Convolution Of Sequences Research Articles

Recurrently Decomposable 2-D Convolvers for FPGA-Based Digital Image Processing

Two-dimensional (2-D) convolution is a widely used operation in image processing and computer vision, characterized by intensive computation and frequent memory accesses. Previous efforts to improve the performance of field-programmable gate array (FPGA) convolvers focused on the design of buffering schemes and on minimizing the use of multipliers. A recently proposed recurrently decomposable (RD) filter design method can reduce the computational complexity of 2-D convolutions by splitting the convolution between an image and a large mask into a sequence of convolutions using several smaller masks. This brief explores how to efficiently implement RD-based 2-D convolvers using FPGA. Three FPGA architectures are proposed based on RD filters, each with a different buffering scheme. The conclusion is that RD-based architectures achieve higher area efficiency than other previously reported state-of-the-art methods, especially for larger convolution masks. An area efficiency metric is also suggested, which allows the most appropriate architecture to be selected.

Reading Scene Text in Deep Convolutional Sequences

We develop a Deep-Text Recurrent Network (DTRN)that regards scene text reading as a sequence labelling problem. We leverage recent advances of deep convolutional neural networks to generate an ordered highlevel sequence from a whole word image, avoiding the difficult character segmentation problem. Then a deep recurrent model, building on long short-term memory (LSTM), is developed to robustly recognize the generated CNN sequences, departing from most existing approaches recognising each character independently. Our model has a number of appealing properties in comparison to existing scene text recognition methods: (i) It can recognise highly ambiguous words by leveraging meaningful context information, allowing it to work reliably without either pre- or post-processing; (ii) the deep CNN feature is robust to various image distortions; (iii) it retains the explicit order information in word image, which is essential to discriminate word strings; (iv) the model does not depend on pre-defined dictionary, and it can process unknown words and arbitrary strings. It achieves impressive results on several benchmarks, advancing the-state-of-the-art substantially.

A low-rank approach to the computation of path integrals

We present a method for solving the reaction-diffusion equation with general potential in free space. It is based on the approximation of the Feynman-Kac formula by a sequence of convolutions on sequentially diminishing grids. For computation of the convolutions we propose a fast algorithm based on the low-rank approximation of the Hankel matrices. The algorithm has complexity of $\mathcal{O}(nr M \log M + nr^2 M)$ flops and requires $\mathcal{O}(M r)$ floating-point numbers in memory, where $n$ is the dimension of the integral, $r \ll n$, and $M$ is the mesh size in one dimension. The presented technique can be generalized to the higher-order diffusion processes.

Multiscale nonlocal flow in a fractured porous medium

We study the flow generated by an incompressible viscoelastic fluid in a fractured porous medium. The model consists of a fluid flow governed by Stokes–Volterra equations evolving in a periodic double-porosity medium. Using the multiscale convergence method associated to some recent tools about the convergence of convolution sequences, we show that the equivalent macroscopic model is of the same type as the microscopic one, but in a fixed domain.

SHEAR ANISOTROPIC INHOMOGENEOUS BESOV SPACES IN ℝd

We define distribution spaces in ℝd via ℓq(Lp) norms of a sequence of convolutions of [Formula: see text] with smooth functions, the shearlet system. Then, we define associated sequence spaces and prove characterization with the shearlet coefficients. We also prove continuous embeddings between some shear anisotropic inhomogeneous spaces and between classical (dyadic isotropic) inhomogeneous spaces and shear anisotropic inhomogeneous spaces.

Linearized viscoelastic Oldroyd fluid motion in an almost periodic environment

In most of the linear homogenization problems involving convolution terms so far studied, the main tool used to derive the homogenized problem is the Laplace transform. Here we propose a direct approach enabling one to tackle both linear and nonlinear homogenization problems that involve convolution sequences without using Laplace transform. To illustrate this, we investigate in this paper the asymptotic behavior of the solutions of a Stokes–Volterra problem with rapidly oscillating coefficients describing the viscoelastic fluid flow in a fixed domain. Under the almost periodicity assumption on the coefficients of the problem, we prove that the sequence of solutions of our ϵ‐problem converges in L2 to a solution of a rather classical Stokes system. One important fact is that the memory disappears in the limit. To achieve our goal, we use some very recent results about the sigma‐convergence of convolution sequences. Copyright © 2013 John Wiley & Sons, Ltd.

