Depth Image Inpainting: Improving Low Rank Matrix Completion with Low Gradient Regularization

We consider the case of inpainting single depth images. Without corresponding color images, previous or next frames, depth image inpainting is quite challenging. One natural solution is to regard the image as a matrix and adopt the low rank regularization just as inpainting color images. However, the low rank assumption does not make full use of the properties of depth images. A shallow observation may inspire us to penalize the non-zero gradients by sparse gradient regularization. However, statistics show that though most pixels have zero gradients, there is still a non-ignorable part of pixels whose gradients are equal to 1. Based on this specific property of depth images , we propose a low gradient regularization method in which we reduce the penalty for gradient 1 while penalizing the non-zero gradients to allow for gradual depth changes. The proposed low gradient regularization is integrated with the low rank regularization into the low rank low gradient approach for depth image inpainting. We compare our proposed low gradient regularization with sparse gradient regularization. The experimental results show the effectiveness of our proposed approach

A Benchmark for Sparse Coding: When Group Sparsity Meets Rank Minimization

Sparse coding has achieved a great success in various image processing tasks. However, a benchmark to measure the sparsity of image patch/group is missing since sparse coding is essentially an NP-hard problem. This work attempts to fill the gap from the perspective of rank minimization. More details please see the manuscript....Comment: arXiv admin note: text overlap with arXiv:1611.0898

Deep Hyperspectral Prior: Denoising, Inpainting, Super-Resolution

Deep learning algorithms have demonstrated state-of-the-art performance in various tasks of image restoration. This was made possible through the ability of CNNs to learn from large exemplar sets. However, the latter becomes an issue for hyperspectral image processing where datasets commonly consist of just a few images. In this work, we propose a new approach to denoising, inpainting, and super-resolution of hyperspectral image data using intrinsic properties of a CNN without any training. The performance of the given algorithm is shown to be comparable to the performance of trained networks, while its application is not restricted by the availability of training data. This work is an extension of original "deep prior" algorithm to HSI domain and 3D-convolutional networks.Comment: Published in ICCV 2019 Workshop

Robust Matrix Completion via Maximum Correntropy Criterion and Half Quadratic Optimization

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In this paper, we propose a novel and fast robust matrix completion method based on maximum correntropy criterion (MCC). The correntropy based error measure is utilized instead of using $l_2$-based error norm to improve the robustness to noises. Using the half-quadratic optimization technique, the correntropy based optimization can be transformed to a weighted matrix factorization problem. Then, two efficient algorithms are derived, including alternating minimization based algorithm and alternating gradient descend based algorithm. The proposed algorithms do not need to calculate singular value decomposition (SVD) at each iteration. Further, the adaptive kernel selection strategy is proposed to accelerate the convergence speed as well as improve the performance. Comparison with existing robust matrix completion algorithms is provided by simulations, showing that the new methods can achieve better performance than existing state-of-the-art algorithms

From Group Sparse Coding to Rank Minimization: A Novel Denoising Model for Low-level Image Restoration

Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with each group contains low-rank property. In this paper, we propose a novel low-rank minimization based denoising model for IR tasks under the perspective of GSC, an important connection between our denoising model and rank minimization problem has been put forward. To overcome the bias problem caused by convex nuclear norm minimization (NNM) for rank approximation, a more generalized and flexible rank relaxation function is employed, namely weighted nonconvex relaxation. Accordingly, an efficient iteratively-reweighted algorithm is proposed to handle the resulting minimization problem combing with the popular L_(1/2) and L_(2/3) thresholding operators. Finally, our proposed denoising model is applied to IR problems via an alternating direction method of multipliers (ADMM) strategy. Typical IR experiments on image compressive sensing (CS), inpainting, deblurring and impulsive noise removal demonstrate that our proposed method can achieve significantly higher PSNR/FSIM values than many relevant state-of-the-art methods.Comment: Accepted by Signal Processin

