Image Inpainting Algorithms Based On Structural Prior And Tensor Algebra

In daily life,during the data acquisition and processing procedures,the digital images may have missing values due to mechanical failure or human-induced factors.Estimating the missing pixels in an image is usually referred to as image inpainting.Almost all of the existing image inpainting methods are designed based on a proven fact that a natural image contains repeating patterns which could be used to estimate the missing values.The mentioned principle is also known as low-rank property.Due to the high-dimensional data Estimating missing pixels in an image is also known as tensor completion.In this thesis,an inpainting framework consisting of interpolation and low-rank tensor completion are proposed.Firstly,in chapter 3,using the concept of t-product,difference tensors A and B that when multiplied by a visual tensor X takes the gradient of X,i.e.?X,are proposed.Moreover,in chapter 4,by tensor nuclear norm and L_1,2,1norm,we impose low-rank regularization on nonlocal similar patches while separating the sparse part from the tensor.Specifically,our algorithm consists of two steps:the first step is initializing the image with triangulation-based linear interpolation and the second step is grouping similar nonlocal patches as a tensor then applying the proposed tensor completion technique.Specifically,with treating a group of patch matrices as a tensor,we impose the low-rank constraint on the tensor through the recently proposed tensor nuclear norm.Moreover,we observe that after the first interpolation step,the image get blurred and thus the similar patches we have found may not exactly match with the reference.We name the problem as Patch Mismatch,and then in order to avoid the error caused by it,we further decompose the patch tensor into a low-rank tensor and a sparse tensor,which means the exceptive horizontal strips in mismatched patches.Furthermore,our theoretical analysis shows that the error caused by Patch Mismatch can be decomposed into two components,one of which can be bounded by a reasonable assumption named local patch similarity,and the other part is lower than that using matrix completion.Extensive experimental results on real-world datasets verify our method's superiority to the state-of-the-art tensor based image inpainting methods.