A Priori Based On Constrained Langevin Dynamics Sampling Learning Methods Study

In practical applications,prior learning has become more and more important.The general method of portraying prior distributions mainly assumes that a model is a priori distributed,but a directly given prior distribution cannot efectively express the complexity of prior information.However,the random sampling method can fully extract the relevant information of the model,which can be used for a priori learning,so the random sampling method becomes an efective method for a priori learning.In modern signal processing and machine learning,stochastic sampling methods occupy an increasingly important position,which can not only realize the simulation of complex systems,the estimation of unknown parameters and hyperparameters of the system,but also use it to learn the unknown prior distribution of the data.Most of the current sampling methods are based on the sampling of smooth unconstrained target distributions,such as Langevin Dynamics sampling,which is a new trend in MCMC sampling that formally combines a gradient ascent algorithm with a random perturbation term to keep the sampling at a high likelihood of the distribution,and the random perturbation term ensures that it does not collapse to a local maximum.However,the data in real applications often belong to specifc feasible sets,such as sound data,image data,etc.Therefore,this paper proposes a Langevin Dynamics sampling method that introduces a projection constraint,by introducing an orthogonal projection operator on the basis of Langevin Dynamics sampling,to project the collected samples into the feasible set so that they satisfy the distribution requirements The method is fnally applied to noisy samples.Finally,this method is applied to the prior knowledge learning of noisy images by using an alternating strategy to collect samples from the posterior distribution through the proposed sampling method,estimate the posterior distribution with the collected samples,and use the updated posterior distribution to make a great posterior estimate of the clean image,and fnally learn the prior knowledge and clean image from the noisy image,i.e.,to achieve the purpose of image noise reduction.Simulation experiments show that the proposed method is efective.