to the light at a series of points. Spatial variations in the cells' performance can then be identified, but the process is time consuming.
In the new method, patterns of light are projected onto the PV cells using a digital micromirror device, such as those found in many office projectors. A technique called compressed sensing is then used to make a map of the current generated by the cells in response to the light, in order to identify malfunctioning areas.
Compressed sensing is a signal processing technique more commonly used to reconstruct images from relatively few pieces of information, through exploitation of the simplicity of real-world images (when compared to, say, an image made up of random pixels).
By assuming that defects are sparse, compressed sensing can identify abnormalities in the PV module using fewer measurements than the traditional raster scanning technique, and without the need for moving parts.
Several large companies have already shown interest in adopting the technology for a variety of scanning applications. The team at NPL have recently patented the method, and are now undertaking the necessary developments for it to be put into practice.
The work was the subject of the winning poster at last month's NPL Science Poster Fair
Find out more about NPL's work in Optical Radiation & Photonics
For more information, contact Simon Hall

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Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Nikos Komodakis just sent the following:

Dear Igor,

Jean-Christophe Pesquet and I have recently finished a tutorial paper entitled "Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems",  which is going to appear as a feature article in an upcoming issue of the highly selective IEEE Signal Processing magazine.

The main goals of the above paper are:
- To provide a thorough introduction that intuitively explains the basic principles and ideas behind primal-dual approaches, including detailing useful connections between primal-dual methods and some widely used optimization techniques like the alternating direction method of multipliers (ADMM).
- To describe how these methods can be employed both in the context of continuous optimization and in the context of discrete optimization.
- To explain some of the recent advances that have taken place concerning primal-dual algorithms for solving large-scale optimization problems.
- And to also provide examples of useful applications in the context of image analysis and signal processing.

The uploaded version of the paper to arxiv can be found here: http://arxiv.org/abs/1406.5429

We believe that this could be of interest to the readers of your blog. If you also feel that this is case, we would be really glad if you could post some relevant information in your blog.

Best regards,
Nikos Komodakis

Thanks Nikos. here is the review:

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems by Nikos Komodakis, Jean-Christophe Pesquet

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness.  

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Streaming Anomaly Detection Using Online Matrix Sketching

Streaming Anomaly Detection Using Online Matrix Sketching by Hao Huang , Shiva Kasiviswanathan

Data is continuously being generated from sources such as machines, network traffic, application logs, etc. Timely and accurate detection of anomalies in massive data streams have important applications in preventing machine failures, intrusion detection, and dynamic load balancing. In this paper, we introduce a new anomaly detection algorithm, which can detect anomalies in a streaming fashion by making only one pass over the data while utilizing limited storage. The algorithm uses ideas from matrix sketching to maintain an approximate low-rank orthogonal basis of the data in a streaming model. Using this constructed orthogonal basis, anomalies in new incoming data are detected based on a simple reconstruction error test. We theoretically prove that our algorithm compares favorably with an offline approach based on global singular value decomposition updates. Additionally, we apply ideas from randomized low-rank matrix approximations to further speedup the algorithm. The experimental results demonstrate the effectiveness and efficiency of our approach over other popular fastanomaly detection methods 

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Three and a half million page views: a million here, a million there and soon enough we're talking real readership...

 

• December 2, 2014, 3.5 million page views
• June 7, 2014 3 million page views
• November 07, 2013, 2.5 million page views
• Monday, May 27, 2013 2 million page views
• October 25, 2012, 1.5 million page views

Here is the increase showing about a million page views every 13 months. That's 77000 page views per month or about 2,500 page views per day.

