Counting Regularization And Solutions For Image Smoothing And Blind Deconvolution

With the advent of the information age,digital images become pervasive,and digital image processing finds a wide variety of applications in national economy,military defense,health care,recreation,and sports,among many others.Image smoothing,which can retain trend component while subduing fluctuant component,is one of the most fundamental image processing operations.Our research about smoothing is restricted to subduing fluctuant component conditionally,so as to preserve the main edges in the original image while smoothing away noise and small oscillations.Image blind deconvolution,whose aim is to restore a sharp image from an observed blurry image without knowledge of the blur kernel,is a classical problem in image processing.Both structure-preserving smoothing and blind deconvolution are ill-posed problems and rely on salient structure extraction.With counting measure as the regularizer,counting regularization plays a vital role in structure-preserving smoothing and blind deconvolution.Guided by the idea of salient structure component extraction,this dissertation pursues research via the counting regularization technique,with image smoothing and blind deconvolution as applications.The detailed contents and main contributions are as follows.Firstly,methods for evaluating proximity operators of three counting regularizers are proposed.For zero crossings counting regularizer,the existence of minimizers of the minimization problem associated with its proximity operator is proved,and several properties of the minimizer are found and proved,including: each element of the minimizer is zero or the corresponding element of the given vector,if the consecutive elements of the given vector are the same in sign then the corresponding elements of the minimizer are all equal to zero or equal to the corresponding elements of the given vector,and that the minimum same sign partition of the given vector corresponds to one same sign partition of the minimizer.It follows that an efficient and accurate method for evaluating the proximity operator of zero crossings counting regularizer can be derived.For linear segments counting regularizer,the optimal substructure of the associated minimization problem is found and a method via dynamic programming is proposed for evaluating its proximity operator.For gray levels counting regularizer,a formula is given for evaluating its proximity operator by projection operator.Secondly,a method for image smoothing based on zero crossings counting regularization is proposed.We use the number of zero crossings of difference as the regularizer,for not blurring salient silhouettes while filtering out textures and details.With the help of proximity operator of zero crossings counting regularizer,a numerical solver of the proposed objective function is derived in the framework of ADMM.Compared with previous methods,our method gives better results in terms of preserving salient structure edges while smoothing away irrelevant textures and details.In addition,we demonstrate the practical value of our method by applications to inverse halftoning,descreening,and text image deblurring.Thirdly,a method for text image deblurring based on gray levels counting regularization is proposed.First intermediate two-tone latent image is estimated by contrastenhancing two-tone counting regularizer,then the blur kernel is obtained by intermediatevalue inhibition counting regularizer.Using the formula for evaluating the proximity operator of gray levels counting regularizer,we derive a numerical solver for the proposed objective function via HQS.Compared with state-of-the-art methods on Pan dataset of blurry text images,our method yields the highest average PSNR value,and is less sensitive to the size of blur kernel.We also validate the effectiveness of our method on real photos.Lastly,a method for natural image deblurring based on linear segments counting regularization is proposed.Through an analysis on the role played by latent image prior in blur kernel estimation,we maintain that modelling salient structure component is more appropriate than modelling natural image.Consequently,we use linear segments counting regularizer as latent image prior and conditional nonzero elements counting regularizer as kernel prior.With the method for evaluating the proximity operator of linear segments counting regularizer,a numerical solver for the proposed objective function is derived via HQS.In comparison with state-of-the-art methods,our method performs better in terms of error ratios on Levin dataset of blurry images,gives higher average PSNR values on K?hler dataset of blurry images,and yields comparable results on real captured photos.In a word,this dissertation proposes novel counting regularizers and associated evaluating methods for their proximity operators,and gives competitive results for image smoothing and blind deconvolution,hence takes existing work on counting regularization a step further.