Homogenization of a Wilson–Cowan model for neural fields

Homogenization of Wilson–Cowan type of nonlocal neural field models is investigated. Motivated by the presence of a convolution term in this type of models, we first prove some general convergence results related to convolution sequences. We then apply these results to the homogenization problem of the Wilson–Cowan-type model in a general deterministic setting. Key ingredients in this study are the notion of algebras with mean value and the related concept of sigma-convergence.

Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment

Bellow and Calderón proved that the sequence of convolution powers μ n f(x)=∑ k∈ℤ μ n (k)f(T k x) converges a.e, when μ is a strictly aperiodic probability measure on ℤ such that the expectation is zero, E(μ)=0, and the second moment is finite, m 2 (μ)<∞. In this paper we extend this result to cases where m 2 (μ)=∞.

An operational calculus framework to characterize droplet size populations from turbulent breakup by a small number of parameters

A systematic operational calculus framework that characterizes droplet/bubble size distributions resulting from turbulent breakup of an immiscible fluid into a carrier one is presented. The proposed formulation is derived from dynamical arguments; a finite-difference formulation of the integro-differential continuous coagulation and fragmentation equation is shown to exhibit the same structure as a discrete sequence of Mellin convolutions between the probability distribution of the evolving dispersed phase and a generic kernel. This kernel may have its physical correspondence with the probability distribution resulting from a single breakup event, e.g. a liquid ligament breakup in a ligament-mediated spray formation. The number of convolution steps in the sequence can be reduced to a single parameter. As an illustration, this procedure is applied to the exponential and the gamma distributions, obtaining as a result the Fréchet distribution earlier used by Rosin and Rammler (1934 Kolloid-Zeitschrift 67 16–26), and by Nukiyama and Tanasawa (1939 Trans. Soc. Mech. Eng. Japan 5 62–7). Thus, the framework introduced in this work provides a physical foundation for the success of the Fréchet distribution in accurately fitting experimentally measured droplet size distributions in sprays and emulsions.

Joint Symbol Synchronization and Turbo Decoding for Photon-limited Optical PPM Channels

We extend the results of similar joint symbol synchronization and decoding schemes proposed earlier by other researchers for joint symbol synchronization and decoding of convolutional sequences via Viterbi decoder, to parallel concatenated convolutional codes and turbo-decoders. We also propose a re-synchronization mechanism such that we restart joint symbol synchronization and decoding again when the synchronization error is significant. The simulation results show that its performance is not far off from that of perfect symbol synchronization and decoding in turbo-coded pulse-position modulation (PPM) optical communication systems in photon-limited channels.

Inversion of potential-type operators with symbols degenerate on hyperboloids and paraboloids

The method of approximative inverse operators is applied to the inversion of certain potential-type operators with symbols degenerate on hyperboloids or paraboloids. Using this method, the inversion is constructed as the limit of a sequence of convolutions with summable kernels that are expressed in terms of elementary or special functions.

Exact algorithm of multidimensional circulant deconvolution

The paper presents an efficient algorithm to solve a one-dimensional as well as n-dimensional circulant convolution system. The proposed algorithm does not introduce computational errors into the solution. Its derivation is based on polynomial algebra operations that allow to express the operation of deconvolution as a sequence of convolutions of both response and output signals.

Maximal Homomorphic Group Image and Convergence of Convolution Sequences on a Semigroup

Let μ be a probability measure generating a locally compact semigroup S. If the convolution sequence μn is tight, in particular if S is compact, S admits a closed minimal ideal K. The convergence of μn is characterized in terms of convergence of a homomorphic image (~μ)n on a factor group of the compact group G in the Rees–Suschkewitsch decomposition of K.

