How to minimize this sparse quadratic function?

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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.