Related papers: Efficient Dealiased Convolutions without Padding
Efficient algorithms for computing linear convolutions based on the fast Fourier transform are developed. A hybrid approach is described that combines the conventional practice of explicit dealiasing (explicitly padding the input data with…
This paper proposes a practical and efficient solution for computing convolutions using hybrid dealiasing. It offers an alternative to explicit or implicit dealiasing and includes an optimized hyperparameter tuning algorithm that uses…
Convolution is a fundamental operation in image processing and machine learning. Aimed primarily at maintaining image size, padding is a key ingredient of convolution, which, however, can introduce undesirable boundary effects. We present a…
Fast multidimensional convolution can be performed naively in quadratic time and can often be performed more efficiently via the Fourier transform; however, when the dimensionality is large, these algorithms become more challenging. A…
One of the most efficient ways to produce unconditional simulations is with the kernel convolution using fast Fourier transform (FFT) [1]. However, when data is located on a surface, this approach is not efficient because data needs to be…
The computation of convolution layers in deep neural networks typically rely on high performance routines that trade space for time by using additional memory (either for packing purposes or required as part of the algorithm) to improve…
The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
Sliding window sums are widely used for string indexing, hashing and time series analysis. We have developed a family of the generic vectorized sliding sum algorithms that provide speedup of O(P/w) for window size $w$ and number of…
In this paper, we present a simple yet effective padding scheme that can be used as a drop-in module for existing convolutional neural networks. We call it partial convolution based padding, with the intuition that the padded region can be…
In this work we characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to…
We study the question of extracting a sequence of functions $\{\boldsymbol{f}_i, \boldsymbol{g}_i\}_{i=1}^s$ from observing only the sum of their convolutions, i.e., from $\boldsymbol{y} = \sum_{i=1}^s \boldsymbol{f}_i\ast…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
This paper introduces a new method for the efficient computation of oscillatory multidimensional lattice sums in geometries with boundaries. Such sums are ubiquitous in both pure and applied mathematics, and have immediate applications in…
A novel energy-efficient edge computing paradigm is proposed for real-time deep learning-based image upsampling applications. State-of-the-art deep learning solutions for image upsampling are currently trained using either resize or…
Neural networks rely on convolutions to aggregate spatial information. However, spatial convolutions are expensive in terms of model size and computation, both of which grow quadratically with respect to kernel size. In this paper, we…
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…