Here are different affiliated communities

• Google+ Community (1287 members), 
• the CompressiveSensing subreddit (609 members), 
• the LinkedIn Compressive Sensing group (3125 members) or 
• the Advanced Matrix Factorization Group (990 members)
•  

Reference pages include

• The Big Picture in Compressive Sensing (and learning Compressive Sensing),
• the Advanced Matrix Factorization Jungle Page and 
• the Reproducible Research page
• Paris Machine Learning Meetup Archives (1541 members), 
• Highly Technical Reference Pages - Aggregators,
• These Technologies Do Not Exist,
• CAI: Cable And Igor's Adventures in Matrix Factorization

 

 

 

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Book: Sketching as a Tool for Numerical Linear Algebra

I just found this somewhat long review article that easily could be considered a book: Sketching as a Tool for Numerical Linear Algebra by David P. Woodruff

This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a (usually) random matrix with certain properties. Much of the expensive computation can then be performed on the smaller matrix, thereby accelerating the solution for the original problem. In this survey we consider least squares as well as robust regression problems, low rank approximation, and graph sparsification. We also discuss a number of variants of these problems. Finally, we discuss the limitations of sketching methods. 

You can download a free copy (for personal use only) from David's page.

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CSjob: Postdoc in Mathematics

Thomas just sent me the following:

Dear Igor,

Would you be so kind and announce the postdoc position described below on your Nuit Blanche blog?

best regards,
Thomas

Sure Thomas, here it is:

POST-DOCTORAL POSITION IN MATHEMATICS University of California, Davis

The Department of Mathematics is soliciting applications for a Postdoctoral Scholar position with a starting date between March 2015 and October 2015.

To be considered for the position, the Department seeks applicants with a strong knowledge base in Sparse Approximations, Compressive Sensing, Numerical Algorithms, and/or Optimization. Applicants must have completed their Ph.D. by August 31, 2014. The position requires working on research related to a defense-based project (sponsored by DTRA/NSF) led by Professor Thomas Strohmer. The research is concerned with developing theory and algorithms for high-dimensional data analysis, imaging and signal recovery in connection with threat detection. The candidate should also have excellent programming skills in Matlab. The annual salary will be $50K. Salary is negotiable based on experience and funding available. The Postdoc may be asked to teach one or two courses depending on experience and the Mathematics department needs. The appointment is renewable for a total of up to two years, assuming satisfactory performance. A US-Citizenship is not required.

The UC Davis Math and Applied Math programs have been ranked among the nation’s top programs by the National Research Council in its most recent report. Additional information about the Department may be found at "http://www.math.ucdavis.edu/" http://www.math.ucdavis.edu/.

Applications will be accepted until the positions are filled. To guarantee full consideration, the application should be received by December 30, 2014 by submitting the AMS Cover Sheet and supporting documentation electronically through
http://www.mathjobs.org/ (see also https://www.mathjobs.org/jobs/jobs/6810).

The University of California, Davis, is an affirmative action/equal opportunity employer and is dedicated to recruiting a diverse faculty community. We welcome all qualified applicants to apply, including women, minorities, individuals with disabilities, and veterans. 

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Cone-constrained Principal Component Analysis

 

From the paper:

 

However we identify a large class of constraints for which estimation appears to be tractable, despite the corresponding maximum likelihood problem is non-convex. This shows that computational tractability is not immediately related to simple considerations of convexity or worst-case complexity.

 ah ! here it is: Cone-constrained Principal Component Analysis by Yash Deshpande, Andrea Montanari, Emile Richard

Estimating a vector from noisy quadratic observations is a task that arises naturally in many contexts, from dimensionality reduction, to synchronization and phase retrieval problems. It is often the case that additional information is available about the unknown vector (for instance, sparsity, sign or magnitude of its entries). Many authors propose non-convex quadratic optimization problems that aim at exploiting optimally this information. However, solving these problems is typically NP-hard. We consider a simple model for noisy quadratic observation of an unknown vector v0. The unknown vector is constrained to belong to a cone C 3v0. While optimal estimation appears to be intractable for the general problems in this class, we provide evidence that it is tractable when C is a convex cone with an efficient projection. This is surprising, since the corresponding optimization problem is non-convex and –from a worst case perspective– often NP hard. We characterize the resulting minimax risk in terms of the statistical dimension of the cone (C).This quantity is already known to control the risk of estimation from gaussian observations and random linear measurements. It is rather surprising that the same quantity plays a role in the estimation risk from quadratic measurements.

