Research On Sparse Signal Denoising Algorithm Based On Total Variational Model

With the progress of science and technology and social development,information digitization has become one of the important characteristics of era,the digital signal has become one of the main ways of access to information,in the process of information generation,transmission and storage is likely to be accompanied by the interference of noise,the existence of noise can make the signal quality to drop,affect people understanding and analysis of the information contained in the signal,Signal denoising process is to process noise signal,suppress or eliminate noise to restore signal quality,and provide strong guarantee for subsequent signal analysis and application.Signal noise reduction technology integrates computer technology,signal processing and application,mathematical analysis and other related knowledge,has a wide range of applications in biomedical,military science,artificial intelligence and other fields.This article from the theoretical analysis to algorithm design to signal noise reduction to waveform detection perspective,in view of the sparse signal de-noising algorithm "staircasing",existing in the process of calculating complex impact noise reduction rate,the problem such as low noise precision of algorithm was improved,and put forward three kinds of improved total variation model noise reduction algorithm,the algorithm is based on a convex penalty term for improvement,Because the non-convex penalty function can improve the sparse characteristics of the signal,which is conducive to signal recovery,noise reduction can be achieved by changing the penalty term and ensuring the convexity of the objective function of the noise reduction algorithm.The forward and backward splitting method is used to iterate the objective function constructed by the penalty term to obtain the optimal solution of the model,and then the accurate sparse signal amplitude is obtained.In order to prove the advantage of non-convex penalty function in total variational denoising algorithm for sparse signal denoising,this thesis carries out denoising verification for piecewise constant signal and biological signal respectively.Gaussian,pulse and mixed noise are added into piecewise constant signal for denoising analysis.The experimental results prove the feasibility of the three noise reduction algorithms.Compared with the classical total variation noise reduction algorithm,the algorithm not only improves the noise reduction accuracy but also improves the noise reduction rate to a certain extent.The results show that the noise reduction errors of the three algorithms are reduced by50.03%,58.45% and 55.62% respectively compared with the classical optimization algorithm based on total variation model.The noise reduction rate increased by 61.37%,67.73% and68.94%,respectively.The average absolute deviation decreased by 11.02%,12.41% and15.03% respectively.At the same time,em G signals and tumor signals with sparse characteristics were verified,and the noise reduction algorithm could reduce the impact of noise on the signal,which verified the effectiveness of the algorithm in practical application.