Related papers: Fast High-Dimensional Kernel Filtering
Many image processing operations involve the modification of the spatial frequency content of images. Here we demonstrate object-plane spatial frequency filtering utilizing the angular sensitivity of a commercial spectral bandstop filter.…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…
This paper describes a set of rational filtering algorithms to compute a few eigenvalues (and associated eigenvectors) of non-Hermitian matrix pencils. Our interest lies in computing eigenvalues located inside a given disk, and the proposed…
This paper introduces a directional multiscale algorithm for the two dimensional $N$-body problem of the Helmholtz kernel with applications to high frequency scattering. The algorithm follows the approach in [Engquist and Ying, SIAM Journal…
We present a simple and effective image super-resolution algorithm that imposes an image formation constraint on the deep neural networks via pixel substitution. The proposed algorithm first uses a deep neural network to estimate…
Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this…
We present a method for improving a Non Local Means operator by computing its low-rank approximation. The low-rank operator is constructed by applying a filter to the spectrum of the original Non Local Means operator. This results in an…
Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating…
We propose a framework for compressive sensing of images with local distinguishable objects, such as stars, and apply it to solve a problem in celestial navigation. Specifically, let x be an N-pixel real-valued image, consisting of a small…
Recently, Nystr\"{o}m method has proved its prominence empirically and theoretically in speeding up the training of kernel machines while retaining satisfactory performances and accuracy. So far, there are several different approaches…
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite…
In this work we consider the {\em image matching} problem for two grayscale $n \times n$ images, $M_1$ and $M_2$ (where pixel values range from 0 to 1). Our goal is to find an affine transformation $T$ that maps pixels from $M_1$ to pixels…
The Non-Local Means (NLM) image denoising algorithm pushed the limits of denoising. But it introduced a new paradigm, according to which one could capture the similarity of images with the NLM weights. We show that, contrary to the…
In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which…
Super-resolution without explicit sub-pixel motion estimation is a very active subject of image reconstruction containing general motion. The Non-Local Means (NLM) method is a simple image reconstruction method without explicit motion…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…
Object localization is an important task in computer vision but requires a large amount of computational power due mainly to an exhaustive multiscale search on the input image. In this paper, we describe a near real-time multiscale search…
Bilateral filtering (BF) is one of the most classical denoising filters, however, the manually initialized filtering kernel hampers its adaptivity across images with various characteristics. To deal with image variation (i.e.,…
Learning the principal eigenfunctions of an integral operator defined by a kernel and a data distribution is at the core of many machine learning problems. Traditional nonparametric solutions based on the Nystr{\"o}m formula suffer from…