Medical Image Compression Scheme Using Number Theoretic Transform

Hegde, Salila; Nagapadma, Rohini

doi:10.1007/978-981-13-8798-2_5

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Because its arithmetic is performed in a finite field, fixed-point implementations can provide exact computation and simple hardware requirements. Several signal processing contexts were benefited by finite fields transforms [4], [5], [6], [7], [8] with applications linked to the computation of the discrete convolution by means of modular arithmetic and to image processing methods [9], [10]. Number-theoretic transforms (NTTs) are finite-field transforms that operate over GF(p), where p is a prime number, as opposed to operating over the extension field GF(q), where q is a power of a prime.…”

Section: Introductionmentioning

confidence: 99%

Geometrical Representation for Number-theoretic Transforms

Oliveira¹,

Cintra²

2020

Anais De XXXVIII Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar chart. As an illustrative example, the binary Hamming transform recently proposed is geometrically interpreted. It is shown that codewords of standard Hamming code H(N = 7, k = 4, d = 3) are invariant vectors under the Hamming transform. These invariant are eigenvectors of the binary Hamming transform. The images are always inscribed in a regular polygon of unity side, resembling triangular rose petals and/or "thorns". A geometric representation of the ternary Golay transform, based on the extended Golay G(N = 12, k = 6, d = 6) code over GF(3) is also showed. This approach is offered as an alternative representation of finite-length sequences over finite prime fields.

show abstract

Section: Introductionmentioning

confidence: 99%

Geometrical Representation for Number-theoretic Transforms

Oliveira¹,

Cintra²

2020

Anais De XXXVIII Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

View full text Add to dashboard Cite

show abstract

Gaussian Hermite polynomial based lossless medical image compression

Kumar¹,

Ahilan²,

Haridhas³

et al. 2020

Multimedia Systems

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Geometrical Representation for Number-theoretic Transforms

Oliveira¹,

Cintra²

2021

Preprint

View full text Add to dashboard Cite

This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar chart. As an illustrative example, the binary Hamming transform recently proposed is geometrically interpreted. It is shown that codewords of standard Hamming code H (N = 7, k = 4, d = 3) are invariant vectors under the Hamming transform. These invariant are eigenvectors of the binary Hamming transform. The images are always inscribed in a regular polygon of unity side, resembling triangular rose petals and/or "thorns". A geometric representation of the ternary Golay transform, based on the extended Golay G (N = 12, k = 6, d = 6) code over GF(3) is also showed. This approach is offered as an alternative representation of finite-length sequences over finite prime fields.

show abstract

Medical Image Compression Scheme Using Number Theoretic Transform

Cited by 3 publications

References 23 publications

Geometrical Representation for Number-theoretic Transforms

Geometrical Representation for Number-theoretic Transforms

Gaussian Hermite polynomial based lossless medical image compression

Geometrical Representation for Number-theoretic Transforms

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