In　recent　years,　matrix-valued　optimization　algorithms　have　been　studied　to　enhance　the　computational　performance　of　vector-valued　optimization　algorithms.　This　paper　presents　two　matrix-type　projection　neural　networks,　continuous-time　and　discrete-time　ones,　for　solving　matrix-valued　optimization　problems.　The　proposed　continuous-time　neural　network　may　be　viewed　as　a　significant　extension　to　the　vector-type　double　projection　neural　network.　More　importantly,　the　proposed　discrete-time　projection　neural　network　is　suitable　for　parallel　implementation　in　terms　of　matrix　state　spaces.　Under　pseudo-monotonicity　and　Lipschitz　continuous　conditions,　the　proposed　two　matrix-type　projection　neural　networks　are　guaranteed　to　be　globally　convergent　to　the　optimal　solution.　Finally,　the　proposed　matrix-type　projection　neural　network　is　effectively　applied　to　image　restoration.　Computed　examples　show　that　the　two　proposed　matrix-type　projection　neural　networks　are　much　superior　to　the　vector-type　projection　neural　networks　in　terms　of　computation　speed.　©　2019,　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.