Research On Image Reconstruction And Denoising Algorithm Based On L0 Norm And Variational Method

Images are an important way for human beings to perceive the world and an important means for human beings to obtain and transmit information,which can help people understand the world more intuitively and accurately.In the process of image generation and transmission,it is necessary to consider the transmission cost and noise interference,so it is particularly important to reconstruct and denoise the image.Under this background,this paper theoretically studies the image reconstruction algorithm based on smoothing L0 norm and the image denoising algorithm based on variational method,and proposes new algorithms to improve the image reconstruction and image denoising effects respectively.In the aspect of image reconstruction,a corrected smoothing L0(CSL0)algorithm based on compressed sensing is proposed to solve the problems of low restoration accuracy and long reconstruction time in existing image reconstruction methods.In CSL0 algorithm,an approximate hyperbolic tangent function more similar to L0 norm is proposed to approximate L0 norm.Secondly,in view of the "sawtooth phenomenon" in the steepest descent method and the shortcoming that the modified Newton method is sensitive to the initial value selection,the steepest descent method and the modified Newton method are combined to optimize the target signal to improve the reconstruction accuracy.In addition,by introducing the compound inverse proportional function,CCSL0 algorithm is proposed,which further optimizes the reconstruction time of CSL0 algorithm.Finally,the CSL0 algorithm and CCSL0 algorithm are simulated.The numerical simulation results show that the CSL0 algorithm and CCSL0 algorithm proposed in this paper not only improve the reconstructed peak signal-to-noise ratio and image clarity of the test image,but also shorten the running time of the algorithm to some extent.In the aspect of image denoising,an I-FOTV model for image denoising is proposed to solve the problem that images are easily disturbed by Poisson noise during transmission,which leads to image degradation and image clarity reduction.The advantage of this model is that it not only considers the relationship between the adjacent pixels of the image,but also establishes the relationship with the distant pixels of the image,so it has strong adaptability for removing Poisson noise in the image.In addition,by introducing auxiliary variables and solving variables alternately,an ADMM algorithm for I-FOTV model is derived,which solves the constrained optimization problem of I-FOTV model.Finally,the numerical simulation experiment of the algorithm is carried out,and the results show that the I-FOTV model proposed in this paper not only improves the visual quality,but also improves the peak signal-to-noise ratio.Finally,several algorithms proposed in this paper are applied to the reconstruction and denoising of medical images and conventional images.Through a large number of experimental simulations and comparison with the existing mainstream algorithms,the performance of the reconstruction and denoising algorithms proposed in this paper is verified,which proves that the algorithms proposed in this paper have certain use value in practical applications.