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Sparse Polynomial Learning and Graph Sketching

Very interesting connection between solving a CS problem  and sketching graph from random queries. I wonder it could help in devising biochemical networks.

Sparse Polynomial Learning and Graph Sketching by Murat Kocaoglu, Karthikeyan Shanmugam,  Alexandros G. Dimakis, Adam Klivans

Let f: \{-1,1\}^n \rightarrow \mathbb{R} be a polynomial with at most s non-zero real coefficients. We give an algorithm for exactly reconstructing f given random examples from the uniform distribution on \{-1,1\}^n that runs in time polynomial in n and 2^{s} and succeeds if the function satisfies the \textit{unique sign property}: there is one output value which corresponds to a unique set of values of the participating parities. This sufficient condition is satisfied when every coefficient of f is perturbed by a small random noise, or satisfied with high probability when s parity functions are chosen randomly or when all the coefficients are positive. Learning sparse polynomials over the Boolean domain in time polynomial in n and 2^{s} is considered notoriously hard in the worst-case. Our result shows that the problem is tractable for almost all sparse polynomials. Then, we show an application of this result to hypergraph sketching which is the problem of learning a sparse (both in the number of hyperedges and the size of the hyperedges) hypergraph from uniformly drawn random cuts. We also provide experimental results on a real world dataset.

earlier: Learning Fourier Sparse Set Functions by Peter Stobbe Andreas Krause

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Thesis : Convex Optimization Algorithms and Recovery Theories for Sparse Models in Machine Learning, Bo Huang

Convex Optimization Algorithms and Recovery Theories for Sparse Models in Machine Learning by Bo Huang

Sparse modeling is a rapidly developing topic that arises frequently in areas such as machine learning, data analysis and signal processing. One important application of sparse modeling is the recovery of a high-dimensional object from relatively low number of noisy observations, which is the main focuses of the Compressed Sensing, Matrix Completion(MC) and Robust Principal Component Analysis (RPCA) . However, the power of sparse models is hampered by the unprecedented size of the data that has become more and more available in practice. Therefore, it has become increasingly important to better harnessing the convex optimization techniques to take advantage of any underlying "sparsity" structure in problems of extremely large size. This thesis focuses on two main aspects of sparse modeling. From the modeling perspective, it extends convex programming formulations for matrix completion and robust principal component analysis problems to the case of tensors, and derives theoretical guarantees for exact tensor recovery under a framework of strongly convex programming. On the optimization side, an efficient first-order algorithm with the optimal convergence rate has been proposed and studied for a wide range of problems of linearly constraint sparse modeling problems.

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A statistical model for tensor PCA

Using AMP to perform dimension reduction on tensors, here is something promising.

A statistical model for tensor PCA by Andrea Montanari, Emile Richard

We consider the Principal Component Analysis problem for large tensors of arbitrary order k under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to establish necessary and sufficient conditions under which the principal component can be estimated using unbounded computational resources. It turns out that this is possible as soon as the signal-to-noise ratio β becomes larger than Cklogk−−−−−√ (and in particular β can remain bounded as the problem dimensions increase).
On the other hand, we analyze several polynomial-time estimation algorithms, based on tensor unfolding, power iteration and message passing ideas from graphical models. We show that, unless the signal-to-noise ratio diverges in the system dimensions, none of these approaches succeeds. This is possibly related to a fundamental limitation of computationally tractable estimators for this problem.
We discuss various initializations for tensor power iteration, and show that a tractable initialization based on the spectrum of the matricized tensor outperforms significantly baseline methods, statistically and computationally. Finally, we consider the case in which additional side information is available about the unknown signal. We characterize the amount of side information that allows the iterative algorithms to converge to a good estimate.  

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