Derivation of Total Variation Norm?

12 July 2022 0 8K Report

I have attached an image of the TV norm. Can anyone show me the proof of derivation I totally confused? I have knowledge of backward difference and partial derivative things. But I was not successful to get the final equation after the partial derivative. Any kind of help is appreciated.

Thanks in Advance.

Paper Name (from where I took the picture): Quantitative X-ray fluorescence imaging of gold nanoparticles using joint L1 and total variation regularized reconstruction.

DOI: 10.21037/qims.2019.10.15

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