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Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
This paper considers the problem of estimating the covariance of roto-translations computed by the Iterative Closest Point (ICP) algorithm. The problem is relevant for localization of mobile robots and vehicles equipped with depth-sensing…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…
Motivated by recent data analyses in biomedical imaging studies, we consider a class of image-on-scalar regression models for imaging responses and scalar predictors. We propose using flexible multivariate splines over triangulations to…
This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
Deep learning methods for graphs have seen rapid progress in recent years with much focus awarded to generalising Convolutional Neural Networks (CNN) to graph data. CNNs are typically realised by alternating convolutional and pooling layers…
In this paper, we propose a novel quadratic optimized model based on the deep convolutional neural network (QODCNN) for full-reference and no-reference screen content image (SCI) quality assessment. Unlike traditional CNN methods taking all…
Sparse local feature matching is pivotal for many computer vision and robotics tasks. To improve their invariance to challenging appearance conditions and viewing angles, and hence their usefulness, existing learning-based methods have…
We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…
Pooling layers are essential building blocks of convolutional neural networks (CNNs), to reduce computational overhead and increase the receptive fields of proceeding convolutional operations. Their goal is to produce downsampled volumes…
Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical…
A deep neural networks based method is proposed to convert single polarization grayscale SAR image to fully polarimetric. It consists of two components: a feature extractor network to extract hierarchical multi-scale spatial features of…
In this paper, we study a smoothness regularization method for a varying coefficient model based on sparse and irregularly sampled functional data which is contaminated with some measurement errors. We estimate the one-dimensional…
Current deep visual local feature detectors do not model the spatial uncertainty of detected features, producing suboptimal results in downstream applications. In this work, we propose two post-hoc covariance estimates that can be plugged…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Model compression and acceleration are attracting increasing attentions due to the demand for embedded devices and mobile applications. Research on efficient convolutional neural networks (CNNs) aims at removing feature redundancy by…
As the deep neural networks are being applied to complex tasks, the size of the networks and architecture increases and their topology becomes more complicated too. At the same time, training becomes slow and at some instances inefficient.…