Generic　deep　learning　(DL)　networks　for　image　restoration　like　denoising　and　interpolation　lack　mathematical　interpretability,　require　voluminous　training　data　to　tune　large　parameter　sets,　and　are　fragile　in　the　face　of　covariate　shift.　To　address　these　shortcomings,　we　build　interpretable　networks　by　unrolling　variants　of　a　graph-based　optimization　algorithm　of　different　complexities.　Specifically,　for　a　general　linear　image　formation　model,　we　first　formulate　a　convex　quadratic　programming　(QP)　problem　with　a　new　ℓ2-norm　graph　smoothness　prior　called　gradient　graph　Laplacian　regularizer　(GGLR)　that　promotes　piecewise　planar　(PWP)　signal　reconstruction.　To　solve　the　posed　unconstrained　QP　problem,　instead　of　computing　a　linear　system　solution　straightforwardly,　we　introduce　a　variable　number　of　auxiliary　variables　and　correspondingly　design　a　family　of　ADMM　algorithms.　We　then　unroll　them　into　variable-complexity　feedforward　networks,　amenable　to　parameter　tuning　via　back-propagation.　More　complex　unrolled　networks　require　more　labeled　data　to　train　more　parameters,　but　have　better　over-all　performance.　The　unrolled　networks　have　periodic　insertions　of　a　graph　learning　module,　akin　to　a　self-attention　mechanism　in　a　transformer　architecture,　to　learn　pairwise　similarity　structure　inherent　in　data.　Experimental　results　show　that　our　unrolled　networks　perform　competitively　to　generic　DL　networks　in　image　restoration　quality　while　using　only　a　fraction　of　parameters,　and　demonstrate　improved　robustness　to　covariate　shift.　©　1992-2012　IEEE.