  In this paper we explore the potential of the double phase functional in an
image processing context. To this end, we study minimizers of the double phase
energy for functions with bounded variation and show that this energy can be
obtained by $\Gamma$-convergence or relaxation of regularized functionals. A
central tool is a capped fractional maximal function of the derivative of $BV$
functions.

Analysis of PDEs;Functional Analysis