Patch-based low rank matrix approximation has shown great potential in image denoising. Among state-of-the-art methods in this topic, the weighted nuclear norm minimization (WNNM) has been attracting significant attention due to its competitive denoising performance. For each local patch in an image, the WNNM method groups nonlocal similar patches by block matching to formulate a low-rank matrix. However, the WNNM often chooses irrelevant patches such that it may lose fine details of the image, resulting in undesirable artifacts in the final reconstruction. In this regards, this paper aims to provide a denoising algorithm which further improves the performance of the WNNM method. For this purpose, we develop a new nonlocal similarity measure by exploiting both pixel intensities and gradients and present a filter that enhances edge information in a patch to improve the performance of low rank approximation. The experimental results on widely used test images demonstrate that the proposed denoising algorithm performs better than other state-of-the-art denoising algorithms in terms of PSNR and SSIM indices as well as visual quality.

A joint demosaicing and denoising task refers to the task of simultaneously reconstructing and denoising a color image from a patterned image obtained by a monochrome image sensor with a color filter array. Recently, inspired by the success of deep learning in many image processing tasks, there has been research to apply convolutional neural networks (CNNs) to the task of joint demosaicing and denoising. However, such CNNs need many training data to be trained, and work well only for patterned images which have the same amount of noise they have been trained on. In this paper, we propose a variational deep image prior network for joint demosaicing and denoising which can be trained on a single patterned image and works for patterned images with different levels of noise. We also propose a new RGB color filter array (CFA) which works better with the proposed network than the conventional Bayer CFA. Mathematical justifications of why the variational deep image prior network suits the task of joint demosaicing and denoising are also given, and experimental results verify the performance of the proposed method.

Over the past decade, deep learning-based computer vision methods have been shown to surpass previous state-of-the-art computer vision techniques in various fields, and have made great progress in various computer vision problems, including object detection, object segmentation, face recognition, etc. Nowadays, major IT companies are adding new deep-learning-based computer technologies to edge devices such as smartphones. However, since the computational cost of deep learning-based models is still high for edge devices, research is being actively carried out to compress deep learning-based models while not sacrificing high performance. Recently, many lightweight architectures have been proposed for deep learning-based models which are based on low-rank approximation. In this paper, we propose an alternating tensor compose-decompose (ATCD) method for the training of low-rank convolutional neural networks. The proposed training method can better train a compressed low-rank deep learning model than the conventional fixed-structure based training method, so that a compressed deep learning model with higher performance can be obtained in the end of the training. As a representative and exemplary model to which the proposed training method can be applied, we propose a rank-1 convolutional neural network (CNN) which has a structure alternatively containing 3-D rank-1 filters and 1-D filters in the training stage and a 1-D structure in the testing stage. After being trained, the 3-D rank-1 filters can be permanently decomposed into 1-D filters to achieve a fast inference in the test time. The reason that the 1-D filters are not being trained directly in 1-D form in the training stage is that the training of the 3-D rank-1 filters is easier due to the better gradient flow, which makes the training possible even in the case when the fixed structured network with fixed consecutive 1-D filters cannot be trained at all. We also show that the same training method can be applied to the well-known MobileNet architecture so that better parameters can be obtained than with the conventional fixed-structure training method. Furthermore, we show that the 1-D filters in a ResNet like structure can also be trained with the proposed method, which shows the fact that the proposed method can be applied to various structures of networks.

In this paper, we present an effective method for analyzing patterns in the Russia–Ukraine war based on the Lanchester model. Due to the limited availability of information on combat powers of engaging forces, we utilize the loss of armored equipment as the primary data source. To capture the intricate dynamics of modern warfare, we partition the combat loss data into disjoint subsets by examining their geometric properties. Separate systems of ordinary differential equations for these subsets are then identified using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm under a generalized formulation of the historical Lanchester model. We provide simulations of our method to demonstrate its effectiveness and performance in analyzing contemporary warfare dynamics.