The Research On Theory,method,and Application Of Deconvolution Total Least Squares

Many models of data processing can be simplified as convolution model with noise in high-resolution earth observation system,such as quality assessment and preprocessing of full-waveform Lidar data,quality improvement of the blurry remote sensing images,the improvement of the azimuth resolution in real aperture radar,and so on.The ideal convolution kernel are noise-free,and classic least-squares（LS）as data processing method are used to restore these degraded signals in usual.However,in practice,observation signal data and recorded convolution kernel affected by noise at the same times.And the ill-conditioned property of the model leads to be unsuitable for the classic LS method to solve it,which involves all errors in its observation vector and coefficient matrix.Therefore,according to the principle of TLS,the theory and methods of the deconvolution TLS are proposed and studied.And it can be applied to solve the practical problems,such as full-waveform Lidar data processing and blurry remote sensing images deblurring.The main researches in this dissertation include as follows:1)The general partial Errors-in-Variables（GPEIV）model with corresponding parameters estimation method and a novel first-order approximate posterior precision estimation method are developed herein.When the coefficient matrix is statistically correlated with the observation vector,a GPEIV model is constructed,and the formula of the corresponding weighted TLS method is derived due to the invalidation of the classic partial EIV model.A posterior precision estimation formula of estimated parameters is proposed.Furthermore,starting from the fact that the estimated parameters necessarily satisfy the partial differential equation of Lagrange multipliers method,a new first-order approximate posterior precision estimation method is put forward.The theoretic difference between the proposed method and existing methods are analyzed by the mathematical formula.What is mentioned above is theoretical basis on the proposal of the deconvolution total least-squares method.（2）Deconvolution least-squares method is presented.From the model of full-waveform Lidar data processing as an intro,the convolution GM model is arisen.For handling the ill-posedness of the waveform deconvolution,we modelled prior regularization term.Under the frame of maximum a posteriori probability（MAP）,the deconvolution LS formula based on nonconvex L₀-norm is derived,and whose algorithm is also designed.A necessary bias analysis of the estimated parameters is implemented and then the bias-correction formula can be derived.（3）On the basis of the deconvolution least-squares method,for the deconvolution problem of one-dimension signal,we derive the formula of the deconvolution TLS with bias-correction.The observation errors,estimated errors,and cumulative errors existing in the computation process of deconvolution LS are analyzed in convolution GM model,the necessarity of the convolution EIV model is determined.The convolution EIV model considering the kernel errors,whose ill-condition can be emphasized.To address the ill-posedness of the convolution EIV model,the jointed prior model between convolution kernel errors and latent signal are established.Moreover,the general formula of the deconvolution TLS is derived by the half-quadratic splitting method,and it can be instantized herein.At the same times,the bias analysis of the deconvolution TLS solution is implemented,and the expressions of bias-correction are derived.Experimental results demonstrate that the proposed methods can restore the reference scattering cross-sections signal,and its effectiveness and feasibility are proven.（4）The image non-blind deblurring model and method based on deconvolution TLS with bias-correction is proposed.For the ill-condition of the problem,we present the jointed sparsity prior of the convolution errors and latent image.The deconvolution TLS method is extended from one-dimensional space to two-dimensional space,the image non-blind image deblurrig based ondecovolution TLS with bias-correction is established.The analytical expressions of unknown parameters are also derived,and the corresponding algorithm is designed.Finally,the effect of the bias originating from the multiplicative errors for restored images is researched in detail.And we use an image filtering method to modify the bias.The experimental results infers that the proposed can improve the quality of the restored images.（5）A new image blind deblurring framework based on deconvolution TLS is developed.We roundly analyze observation errors in blind image deblurring flow.On the basis of the theory of the deconvoltion TLS,the new blind deblurring framework is established.The proposed framework is“plug and play”,which can be embedded different advanced image priors.The experiemental results can demonstrate that the proposed new framework can estimate more accurate convolution kernel and further to improve the quality of the restored images.