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Minimization problem image processing

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OJ27
OJ27 2017-12-27
关闭： John D'Errico 2017-12-28
Hello,
I'm trying to minimize this function (by p):
where:
p is a NxN image
k is NxN image
tc is NxN image
* is the convolution of image k and image p
grad() is the gradient of the image
||·||_L1 is the L1 norm
||·||_L2 is the L2 norm
theta is a constant
I need a little bit of help coding this one in vector form.
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OJ27
OJ27 2017-12-28
I have looked at some implementations without the convolution, but this part is just throwing me off. I have read Young's inequality but don't know how to implement it.

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