Saturday, July 3, 2010
Best catch of all times
The best catch in cricket there ever has been. I am a big fan of cricket and have been following it for quite a number of years now, my all time list had a number of players line-up for the best catch in cricket. Some of them included by hometown hero Yuvraj Singh and the most agile player there ever was Jonty Rhodes, but this catch is special, it has redefined laws of physics, its impossible to do almost a 360 and diving backwards and still managing a one hand catch, I see Lebron doing some superman dunks, or some receivers in the NFL catching some freakish throw, but this catch beats them all. AB De Villiers you are a gem to watch, its because of players like you that cricket is so much fun, gone are the days when cricket used to be fun just because of some mean west indies bowler's who were humongous and used to literally break the batsmen or at least shatter their self confidence. You have redefined cricket and due to catches like the one above my buddies call you the lean white beast
Friday, July 2, 2010
Compressed Sensing
This summer I am on my third work term in TO in this company called IFDS. I have been assigned a task like always to research on this term called compressed sensing, brainstorm this idea and implement it in the real world. But what is COMPRESSED SENSING, this idea has made me believe that once implemented it can lead to a new technology while clicking images and saving them.
The main idea behind compressed sensing is to exploit that there is some structure and redundancy in the majority of interesting signals—they are not pure noise. In particular, most signals are sparse, that is, they contain many coefficients close to or equal to zero, when represented in some domain. (This is the same insight used in many forms of lossy compression.) Compressed sensing typically starts with taking a weighted linear combination of samples also called compressive measurements in a basis different from the basis in which the signal is known to be sparse. The results found by David Donoho, Emmanuel Candès, Justin Romberg and Terence Tao showed that the number of these compressive measurements can be small and still contain all the useful information. Therefore, the task of converting the image back into the intended domain involves solving an underdetermined matrix equation since the number of compressive measurements taken is smaller than the number of pixels in the full image. However, adding the constraint that the initial signal is sparse enables one to solve this underdetermined system of linear equations. The classical solution to such problems is to minimize the L2 norm—that is, minimize the amount of energy in the system. This is usually simple mathematically (involving only a matrix multiplication by the pseudo-inverse of the basis sampled in). However, this leads to poor results for most practical applications, as the unknown coefficients seldom have zero energy. In order to enforce the sparsity constraint when solving for the underdetermined system of linear equations, one should be minimizing the L0 norm, or equivalently maximizing the number of zero coefficients in the new basis. However, searching a solution with this constraint is NP-hard (it contains the subset-sum problem), and so is computationally infeasible for all but the tiniest data sets. Following Tao et al., where it was shown that the L1 norm is equivalent the L0 norm, leads one to solve an easier problem. Finding the candidate with the smallest L1 norm can be expressed relatively easily as a linear program, for which efficient solution methods already exist. These solution methods have been refined over the past few years yielding enormous gain. A more technical insight on the different techniques employed in sampling and decoding signals with compressive sensing can be gained in.
The field of compressive sensing has direct connections to Group Testing, Heavy-hitters, Sparse Coding, Multiplexing, Sparse Sampling, Finite Rate of Innovation. Imaging techniques having a strong affinity with compressive sensing include Coded aperture and Computational Photography. As a generic rule of thumb, any two stage techniques or indirect imaging involving the use of a computer for the reconstruction of a signal or an image is bound to find a use for compressive sensing techniques.
Starting with the famous single-pixel camera from Rice University an up-to-date list of the most recent implementations of compressive sensing in hardware at different technology readiness level is listed in. Some hardware implementation like the one used in MRI or Compressed Genotyping do not require an actual physical change whereas other hardware require substantial re-engineering to perform this new type of sampling. Similarly, a number of hardware implementation already existed before 2004 but while they were acquiring signals in a compressed manner, they generally did not use compressive sensing reconstruction techniques to reconstruct the original signal. The result of these reconstruction were suboptimal and have been greatly enhanced thanks to compressive sensing. Hence there is a large disparity of implementation of compressive sensing in different areas of engineering and science.
Compressed Sensing was initially featured in the news as part of the Single-pixel camera from Rice University. Some aspect of Compressed Sensing was featured in Wired's Engineers Test Highly Accurate Face Recognition. A more recent article in Wired described Compressed Sensing as a full fledged technique in Using Math to Turn Lo-Res Datasets Into Hi-Res Samples. Because the article was talking about sampling for MRI, some confusion might have occurred and was addressed in and in.
