Compress Sensing Algorthimically

Let m be the Final Image which we are planning to arrive at

Let phi be the transform in which the image m is sparse

let y be the undersampled k-space

FFTU be the Fourier Transform operator based on the sampling pattern

Then we want to minimize of l1 norm of phi*m

with the constraint  | FFTU*m – y| < epsilon

SO here sparsity is important because we are trying to minimize and sparsity helps …

Now why is the incoherence needed ? Looks like the incoherence doesnt give any visible artifacts ,

so we should ensure that the sampling pattern is incoherent …

Point spread function gives good estimate of coherence i.e incoherence ….

Point spread function is Fourier Transform of the filter i.e the sampling pattern we have.


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