Journal ArticleDOI
Image Processing by Transforms Over a Finite Field
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TLDR
The fast Fourier transform (FFT) algorithm of this transform is faster than the conventional radix-2 FFT and is used to filter a two-dimensional picture, and the results are presented with a comparison to the standard FFT.Abstract:
A transform analogous to the discrete Fourier transform is defined on the Galois field GF(p), where p is a prime of the form k X 2n + 1, where k and n are integers. Such transforms offer a substantial variety of possible transform lengths and dynamic ranges. The fast Fourier transform (FFT) algorithm of this transform is faster than the conventional radix-2 FFT. A transform of this type is used to filter a two-dimensional picture (e.g., 256 X 256 samples), and the results are presented with a comparison to the standard FFT. An absence of roundoff errors is an important feature of this technique.read more
Citations
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Book ChapterDOI
Cancelable Biometrics with Perfect Secrecy for Correlation-Based Matching
Shinji Hirata,Kenta Takahashi +1 more
TL;DR: It is proved theoretically that in this proposed method the masked version of the biometric image does not leak any information of the original image, in other words, the proposed method has perfect secrecy.
Journal ArticleDOI
Number Theoretic Transforms for Secure Signal Processing
TL;DR: In this article, the authors present a set of approaches and primitives to efficiently process signals in an encrypted form, by using Number Theoretic Transforms (NTTs) in innovative ways.
Journal ArticleDOI
On the application of a fast polynomial transform and the Chinese remainder theorem to compute a two-dimensional convolution
TL;DR: This new algorithm requires fewer multiplications and about the same number of additions as the conventional FFT method for computing the two-dimensional convolution, but has the advantage that the operation of transposing the matrix of data can be avoided.
Posted Content
Number Theoretic Transforms for Secure Signal Processing
TL;DR: This paper presents a novel and comprehensive set of approaches and primitives to efficiently process signals in an encrypted form, by using Number Theoretic Transforms (NTTs) in innovative ways, and proves that the proposed framework opens up a wide variety of new applications for secured outsourced-processing of multimedia contents.
Book ChapterDOI
Number Theoretic Transforms and their Applications in Image Processing
Said Boussakta,A.G.J. Holt +1 more
TL;DR: This chapter provides an overview of how this Transform based upon the Mersenne numbers can be combined with the 2-D FNT to provide extended dynamic range and great parallelism using simple and convenient moduli leading to an efficient method for parallel image-processing applications.
References
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Journal ArticleDOI
An algorithm for computing the mixed radix fast Fourier transform
TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.
Journal ArticleDOI
The fast Fourier transform in a finite field
TL;DR: A transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the Fast Fourier Transform (FFT) algorithm as discussed by the authors.
Journal ArticleDOI
Effects of finite register length in digital filtering and the fast Fourier transform
Alan V. Oppenheim,C. Weinstein +1 more
TL;DR: The groundwork is set through a discussion of the relationship between the binary representation of numbers and truncation or rounding, and a formulation of a statistical model for arithmetic roundoff, to illustrate techniques of working with particular models.
Journal ArticleDOI
Fast Convolution using fermat number transforms with applications to digital filtering
R. Agarwal,C.S. Burrus +1 more
TL;DR: In this paper, a Fermat number transform (FNT) is proposed for digital computation, requiring on the order of N \log N additions, subtractions and bit shifts, but no multiplications.
Journal Article
Fast convolution using Fermat number transforms with applications to digital filtering
TL;DR: The structure of transforms having the convolution property is developed and an implementation on the IBM 370/155 is presented and compared with the fast Fourier transform (FFT) showing a substantial improvement in efficiency and accuracy.