The main idea behind compressed sensing is to exploit that there is some structure and redundancy in the majority of interesting signals—they are not pure noise. In particular, most signals are sparse, that is, they contain many coefficients close to or equal to zero, when represented in some domain. (This is the same insight used in many forms of lossy compression.) Compressed sensing typically starts with taking a weighted linear combination of samples also called compressive measurements in a basis different from the basis in which the signal is known to be sparse. The results found by David Donoho, Emmanuel Candès, Justin Romberg and Terence Tao showed that the number of these compressive measurements can be small and still contain all the useful information. Therefore, the task of converting the image back into the intended domain involves solving an underdetermined matrix equation since the number of compressive measurements taken is smaller than the number of pixels in the full image. However, adding the constraint that the initial signal is sparse enables one to solve this underdetermined system of linear equations. The classical solution to such problems is to minimize the L2 norm—that is, minimize the amount of energy in the system. This is usually simple mathematically (involving only a matrix multiplication by the pseudo-inverse of the basis sampled in). However, this leads to poor results for most practical applications, as the unknown coefficients seldom have zero energy. In order to enforce the sparsity constraint when solving for the underdetermined system of linear equations, one should be minimizing the L0 norm, or equivalently maximizing the number of zero coefficients in the new basis. However, searching a solution with this constraint is NP-hard (it contains the subset-sum problem), and so is computationally infeasible for all but the tiniest data sets. Following Tao et al., where it was shown that the L1 norm is equivalent the L0 norm, leads one to solve an easier problem. Finding the candidate with the smallest L1 norm can be expressed relatively easily as a linear program, for which efficient solution methods already exist. These solution methods have been refined over the past few years yielding enormous gain. A more technical insight on the different techniques employed in sampling and decoding signals with compressive sensing can be gained in.
The field of compressive sensing has direct connections to Group Testing, Heavy-hitters, Sparse Coding, Multiplexing, Sparse Sampling, Finite Rate of Innovation. Imaging techniques having a strong affinity with compressive sensing include Coded aperture and Computational Photography. As a generic rule of thumb, any two stage techniques or indirect imaging involving the use of a computer for the reconstruction of a signal or an image is bound to find a use for compressive sensing techniques.
Starting with the famous single-pixel camera from Rice University an up-to-date list of the most recent implementations of compressive sensing in hardware at different technology readiness level is listed in. Some hardware implementation like the one used in MRI or Compressed Genotyping do not require an actual physical change whereas other hardware require substantial re-engineering to perform this new type of sampling. Similarly, a number of hardware implementation already existed before 2004 but while they were acquiring signals in a compressed manner, they generally did not use compressive sensing reconstruction techniques to reconstruct the original signal. The result of these reconstruction were suboptimal and have been greatly enhanced thanks to compressive sensing. Hence there is a large disparity of implementation of compressive sensing in different areas of engineering and science.
Compressed Sensing was initially featured in the news as part of the Single-pixel camera from Rice University. Some aspect of Compressed Sensing was featured in Wired's Engineers Test Highly Accurate Face Recognition. A more recent article in Wired described Compressed Sensing as a full fledged technique in Using Math to Turn Lo-Res Datasets Into Hi-Res Samples. Because the article was talking about sampling for MRI, some confusion might have occurred and was addressed in and in.
Thursday, July 1, 2010
Fake Patriotism
I am so glad to learn that the soccer world cup is about to end… Now all the obnoxious, pretend and retarded soccer fans can finally settle down into their normal lives
Soccer isn’t a big deal in Canada or the States as compared to Europe. There are other sports here that people seem to be into and you just never really seem to hear about Soccer….. Until the world cup comes along .. and then all of a sudden, everyone pretends to be a long time Soccer Fanatic from way back. Why do they have flags hanging out of their car? Why? why do they do that? Why are they all of a sudden a massive fan just because a team from their country is in the competition? The thing that annoys me the most is when someone asks me which team I was supporting ( and as always I have to tell them I am Indian and India doesn't play soccer, let alone making it to the world cup ) and they out of no reason are supporting Brazil/Argentina ( most of these people have no clue regarding soccer and its rules ) just because they are in the last 8 or will be champions. Another annoying thing is at work how one has to support some team so that the boss or his boss is happy.
I don’t get peoples mentality when it comes to sport… Though i am sure most of those people don’t get why people like me are so into Techno-house music and undeveloped countries politics
Oh well… live and let live i guess.
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