Monday, December 26, 2011

Sparse Processing: Time to Unlearn Shannon-Nyquist Theorem?

 Signal Processing: An ever dynamic domain since its evolution keeps changing its course day after day. With the increasing number of functions being pushed to sophisticated software algorithms there is very little room for the circuit level processing. This calls for a high degree of visualization and mathematical thought for the budding up engineers.

 The inevitable technique which when one looks forward for sampling the natural signals to the discrete domain was the all famous Shannon-Nyquist criterion. This calls for a very ideal condition of the band limited signal that would never in the universe ever. As the expansion of the frequency domain would call for a very high compression of the time domain and vice-versa which is the reason for all the errors arising due to the approximation of signals to band limited signals. Though we sample and transform the entire spectra of the signal we see that the required information is concentrated to certain hot-spots in the transformed signal. This is the feature that is well exploited in the convectional compressing technique.

  "Compressive sampling" has emerged. By using nonlinear recovery algorithms, super-resolved signals and images can be reconstructed from what appears to be highly incomplete data. Compressive sampling shows us how data compression can be implicitly incorporated into the data acquisition process, a gives us a new vantage point for a diverse set of applications including accelerated tomographic imaging, analog-to-digital conversion, and digital photography. 

 The recently discussed Sparse technology defines every signal in the universe as Sparsely distributed and aims at the acquisition of these sparsely distributed elements from the signal. Thus saving the energy, memory and also the computational complexity. Interestingly to be well versed in Sparse processing the only mathematical tool is solving the linear system of equation. With a mathematical mind and proper understanding of the L1 - Magic the entire compressive sensing problems can be computed easily. All it requires is a team of efficient mathematicians and engineers with proper visualization to the nature.

 The optimization techniques through this method has proved much efficient and faster than the convectional method. The mathematical proof for the Compressive sensing was provided by a Field Medalist " Terence Tao.

 This arena calls for a wide scope of research as various techniques like Inpainiting, Deionisation etc. which are otherwise complex could be solved by just the usual differential equation of heat.

We shall discuss in much more detail in the upcoming days.

Links that might help you.

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