This　paper　introduces　an　L1-norm-based　probabilistic　principal　component　analysis　model　on　2D　data　(L1-2DPPCA)　based　on　the　assumption　of　the　Laplacian　noise　model.　The　Laplacian　or　L1　density　function　can　be　expressed　as　a　superposition　of　an　infinite　number　of　Gaussian　distributions.　Under　this　expression,　a　Bayesian　inference　can　be　established　based　on　the　variational　expectation　maximization　approach.　All　the　key　parameters　in　the　probabilistic　model　can　be　learned　by　the　proposed　variational　algorithm.　It　has　experimentally　been　demonstrated　that　the　newly　introduced　hidden　variables　in　the　superposition　can　serve　as　an　effective　indicator　for　data　outliers.　Experiments　on　some　publicly　available　databases　show　that　the　performance　of　L1-2DPPCA　has　largely　been　improved　after　identifying　and　removing　sample　outliers,　resulting　in　more　accurate　image　reconstruction　than　the　existing　PCA-based　methods.　The　performance　of　feature　extraction　of　the　proposed　method　generally　outperforms　other　existing　algorithms　in　terms　of　reconstruction　errors　and　classification　accuracy.