Hand gesture recognition has been playing an important role in robotic applications, which allows robots to communicate with humans in an effective way. However, it typically desires to process high-dimensional data, such as images or sensor measurements. To address the computational challenges due to the data growth, it is desirable to select most relevant features during recognition by reducing the redundancy of the data. In this paper, we propose a novel feature selection approach based on the separable nonnegative matrix factorization (NMF) framework for hand gesture recognition. In particular, we adopt a nonconvex regularization term, i.e., the ratio of matrix nuclear norm and Frobenius norm. The proposed method reduces the data dimension by utilizing the data low-rankness in an adaptive way. To address the nonconvexity of the proposed model, we reformulate it by introducing an auxiliary variable and then apply the alternating direction method of multipliers (ADMM). Furthermore, a variety of numerical experiments on binary and grayscale hand gesture images demonstrate the efficiency of the proposed feature selection approach in improving the quality of factorization and its potential impact on robotic applications.

Traditional machine learning techniques require centralizing all training data on one server or data hub. However, with the development of communication technologies and a huge amount of decentralized data on many clients, collaborative machine learning has become the main interest while providing privacy-preserving frameworks. Federated learning (FL) provides such a solution to learn a shared model while keeping training data at local clients. On the other hand, in a wide range of machine learning and signal processing applications, the desired solution naturally has a certain structure that can be framed as sparsity with respect to a certain dictionary. This problem can be formulated as an optimization problem with sparsity constraints and solving it efficiently has been one of the primary research topics in the traditional centralized setting. In this paper, we propose a novel algorithmic framework, federated gradient matching pursuit (FedGradMP), to solve the sparsity constrained minimization problem in the FL setting. We also generalize our algorithms to accommodate various practical FL scenarios when only a subset of clients participate per round, when the local model estimation at clients could be inexact, or when the model parameters are sparse with respect to general dictionaries. Our theoretical analysis shows the linear convergence of the proposed algorithms. A variety of numerical experiments are conducted to demonstrate the great potential of the proposed framework – fast convergence both in communication rounds and computation time for many important scenarios without intricate parameter tuning.

We present a spatio-temporal super-resolution method for reconstructing a sequence of observations collected by imaging satellites. A sequence of observations is assumed to be defined on a low resolution spatio-temporal grid. It is further assumed that the sequence is generated by blurring of a captured scene with a spatio-temporal convolution kernel and is degraded by noise. Our method simultaneously exhibits deconvolution of the sequence of images from the effects of spatio-temporal blur, denoising of the data, and upsampling of the low-resolution sequence to a high resolution spatiotemporal grid. We perform the super-resolution in the spacetime domain, as opposed to super-resolving the sequence separately and sequentially to a higher spatial and then temporal resolution grid. Simultaneous space-time optimization achieves a more efficient and more accurate reconstruction than reconstructing a sequence frame by frame. The proposed super-resolution methodology is based on total variation regularization and computes the solution using the alternating direction method of multipliers. Numerical results show our approach to be robust and computationally efficient.

Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging, and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have been developed to apply various regularization techniques together with the operator-splitting type of algorithms. Due to the unprecedented growth of data, it becomes increasingly desirable to use streamlined algorithms to achieve real-time computation, such as stochastic optimization algorithms that have recently emerged as an efficient family of methods in machine learning. In this work, we propose a novel algorithmic framework based on the Kaczmarz algorithm for tensor recovery. We provide thorough convergence analysis and its applications from the vector case to the tensor one. Numerical results on a variety of tensor recovery applications, including sparse signal recovery, low-rank tensor recovery, image inpainting, and deconvolution, illustrate the enormous potential of the proposed methods.

Remote sensing data from hyperspectral cameras suffer from limited spatial resolution, in which a single pixel of a hyperspectral image may contain information from several materials in the field of view. Blind hyperspectral image unmixing is the process of identifying the pure spectra of individual materials (i.e., endmembers) and their proportions (i.e., abundances) at each pixel. In this article, we propose a novel blind hyperspectral unmixing model based on the graph total variation (gTV) regularization, which can be solved efficiently by the alternating direction method of multipliers (ADMM). To further alleviate the computational cost, we apply the Nyström method to approximate a fully connected graph by a small subset of sampled points. Furthermore, we adopt the Merriman-Bence-Osher (MBO) scheme to solve the gTV-involved subproblem in ADMM by decomposing a gray-scale image into a bitwise form. A variety of numerical experiments on synthetic and real hyperspectral images are conducted, showcasing the potential of the proposed method in terms of identification accuracy and computational efficiency.

Due to the limitations of imaging sensors, remote sensing images often have limited resolution. To address this issue, various super-resolution (SR) image reconstruction techniques have been developed to reconstruct a high-resolution image from a sequence of low-resolution, noisy and blurry observations. In this paper, we propose an efficient super-resolution image reconstruction method for geometrically deformed remote sensing images, based on the nonlocal total variation (NLTV) regularization. The proposed minimization problem is solved by a fast primal-dual algorithm. Numerical experiments demonstrate the performance of the proposed method.

A variant of fuzzy c‐means (FCM) clustering algorithm for image segmentation is provided. Unlike the ‐norm distance in FCM, with norm is used to measure the distance of the pixel intensity to its cluster centre in the energy functional. Moreover, local spatial information and colour information are incorporated into the model to enhance the robustness to noise and outliers. The proposed algorithm is called fuzzy local information (FLILp) clustering. To overcome the difficulty of finding cluster centres, ‐norm distance is approximated by weighted distance. The advantages of FLILp are: (i) it is strongly robust to noise and outliers, (ii) it is applied to the original image and (iii) it preserves image edges. Numerical examples and comparisons of image segmentation on both synthetic and real images illustrate the outstanding performance and robustness of the proposed method.

It is a challenging task to reconstruct images from their noisy, blurry, and/or incomplete measurements, especially those with important details and features such as medical magnetic resonance (MR) and CT images. We propose a novel regularization model that integrates two recently developed regularization tools: total generalized variation (TGV) by Bredies, Kunisch, and Pock; and shearlet transform by Labate, Lim, Kutyniok, and Weiss. The proposed model recovers both edges and fine details of images much better than the existing regularization models based on the total variation (TV) and wavelets. Specifically, while TV preserves sharp edges but suffers from oil painting artifacts, TGV “selectively regularizes” different image regions at different levels and thus largely avoids oil painting artifacts. Unlike the wavelet transform, which represents isotropic image features much more sparsely than anisotropic ones, the shearlet transform can efficiently represent anisotropic features such as edges, curves, and so on. The proposed model based on TGV and the shearlet transform has been tested in the compressive sensing context and produced high-quality images using fewer measurements than the state-of-the-art methods. The proposed model is solved by splitting variables and applying the alternating direction method of multiplier (ADMM). For certain sensing operators, including the partial Fourier transform, all the ADMM subproblems have closed-form solutions. Convergence of the algorithm is briefly mentioned. The numerical simulations presented in this paper use the incomplete Fourier, discrete cosine, and discrete wavelet measurements of MR images and natural images. The experimental results demonstrate that the proposed regularizer preserves various image features (including edges and textures), much better than the TV/wavelet based methods.