Background:　The　infrared　image　of　electrical　equipment　often　contains　snow　or　is　blurred,　which　makes　it　difficult　to　detect　and　analyze　its　state.　Methods:　A　prior　infrared　image　denoising　and　restoring　method　based　on　L2-relaxation　L0　analysis　is　proposed.　Through　the　prior　image　estimation,　the　problem　of　image　de-blurring　and　denoising　is　transformed　into　the　problem　of　solving　the　maximum　entropy　of　a　posteriori　probability,　and　then　the　parameters　are　jointly　optimized　to　widely　degrade　the　image,　so　that　the　image　is　locally　sparse　from　the　strip　and　edge　to　the　linear　predictable　texture,　and　the　target　object　to　be　extracted　is　obtained　by　using　the　alternative　iterative　solution,　to　achieve　the　purpose　of　denoising　and　restoring　of　the　original　fuzzy　infrared　image　with　noise.　Two　kinds　of　infrared　images　with　different　brightness　levels　in　a　220kV　booster　station　are　used　for　the　experiments.　Results:　Compared　with　BM3D,　TwIST,　TVL1C,　TVL2C,　the　experimental　results　show　that　the　denoising　and　restoration　effect　of　the　proposed　method　is　clearly　better　than　the　four　methods.　The　PSNR,　ISNR,　and　SSIM　of　the　proposed　method　are　greater　than　the　others,　and　the　calculation　time　is　shorter.　Conclusion:　This　method　can　not　only　enhance　the　sparsity　of　the　infrared　image　target　and　improve　the　estimation　accuracy,　but　also　has　the　advantages　of　minimum　image　distortion,　fast　convergence　speed,　and　preserving　the　target　detail　edge.　This　method　can　provide　a　new　idea　for　other　types　of　infrared　image　denoising　and　restoration.　©　2022　Bentham　Science　Publishers.