Related papers: Fast cosine transform for FCC lattices

In this paper we introduce learnable lattice vector quantization and demonstrate its effectiveness for learning discrete representations. Our method, termed LL-VQ-VAE, replaces the vector quantization layer in VQ-VAE with lattice-based…

Most robot mapping techniques for lidar sensors tessellate the environment into pixels or voxels and assume uniformity of the environment within them. Although intuitive, this representation entails disadvantages: The resulting grid maps…

Cluster expansion approximates an on-lattice potential with polynomial regression. We show that using a convolutional neural network (CNN) instead leads to more accurate prediction due to the depth of the network. We construct our CNN…

Federated learning (FL) has emerged as a promising approach to medical image analysis that allows deep model training using decentralized data while ensuring data privacy. However, in the field of FL, communication cost plays a critical…

This paper introduced a matrix parametrization method based on the Loeffler discrete cosine transform (DCT) algorithm. As a result, a new class of eight-point DCT approximations was proposed, capable of unifying the mathematical formalism…

Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula,…

Convolutional Neural Networks (CNNs) have been recently employed to solve problems from both the computer vision and medical image analysis fields. Despite their popularity, most approaches are only able to process 2D images while most…

Despite recent advances in multi-scale deep representations, their limitations are attributed to expensive parameters and weak fusion modules. Hence, we propose an efficient approach to fuse multi-scale deep representations, called…

The high dimensionality of images presents architecture and sampling-efficiency challenges for likelihood-based generative models. Previous approaches such as VQ-VAE use deep autoencoders to obtain compact representations, which are more…

In this paper, we introduce a low-complexity approximation for the discrete Tchebichef transform (DTT). The proposed forward and inverse transforms are multiplication-free and require a reduced number of additions and bit-shifting…

Binary grid mask representation is broadly used in instance segmentation. A representative instantiation is Mask R-CNN which predicts masks on a $28\times 28$ binary grid. Generally, a low-resolution grid is not sufficient to capture the…

In the era of big data, it is desired to develop efficient machine learning algorithms to tackle massive data challenges such as storage bottleneck, algorithmic scalability, and interpretability. In this paper, we develop a novel efficient…

The problem of faces detection in images or video streams is a classical problem of computer vision. The multiple solutions of this problem have been proposed, but the question of their optimality is still open. Many algorithms achieve a…

An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…

We address the problem of discretizing continuous cosmological signals such as a galaxy distribution for further processing with Fast Fourier techniques. Discretizing, in particular representing continuous signals by discrete sets of sample…

The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. The solution to such an equation is given as the…

We present a new method to bake classical facial animation blendshapes into a fast linear blend skinning representation. Previous work explored skinning decomposition methods that approximate general animated meshes using a dense set of…

Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…

We propose methods for synthesizing multilayer optical lattices of cold atoms in a layer-by-layer manner, to unlock the potential of optical lattices in simulating the fascinating physics of multilayer systems. Central to the approach is to…

The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…