To　overcome　the　biases　in　estimating　the　L1-norm　data　fidelity　term　and　staircase　artifacts　of　the　total　variation　regularization　term,　we　propose　a　nonconvex+nonconvex　model　with　box　constraints　to　recover　images　degraded　by　blurring　and　impulse　noise.　Owing　to　the　data　fidelity　term　and　the　regularization　term　being　nonconvex,　we　apply　a　proximal　linearized　minimization　algorithm　to　solve　the　problem.　To　deal　with　a　subproblem,　we　utilize　the　alternating　direction　multiplier　method.　The　global　convergence　of　the　proposed　algorithm　is　established　under　the　assumption　that　the　objective　function　satisfies　the　Kurdyka-Lojasiewicz　property.　We　also　present　numerical　results　to　demonstrate　that　the　proposed　nonconvex+nonconvex　model　outperforms　existing　models　in　terms　of　both　numerical　accuracy　and　visual　quality.　The　proposed　model　also　exhibits　much　better　performance　than　the　other　methods,　especially　for　piecewise-constant　images.　©　2024　Journal　of　Applied　and　Numerial　Optimization.