Sparse　representation　based　on　over-complete　dictionaries　is　a　hot　issue　in　the　field　of　computer　vision　and　machine　learning.　In　probability　theory,　over-complete　dictionary　can　be　learned　by　non-parametric　Bayesian　techniques　with　Beta　Process.　However,　traditional　probabilistic　dictionary　learning　method　assumes　noise　follows　Gaussian　distribution,　which　can　only　remove　Gaussain　noise.　In　order　to　remove　outlier　or　complex　noise,　we　propose　a　dictionary　learning　method　based　on　non-parametric　Bayesian　technology　by　assuming　the　noise　follows　Laplacian　distribution.　Because　the　non-conjugacy　of　Laplacian　distribution　makes　the　calculation　of　posteriors　of　latent　variables　more　complicate,　thus　we　utilize　a　superposition　of　an　infinite　number　of　Gaussian　distributions　to　substitute　for　L1　density　function.　The　weights　of　mixture　Gaussian　distribution　are　controlled　by　an　extra　hidden　variable.　Then　the　Bayesian　inference　is　applied　to　learn　all　the　key　parameters　in　the　proposed　probabilistic　model,　which　avoids　the　processing　of　parameter　setting　and　fine　tuning.　In　the　experiments,　we　mainly　test　the　performance　of　different　algorithms　in　removing　salt-and-pepper　noise　and　mixture　noises.　The　experimental　results　show　that　the　PSNRs　of　our　algorithm　are　higher　2-4　dB　at　least　than　other　classic　algorithms.