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There is a problem when I'm reading a paper.

Equation:

$min_p|p-p^*|^2+\alpha |R(p)|^2 + \beta |D(p)-\delta|^2$,

where $p, p^*, R(p), D(p), \delta$ are all $M\times N$ matrices, and $p^*, R(), D(), \delta$ are known.

The paper just mentioned "which (this equation) represents a sparse quadratic in $p$". According to this sentence, I cannot figure out how to solve this equation. Any hints would be appreciated.

Here is the paper. The equation is on Page 4, eq.6.

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  • $\begingroup$ Have you tried asking the authors of the paper directly? $\endgroup$
    – Joonas Ilmavirta
    Commented Feb 27, 2015 at 21:33
  • $\begingroup$ Yes, I have sent an email to the author, but he has graduated and I can only find his university email. $\endgroup$
    – Sfe
    Commented Feb 27, 2015 at 21:35

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The quadratic form is positive semidefinite, so minimizing it requires solving a system of sparse linear equations corresponding to the gradient. The paper mentions that TAUCS was used for solving this.

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  • $\begingroup$ Thank you. Could you please give me more information or references about "solving a system of sparse linear equations corresponding to the gradient"? Is this $D()$ needs to be applied to the regular structure (image pixel or 3D vertex)? $\endgroup$
    – Sfe
    Commented Feb 27, 2015 at 22:49

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