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Showing papers on "Kernel (image processing) published in 1977"


Journal ArticleDOI
TL;DR: In this paper, a new formulation of digital filters that combines the description of signal processing and arithmetic operations is presented, where multiplication is a form of convolution and normal one-dimensional scalar convolution is in fact two-dimensional binary convolution.
Abstract: This paper presents a new formulation of digital filters that combines the description of signal-processing and arithmetic operations. This is done by noting that multiplication is a form of convolution and therefore normal one-dimensional scalar convolution is in fact two-dimensional binary convolution. This is generalized to multidimensions and can be applied with table-look-up and transform techniques. The result is a unified description that describes a digital filter structure down to the bit level.

100 citations


Proceedings ArticleDOI
R. Agarwal1, J. Cooley1
01 May 1977
TL;DR: In this article, it is shown how the Chinese Remainder theorem (CRT) can be used to convert a one-dimensional cyclic convolution to a multi-dimensional convolution which is cyclic in all dimensions.
Abstract: It is shown how the Chinese Remainder Theorem (CRT) can be used to convert a one-dimensional cyclic convolution to a multi-dimensional convolution which is cyclic in all dimensions. Then, special algorithms are developed which, compute the relatively short convolutions in each of the dimensions. The original suggestion for this procedure was made in order to extend the lengths of the convolutions which one can compute with number-theoretic transforms. However, it is shown that the method can be more efficient, for some data sequence lengths, than the fast Fourier transform (FFT) algorithm. Some of the short convolutions are computed by methods in an earlier paper by Agarwal and Burrus. Recent work of Winograd, consisting of theorems giving the minimum possible numbers of multiplications and methods for achieving them, are applied to these short convolutions.

54 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed a deconvolution method based on the general Liouville-Neuman theory of solving integral equations, which incorporates and extends Ville's analytic continuation and Van Cittert's successive convolution method.
Abstract: A short study on the general deconvolution problem when the kernel has no inverse proves that a priori information on the signal to be restored is a necessary condition for deconvolution. The proposed deconvolution method uses the following information: the signal to be restored has a bounded support; this support is known or is inside a known interval. This method concerns the convolution kernels whose Fourier transform has a cutoff frequency. This type of kernel has a wide practical field. The image restoration and the processing of "the principal value solution" of the deconvolution problem are the most characteristic elements. The method is derived from the general Liouville-Neuman theory of solving integral equations. This new method incorporates and extends Ville's analytic continuation and Van Cittert's successive convolution method. The iterative deconvolution algorithm is very simple. The advantages of this method are shown by numerical results and, in particular, by an experimental spectroscopic application.

31 citations


Journal ArticleDOI
TL;DR: An interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies and is shown to operate faster than zero fill, since fewer operations are required.
Abstract: Zero fill, or augmentation by zeros, is a method used in conjunction with fast Fourier transforms to obtain spectral spacing at intervals closer than obtainable from the original input data set. In the present paper, an interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies. The technique is shown to operate faster than zero fill, since fewer operations are required. The major advantages of interpolation by repetitive convolution are that efficient use of memory is possible (thus avoiding the difficulties encountered in decimation in time FFTs) and that is is easy to implement.

13 citations


Journal ArticleDOI
01 Jan 1977
TL;DR: In this paper, a generalized kernel of the resulting integral equation is used to describe currently well understood coherent linear processors as simple examples of a more general n-plane processor, and the kernel of a 4-plane system is shown to represent an oblique to rectangular plane inverter, when an appropriate assumption is made about the complex amplitude-transmittance function of one optical plane.
Abstract: Generalized optical processors are examined from the point-of-view of developing a systematic method for determining which linear processing operations may be performed in a coherent optical system. In this paper a procedure is presented for examining a general n-plane processor and expressing the resulting system in terms of a conventional linear processing model. The generalized kernel of the resulting integral equation is used to describe currently well understood coherent linear processors as simple examples of a more general n-plane processor. A 2-plane processor is shown to correspond to the Fourier transform operation with a simple lens, and the 3-plane processor is associated with convolution or correlation. The kernel of a 4-plane system is shown to resemble the ambiguity function, and to represent an oblique to rectangular plane inverter, when an appropriate assumption is made about the complex amplitude-transmittance function of one optical plane. The more general n-plane kernels have integral representations for which simple physical realizations remain to be developed.

