Compressed sensing is a relatively new sensing paradigm that proposes acquisition of images directly in compressed format. This is different from the more conventional sensing methods where the entire 2D image array is first measured followed by JPEG/MPEG compression after acquisition. Compressed sensing basically aims to reduce *acquisition time*. It has shown great results in speeding up MRI (magnetic resonance imaging) acquisition where time is critical, in improving frame rates of videos, and in general in improving acquisition rates in a variety of imaging modalities. Central to compressed sensing is the solution to a seemingly under-determined system of linear equations, i.e. a system of equations where the number of unknowns (n) is greater than the number of knowns (m). Hence at first glance, there will be infinitely many solutions. However the theory of compressed sensing states that if the vector of unknowns is sparse, and the system's sensing matrix obeys certain properties, then the system is provably well-posed and unique solutions can be guaranteed. Moreover, the theory also states that the solution can be computed efficiently, and is robust to measurement noise or slight deviations from sparsity. In this talk, I will give an introduction to the above concepts. I will also introduce a few applications, and enumerate a few research challenges/directions.
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