Low-Rank Laplacian Convolution Model for Color Image Inpainting

Step-by-Step Implementation of Low-Rank Laplacian Convolution Model with NumPy

Image inpainting is a classical inverse problem in the field of computer vision. To reconstruct the missing regions of an image from partially observed pixels, low-rank models such as matrix factorization/completion and tensor factorization/completion play an important role. The basic idea of these low-rank model lies in revealing the low-rankness property of partial observations in the form of matrix or tensor. In this story, we introduce a simple image inpainting approach by utilizing the low-rankness and establishing the local correlations in a color image. For reproducing the experiment, we provide Python codes with the NumPy package.

Color Images are indeed Tensors

Generally speaking, we can see the rows and the columns in an image, just in the form of matrix. But in fact, for a color image, there are some special settings: 1) a RGB image has three channels: red, green, and blue; 2) a CMYK image has four channels: cyan, magenta, yellow, and black. As a result, a color image is usually in the form of tensor (e.g., Figure 1).

Figure 1: A color image is indeed a third-order tensor with m rows, n columns, and t channels. In terms of RGB images, t = 3; In terms of CMYK images, t = 4.

To carry out an image inpainting task, it is usually established as a tensor…