13 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the asymptotic behavior of the bounded solutions of a nonlinear Volterra integrodifferential equation with a positive definite convolution kernel.

7 citations


Book ChapterDOI
01 Jan 1977
TL;DR: It is shown that the analysis is considerably simplified if one works in the Fourier domain, and the error made by constructing an approximation to the desired kernel by linear interpolation is roughly proportional to 1/m2.
Abstract: Computer assisted tomography is a new technique for producing X-ray images of exceptional clarity The basic data consist of transmitted intensities at a series of uniformly spaced positions and angles These data can then be used to reconstruct the image by a Fourier transform algorithm first developed in the context of radio- astronomy A brief summary of the general technique is given We then discuss the discretization error arising from the necessity of using a discrete approximation to the final integral in the reconstruction, restricting ourselves to objects with circular symmetry We show that the analysis is considerably simplified if one works in the Fourier domain, and consider the error made by constructing an approximation to the desired kernel by linear interpolation We show that the error is roughly proportional to 1/m2, where m is the number of scans

1 citations


Journal ArticleDOI
TL;DR: In this paper, a general formulation of the problem of extracting information about random wave sources is presented, where the general problem may be cast into the form of an integral equation, the kernel of which contains the physics of the propagation and the solution of which describes the location and spectral content of all sources.
Abstract: A general formulation of the problem of extracting information about random wave sources is presented. The formulation places no restrictions upon the complexity of the propagation and applies to any situation where the propagation may be adequately described by a deterministic Green’s function. It is shown that the general problem may be cast into the form of an integral equation, the kernel of which contains the physics of the propagation and the solution of which describes the location and spectral content of all sources. The special case of a homogeneous medium is examined in detail, and it is shown that conventional processing techniques may be viewed as attempts to solve an approximate version of the integral equation. An exact formal solution for the case of an arbitrary medium is derived. This formal solution, although it may not be implemented per se, is nonetheless expressed in such a form that a useful procedure for generating approximate solutions is suggested. This procedure, which is a gener...

1 citations


Proceedings ArticleDOI
01 May 1977
TL;DR: The step by step recursive analysis of cyclic convolution operators towards the associated diagonal spectral operators under the fast Fourier transform outlines a clear and deep insight into the algebraic structure of the intermediate operators and operations as well as into the mechanism of reducing redundant operations.
Abstract: The non-diagonal convolution theory is introduced as a normed commutative algebra based upon the isomorphism between time-discrete linear function spaces and arbitrary spectral spaces. The step by step recursive analysis of cyclic convolution operators towards the associated diagonal spectral operators under the fast Fourier transform outlines a clear and deep insight into the algebraic structure of the intermediate operators and operations as well as into the mechanism of reducing redundant operations. Finally, a new class of non-diagonal fast convolution algorithms for pipelined transforms and for the enhanced applicability of residue arithmetic in finite rings is presented.

1 citations


Proceedings ArticleDOI
01 Oct 1977
TL;DR: In this paper, a variational approach using isoparametric finite-elements is presented for the solution of three-dimensional electromagnetic scattering problems, which allows a higher-order approximation of the unknown function over a bounding surface described by non-planar elements.
Abstract: A refined numerical technique, based on a variational approach using isoparametric finite-elements is presented for the solution of three-dimensional electromagnetic scattering problems. This technique allows a higher-order approximation of the unknown function over a bounding surface described by non-planar elements. The Rayleigh-Ritz procedure is used to discretize the integral equation. Kernel singularities are treated by separating them from the main integral and solving them analytically. A procedure for establishing the system matrix in a block-sparse form will be described [5].

1 citations