774 research outputs found
Using the discrete hadamard transform to detect moving objects in surveillance video
In this paper we present an approach to object detection in surveillance video based on detecting moving edges
using the Hadamard transform. The proposed method is characterized by robustness to illumination changes
and ghosting effects and provides high speed detection, making it particularly suitable for surveillance applications.
In addition to presenting an approach to moving edge detection using the Hadamard transform, we
introduce two measures to track edge history, Pixel Bit Mask Difference (PBMD) and History Update Value
(H UV ) that help reduce the false detections commonly experienced by approaches based on moving edges.
Experimental results show that the proposed algorithm overcomes the traditional drawbacks of frame differencing
and outperforms existing edge-based approaches in terms of both detection results and computational
complexity
Learning Fast Algorithms for Linear Transforms Using Butterfly Factorizations
Fast linear transforms are ubiquitous in machine learning, including the
discrete Fourier transform, discrete cosine transform, and other structured
transformations such as convolutions. All of these transforms can be
represented by dense matrix-vector multiplication, yet each has a specialized
and highly efficient (subquadratic) algorithm. We ask to what extent
hand-crafting these algorithms and implementations is necessary, what
structural priors they encode, and how much knowledge is required to
automatically learn a fast algorithm for a provided structured transform.
Motivated by a characterization of fast matrix-vector multiplication as
products of sparse matrices, we introduce a parameterization of
divide-and-conquer methods that is capable of representing a large class of
transforms. This generic formulation can automatically learn an efficient
algorithm for many important transforms; for example, it recovers the Cooley-Tukey FFT algorithm to machine precision, for dimensions up to
. Furthermore, our method can be incorporated as a lightweight
replacement of generic matrices in machine learning pipelines to learn
efficient and compressible transformations. On a standard task of compressing a
single hidden-layer network, our method exceeds the classification accuracy of
unconstrained matrices on CIFAR-10 by 3.9 points---the first time a structured
approach has done so---with 4X faster inference speed and 40X fewer parameters
Quantum Algorithm Implementations for Beginners
As quantum computers become available to the general public, the need has
arisen to train a cohort of quantum programmers, many of whom have been
developing classical computer programs for most of their careers. While
currently available quantum computers have less than 100 qubits, quantum
computing hardware is widely expected to grow in terms of qubit count, quality,
and connectivity. This review aims to explain the principles of quantum
programming, which are quite different from classical programming, with
straightforward algebra that makes understanding of the underlying fascinating
quantum mechanical principles optional. We give an introduction to quantum
computing algorithms and their implementation on real quantum hardware. We
survey 20 different quantum algorithms, attempting to describe each in a
succinct and self-contained fashion. We show how these algorithms can be
implemented on IBM's quantum computer, and in each case, we discuss the results
of the implementation with respect to differences between the simulator and the
actual hardware runs. This article introduces computer scientists, physicists,
and engineers to quantum algorithms and provides a blueprint for their
implementations
Digital processing of signals in the presence of inter-symbol interference and additive noise
Imperial Users onl
A fast-initializing digital equalizer with on-line tracking for data communications
A theory is developed for a digital equalizer for use in reducing intersymbol interference (ISI) on high speed data communications channels. The equalizer is initialized with a single isolated transmitter pulse, provided the signal-to-noise ratio (SNR) is not unusually low, then switches to a decision directed, on-line mode of operation that allows tracking of channel variations. Conditions for optimal tap-gain settings are obtained first for a transversal equalizer structure by using a mean squared error (MSE) criterion, a first order gradient algorithm to determine the adjustable equalizer tap-gains, and a sequence of isolated initializing pulses. Since the rate of tap-gain convergence depends on the eigenvalues of a channel output correlation matrix, convergence can be improved by making a linear transformation on to obtain a new correlation matrix
Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements
Background subtraction has been a fundamental and widely studied task in
video analysis, with a wide range of applications in video surveillance,
teleconferencing and 3D modeling. Recently, motivated by compressive imaging,
background subtraction from compressive measurements (BSCM) is becoming an
active research task in video surveillance. In this paper, we propose a novel
tensor-based robust PCA (TenRPCA) approach for BSCM by decomposing video frames
into backgrounds with spatial-temporal correlations and foregrounds with
spatio-temporal continuity in a tensor framework. In this approach, we use 3D
total variation (TV) to enhance the spatio-temporal continuity of foregrounds,
and Tucker decomposition to model the spatio-temporal correlations of video
background. Based on this idea, we design a basic tensor RPCA model over the
video frames, dubbed as the holistic TenRPCA model (H-TenRPCA). To characterize
the correlations among the groups of similar 3D patches of video background, we
further design a patch-group-based tensor RPCA model (PG-TenRPCA) by joint
tensor Tucker decompositions of 3D patch groups for modeling the video
background. Efficient algorithms using alternating direction method of
multipliers (ADMM) are developed to solve the proposed models. Extensive
experiments on simulated and real-world videos demonstrate the superiority of
the proposed approaches over the existing state-of-the-art approaches.Comment: To appear in IEEE TI
QuicK-means: Acceleration of K-means by learning a fast transform
K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as indexing, nearest-neighbor search and prediction, data compression, Radial Basis Function networks; its beneficial use has been shown to carry over to the acceleration of kernel machines (when using the Nyström method). Here, we propose a fast extension of K-means, dubbed QuicK-means, that rests on the idea of expressing the matrix of the centroids as a product of sparse matrices, a feat made possible by recent results devoted to find approximations of matrices as a product of sparse factors. Using such a decomposition squashes the complexity of the matrix-vector product between the factorized centroid matrix and any vector from to , with and , where is the dimension of the training data. This drastic computational saving has a direct impact in the assignment process of a point to a cluster, meaning that it is not only tangible at prediction time, but also at training time, provided the factorization procedure is performed during Lloyd's algorithm. We precisely show that resorting to a factorization step at each iteration does not impair the convergence of the optimization scheme and that, depending on the context, it may entail a reduction of the training time. Finally, we provide discussions and numerical simulations that show the versatility of our computationally-efficient QuicK-means algorithm
Cocyclic Hadamard Matrices: An Efficient Search Based Algorithm
This dissertation serves as the culmination of three papers. “Counting the decimation classes of binary vectors with relatively prime fixed-density presents the first non-exhaustive decimation class counting algorithm. “A Novel Approach to Relatively Prime Fixed Density Bracelet Generation in Constant Amortized Time presents a novel lexicon for binary vectors based upon the Discrete Fourier Transform, and develops a bracelet generation method based upon the same. “A Novel Legendre Pair Generation Algorithm expands upon the bracelet generation algorithm and includes additional constraints imposed by Legendre Pairs. It further presents an efficient sorting and comparison algorithm based upon symmetric functions, as well as multiple unique Legendre Pairs
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