M∗\mathbf{M^*}-Regularized Dictionary Learning

Classical dictionary learning methods simply normalize dictionary columns at each iteration, and the impact of this basic form of regularization on generalization performance (e.g. compression ratio on new images) is unclear. Here, we derive a tractable performance measure for dictionaries in compressed sensing based on the low $M^*$ bound and use it to regularize dictionary learning problems. We detail numerical experiments on both compression and inpainting problems and show that this more principled regularization approach consistently improves reconstruction performance on new images

Constrained Deep Learning using Conditional Gradient and Applications in Computer Vision

A number of results have recently demonstrated the benefits of incorporating various constraints when training deep architectures in vision and machine learning. The advantages range from guarantees for statistical generalization to better accuracy to compression. But support for general constraints within widely used libraries remains scarce and their broader deployment within many applications that can benefit from them remains under-explored. Part of the reason is that Stochastic gradient descent (SGD), the workhorse for training deep neural networks, does not natively deal with constraints with global scope very well. In this paper, we revisit a classical first order scheme from numerical optimization, Conditional Gradients (CG), that has, thus far had limited applicability in training deep models. We show via rigorous analysis how various constraints can be naturally handled by modifications of this algorithm. We provide convergence guarantees and show a suite of immediate benefits that are possible -- from training ResNets with fewer layers but better accuracy simply by substituting in our version of CG to faster training of GANs with 50% fewer epochs in image inpainting applications to provably better generalization guarantees using efficiently implementable forms of recently proposed regularizers

The Power of Complementary Regularizers: Image Recovery via Transform Learning and Low-Rank Modeling

Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properties, we develop an image restoration framework using a transform learning scheme with joint low-rank regularization. The approach owes some of its computational efficiency and good performance to the use of transform learning for adaptive sparse representation rather than the popular synthesis dictionary learning algorithms, which involve approximation of NP-hard sparse coding and expensive learning steps. We demonstrate the proposed framework in various applications to image denoising, inpainting, and compressed sensing based magnetic resonance imaging. Results show promising performance compared to state-of-the-art competing methods.Comment: 13 pages, 7 figures, submitted to TI

Novel variational model for inpainting in the wavelet domain

Wavelet domain inpainting refers to the process of recovering the missing coefficients during the image compression or transmission stage. Recently, an efficient algorithm framework which is called Bregmanized operator splitting (BOS) was proposed for solving the classical variational model of wavelet inpainting. However, it is still time-consuming to some extent due to the inner iteration. In this paper, a novel variational model is established to formulate this reconstruction problem from the view of image decomposition. Then an efficient iterative algorithm based on the split-Bregman method is adopted to calculate an optimal solution, and it is also proved to be convergent. Compared with the BOS algorithm the proposed algorithm avoids the inner iteration and hence is more simple. Numerical experiments demonstrate that the proposed method is very efficient and outperforms the current state-of-the-art methods, especially in the computational time.Comment: 20page

Unsupervised Deep Context Prediction for Background Foreground Separation

In many advanced video based applications background modeling is a pre-processing step to eliminate redundant data, for instance in tracking or video surveillance applications. Over the past years background subtraction is usually based on low level or hand-crafted features such as raw color components, gradients, or local binary patterns. The background subtraction algorithms performance suffer in the presence of various challenges such as dynamic backgrounds, photometric variations, camera jitters, and shadows. To handle these challenges for the purpose of accurate background modeling we propose a unified framework based on the algorithm of image inpainting. It is an unsupervised visual feature learning hybrid Generative Adversarial algorithm based on context prediction. We have also presented the solution of random region inpainting by the fusion of center region inpaiting and random region inpainting with the help of poisson blending technique. Furthermore we also evaluated foreground object detection with the fusion of our proposed method and morphological operations. The comparison of our proposed method with 12 state-of-the-art methods shows its stability in the application of background estimation and foreground detection.Comment: 17 page