Compressed Sensing


Compressive Sampling of Polynomial Chaos Expansions: Convergence By 4.bp.blogspot.com
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The theory is called compressed sensing, and enables compressive sampling without having to look at the raw data first. Physicists at the University of Oslo refer to the method as one of this century's most significant mathematical discoveries. National Physical Laboratory (NPL) researchers have designed a new technique for identifying the defective areas in photovoltaic (PV) cells with the help of ‘compressed sensing. PV cells or solar panels are being widely employed with the increasing So a camera without a lens is kind of deal-breaker, right? Maybe not. But before we go there, you need to understand something called “compressed sensing” — or at least I did. Compressed (alternatively, compressive) sensing involves the notion that Using a mathematical concept called sparsity, the compressed-sensing algorithm takes lo-res files and transforms them into sharp images. Illustration: Gabriel Peyre In the early spring of 2009, a team of doctors at the Lucile Packard Children’s Hospital compressed sensing, the use of sensors for imaging (or other sensing) of an object in a manner that uses a limited subset of the available data in order to improve efficiency or conserve resources, holds potential benefits for Defense Department systems The proposed approach exploits and builds on recent results in the field of compressed sensing to jointly estimate the common frame and the innovative frames for each video segment. We refer to the proposed modeling framework by common and innovative .

This same technique of acquiring the minimum amount of information needed for a measurement seemed to offer a way around the uncertainty principle. To test compressive sensing in the quantum world, physicist John C. Howell and his team at the University of In quantum physics, momentum and position are an example of conjugate variables. This means they are connected by Heisenberg's Uncertainty Principle, which says that both quantities cannot be simultaneously measured precisely. Recently, researchers have Now University of Rochester physicists have shown that a technique called compressive sensing also offers a way to measure both variables at the same time, without violating the Uncertainty Principle. In a paper published in Physical Review Letters this In quantum physics, momentum and position are an example of conjugate variables. This means they are connected by Heisenberg’s Uncertainty Principle, which says that both quantities cannot be simultaneously measured precisely. Recently, researchers have .





Another Picture of compressed sensing:




Nuit Blanche



Here is another simple but very impressive implementation:



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The ADMM for dictionary learning Toolbox is here while the paper



David Rousseau whom I spoke to while at JIONC , pointed me to one of

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