Related papers: Color Image Recovery Using Generalized Matrix Comp…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
Handling various objects with different colors is a significant challenge for image colorization techniques. Thus, for complex real-world scenes, the existing image colorization algorithms often fail to maintain color consistency. In this…
In recent years, the field of image inpainting has developed rapidly, learning based approaches show impressive results in the task of filling missing parts in an image. But most deep methods are strongly tied to the resolution of the…
Color information is the most commonly used prior knowledge for depth map super-resolution (DSR), which can provide high-frequency boundary guidance for detail restoration. However, its role and functionality in DSR have not been fully…
A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…
An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then solving a convex program that minimizes the nuclear norm. In many applications, in addition to these entries,…
Image restoration models are typically trained with a pixel-wise distance loss defined over the RGB color representation space, which is well known to be a source of blurry and unrealistic textures in the restored images. The reason, we…
Optical coherence tomography (OCT) captures cross-sectional data and is used for the screening, monitoring, and treatment planning of retinal diseases. Technological developments to increase the speed of acquisition often results in systems…
This paper proposes a general framework to use the cross tensor approximation or tensor ColUmn-Row (CUR) approximation for reconstructing incomplete images and videos. The key importance of the new algorithms is their simplicity and ease of…
General image completion and extrapolation methods often fail on portrait images where parts of the human body need to be recovered - a task that requires accurate human body structure and appearance synthesis. We present a two-stage deep…
Despite the significant progress made by all-in-one models in universal image restoration, existing methods suffer from a generalization bottleneck in real-world scenarios, as they are mostly trained on small-scale synthetic datasets with…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be…
In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…
Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a…
This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix…
Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix.…
We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…