Gray scale image compression based on multiple-valued input binary functions, Walsh and Reed-Muller spectra

Falkowski, B.J.; Lim, Lip-San

doi:10.1109/ismvl.2000.848632

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…Reed-Muller-like spectral transforms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] have found a variety of useful applications in minimizing Exclusive Sum-Of-Products (ESOP) and Galois field SOP (GF-SOP) expressions, creation of new forms, binary and spectral decision diagrams, regular structures, besides the well-known uses in digital communications, digital signal * Received: July 15, 2015 101 An Extended Green -Sasao Hierarchy of Canonical Ternary Galois Forms ... and image processing, and fault detection and testing [1-9, 12-14, 16, 17, 19, 20, 21]. The method of generating the new families of multiple-valued Shannon and Davio spectral transforms is based on the fundamental multiple-valued Shannon and Davio expansions.…”

Section: Normal Galois Formsmentioning

confidence: 99%

“…The method of generating the new families of multiple-valued Shannon and Davio spectral transforms is based on the fundamental multiple-valued Shannon and Davio expansions. Dyadic families of discrete transforms; Reed-Muller and Green-Sasao hierarchy, Walsh, Arithmetic, Adding and Haar transforms and their generalizations to multiple-valued transforms, have also found important applications in digital system design and optimization [1,6,19,[7][8][9][10][11][12][13][14][15][16][17][18][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Normal Galois Formsmentioning

confidence: 99%

“…Reed-Muller-like spectral transforms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] have found a variety of useful applications in minimizing Exclusive Sum-Of-Products (ESOP) and Galois field SOP (GF-SOP) expressions, creation of new forms, binary and spectral decision diagrams, regular structures, besides the well-known uses in digital communications, digital signal In binary, for example, GF(2) addition gate, the EXOR, has the cyclic group property. The cyclic group property can be explained, for example, using the three-valued (ternary) GF operators as shown in Figures 1(a) and 1(b), respectively.…”

Section: Normal Galois Formsmentioning

confidence: 99%

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An extended Green-Sasao hierarchy of canonical ternary Galois forms and Universal Logic Modules

Al‐Rabadi

2017

FACTA U EE

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A new extended Green-Sasao hierarchy of families and forms with a new sub-family for many-valued Reed-Muller logic is introduced. Recently, two families of binary canonical Reed-Muller forms, called Inclusive Forms (IFs) and Generalized Inclusive Forms (GIFs) have been proposed, where the second family was the first to include all minimum Exclusive Sum-Of-Products (ESOPs). In this paper, we propose, analogously to the binary case, two general families of canonical ternary Reed-Muller forms, called Ternary Inclusive Forms (TIFs) and their generalization of Ternary Generalized Inclusive Forms (TGIFs), where the second family includes minimum Galois Field Sum-Of-Products (GFSOPs) over ternary Galois field GF(3). One of the basic motivations in this work is the application of these TIFs and TGIFs to find the minimum GFSOP for many-valued input-output functions within logic synthesis, where a GFSOP minimizer based on IF polarity can be used to minimize the many-valued GFSOP expression for any given function. The realization of the presented S/D trees using Universal Logic Modules (ULMs) is also introduced, whereULMs are complete systems that can implement all possible logic functions utilizing the corresponding S/D expansions of many-valued Shannon and Davio spectral transforms.

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Section: Normal Galois Formsmentioning

confidence: 99%

Section: Normal Galois Formsmentioning

confidence: 99%

“…Reed-Muller-like spectral transforms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] have found a variety of useful applications in minimizing Exclusive Sum-Of-Products (ESOP) and Galois field SOP (GF-SOP) expressions, creation of new forms, binary and spectral decision diagrams, regular structures, besides the well-known uses in digital communications, digital signal In binary, for example, GF(2) addition gate, the EXOR, has the cyclic group property. The cyclic group property can be explained, for example, using the three-valued (ternary) GF operators as shown in Figures 1(a) and 1(b), respectively.…”

Section: Normal Galois Formsmentioning

confidence: 99%

See 1 more Smart Citation

An extended Green-Sasao hierarchy of canonical ternary Galois forms and Universal Logic Modules

Al‐Rabadi

2017

FACTA U EE

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“…Falkowski, et al [18,21] considered using Kleene Algebra, Multiple-valued functions and spectral analysis for lossless compression of gray scale images [19]. Their method consists of preprocessing, prediction, splitting of bit planes and variable block-size segmentation and coding .They applied similar ideas to gray scale and color biomedical images [22].…”

Section: Related Workmentioning

confidence: 99%

A New Case for Image Compression Using Logic Function Minimization

Zolfaghari¹,

Sheidaeian²

2011

IJMA

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This paper proposes implements and evaluates an image compression method called YALMIC (Yet Another Logic Minimization Based Image Compression) which depends on logic function minimization. This method considers adjacent pixels of the image as disjointed minterms constructing a logic function and compresses the 24-bit color images through minimizing the function. We compare the compression ratio of the proposed method to those of existing methods and show that YALMIC improves the compression ratio by about 25% on average.

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“…Reed-Muller-like spectral transforms [240] have found a variety of useful applications in minimizing Exclusive Sum-Of-Products (ESOP) and Galois field SOP (GFSOP) expressions [9,76,77,79,80,171,264], creation of new forms [4,78,104,173,265,266], binary decision diagrams [2,45,142], spectral decision diagrams [82,238,239], regular structures [5,7,13,18,50,51,84,177], besides their well-known uses in digital communications [125], digital signal processing [89,257,260], digital image processing [90], and fault detection (testing) [99,124,147,198,199,204,218]. Ternary Reduced Post Galois field Sum-Of-Products (RP-GFSOPs), their generalized Green/Sasao hierarchies, and the extensions of such hierarchies to the case of quaternary Galois field hierarchy were recently developed [4,9].…”

Section: Fundamentalsmentioning

confidence: 99%

Reversible Logic Synthesis

Al‐Rabadi¹

2004

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A function is reversible if each input vector produces a unique output vector. Reversible functions find applications in low power design, quantum computing, and nanotechnology. Logic synthesis for reversible circuits differs substantially from traditional logic synthesis. In this paper, we present the first practical synthesis algorithm and tool for reversible functions with a large number of inputs. It uses positive-polarity Reed-Muller decomposition at each stage to synthesize the function as a network of Toffoli gates. The heuristic uses a priority queue based search tree and explores candidate factors at each stage in order of attractiveness. The algorithm produces near-optimal results for the examples discussed in the literature. The key contribution of the work is that the heuristic finds very good solutions for reversible functions with a large number of inputs.

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Gray scale image compression based on multiple-valued input binary functions, Walsh and Reed-Muller spectra

Cited by 5 publications

References 16 publications

An extended Green-Sasao hierarchy of canonical ternary Galois forms and Universal Logic Modules

An extended Green-Sasao hierarchy of canonical ternary Galois forms and Universal Logic Modules

A New Case for Image Compression Using Logic Function Minimization

Reversible Logic Synthesis

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