Distance Approach to Window Decoding

In convolutional coding, code sequences have infinite length; thus, a maximum-likelihood decoder implies an infinite delay. Due to memory and delay constraints in practical coding schemes, convolutional codes often are either terminated or decoded by a window decoder. When a window decoder is used, the convolutional code sequence is not terminated; instead, the window decoder estimates information digits after receiving a finite number of noise-corrupted code symbols, thereby keeping the decoding delay short. An exact characterization of the error-correcting capability of window decoded convolutional codes is given by using active distances of convolutional codes.

Algebras of Operators on Holomorphic Functions and Applications

We develop the theory of operators defined on a space of holomorphic functions. First, we characterize such operators by a suitable space of holomorphic functions. Next, we show that every operator is a limit of a sequence of convolution and multiplication operators. Finally, we define the exponential of an operator which permits us to solve some quantum stochastic differential equations.

On summability of pairs of convolution sequences of probability measures on locally compact semigroups

In this paper we study the problem of convergence in the weak and the vague topology of the sequence $$\left( {\mathop \Sigma \limits_{i = 1}^\infty \mathop \Sigma \limits_{j = 1}^\infty a_{ij}^{(n)} \mu ^i *v^j ,n \in \mathbb{N}} \right)$$ where μ and ν are probability measures on locally compact commutative semigroupS andAn=[aij(n)(i, j, n ɛ N) are double stochastic matrices satisfying some additional conditions. Our results generalize the results in [9]. Theorem 1 also holds if we make some changes on the topological assumptions onS, i.e. if we suppose thatS is a polish space.

Processing of a nine‐component near‐offset VSP for seismic anisotropy

A convolutional sequence of matrix operators is offered as a convenient deterministic scheme for processing a multicomponent vertical seismic profile (VSP). This sequence is applied to a nine‐component near‐offset VSP recorded at the Conoco borehole test facility, Kay County, Oklahoma. These data are corrected for tool spin and near‐surface anisotropy together with source coupling or imbalance. After wave‐field separation using a standard f‐k filter, each source and receiver pair for the upgoing waves is adjusted to a common reference depth using a matrix operator based on the downgoing wave‐field. The up‐ and downgoing waves are then processed for anisotropy by a similarity transformation, to separate the [Formula: see text] and [Formula: see text] waves, from which the anisotropic properties are estimated. These estimates reveal a strong (apparent) vertical birefringence in the near‐surface, but weak or moderate values for the majority of the subsurface. The target zone consists of a thin sandstone and deeper shale layer, both of which possess a strong vertical birefringence. The sandstone corresponds to a zone of known fluid flow. An observed [Formula: see text] attenuation and polarization change in the shale suggest it contains large fractures.

Analytical modeling of chronological reservoir operation in probabilistic production costing [of hydrothermal power systems

This paper describes an extension of the Baleriaux methodology that represents chronological aspects of hydrothermal power system reservoir operation. The production costing problem is decomposed into a sequence of chronological hydro reliability problems. Those reliability problems are analytically solved by a sequence of convolutions of reservoir storage levels, demand, inflows and generation capacity. The methodology is illustrated in a case study with a utility-derived system, and the results are compared with existing solution schemes.

Approximate estimation of non-identifiable parameters in a convolution

In this paper we introduce a general method for the estimation of parameters in a convolution when these are non-identifiable or confounded as in the case of Gaussian signal plus Gaussian noise model. The method proposed is to replace the original convolution by a sequence of convolutions M v converging in distribution to the distribution of the convolution but the parameters are identifiable in each term of the sequence M v . For example in Gaussian signal plus noise models, X = Y + Z, where Y is the signal and Z is the noise, we approximate the error distribution N(0, φ 2) by a sequence of t-distributions with v degrees of freedom and φ as a scale parameter. We show that it is possible to construct consistent estimators of the parameters of signal Y which is N( θ, σ 2) whereas in the original model σ 2 is not identifiable.

Convergence of Convolutions of Concentration Functions to Degenerate, Normal, and Poisson Laws

The paper compares the behavior of convolutions of distribution functions and that of convolutions of corresponding concentration functions. It is shown that the weak convergence of a sequence of convolutions of distribution functions is equivalent to the weak convergence of a sequence of convolutions of corresponding concentration functions to normal, Poisson, and degenerate laws. The most of statements are supposed to be uniform, inside the convolution, closeness of the concentration components to degenerate laws.