I have a 2D matrix corresponding to the shown image in Cartesian coordinates. In image, the horizontal axis is x and vertical corresponds to y-axis. How to change this 2D matrix to polar coordinate system using mathematica ? 
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Image, do a polar transform, then convert the result back into a matrix usingImageData. Some things in Mathematica are easier withImages and some are easier with matrices, so converting between the two representations is pretty common in image processing in Mathematica. $\endgroup$