Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms
type: Item
instance of: scholarly article
title: Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms
zbMATH Open document ID: 1247.42041
author: Myung-Sin Song
author: Palle Jorgensen
published in: Acta Applicandae Mathematicae
publication date: 2010-01-18T00:00:00Z
review text: This interesting paper considers the mathematical formulation of problems in signal transmission, coding, and image processing on the one hand, and techniques from operator theory and functional analysis used to study relations on finite sets of operators on Hilbert space on the other. The formulation in Hilbert space gives a unified approach to a diverse array of problems that admit multiple scales, including entropic coding, the Karhunen--Loève analysis of correlation matrices, fractional Brownian motion, wavelet expansions, the geometry of self-similar fractals, and so on. Throughout the emphasis is both on formulating some problems motivated by engineering in a precise mathematical way, and then in drawing out the common underlying features using the language of Hilbert space.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 94A29
Mathematics Subject Classification ID: 68P30
zbMATH DE Number: 5659975
zbMATH Keywords: fractals
zbMATH Keywords: self-similarity
zbMATH Keywords: coding
zbMATH Keywords: Hilbert space
reviewed by: Thomas B. Ward
MaRDI profile type: Publication
full work available at URL: s10440-009-9529-y
OpenAlex ID: W2024397555
cites work: A NUMERICAL ANALYSIS OF THE EXTENDED BLACK–SCHOLES MODEL
cites work: Diagonals of normal operators with finite spectrum
cites work: Q3414363
cites work: Q5516510
cites work: Subsampling needlet coefficients on the sphere
cites work: Fractal image compression.
cites work: Q4431959
cites work: Q5393664
cites work: Q4343569
cites work: Recurrent iterated function systems
cites work: A FRACTAL VALUED RANDOM ITERATION ALGORITHM AND FRACTAL HIERARCHY
cites work: Wavelets through a looking glass. The world of the spectrum
cites work: Parabolic Julia sets are polynomial time computable
cites work: Non-computable Julia sets
cites work: Q4656813
cites work: The Kadison–Singer Problem in mathematics and engineering
cites work: An introduction to frames and Riesz bases
cites work: Q4310044
cites work: Simple \(C^*\)-algebras generated by isometries
cites work: Wandering vectors for unitary systems and orthogonal wavelets
cites work: Q4381495
cites work: Ten Lectures on Wavelets
cites work: Q4283390
cites work: Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals
cites work: Q4251622
cites work: High-resolution quantization and entropy coding for fractional Brownian motion
cites work: Q3593910
cites work: Rational maps with generalized Sierpinski gasket Julia sets
cites work: Data compression and harmonic analysis
cites work: Iterated function systems, Ruelle operators, and invariant projective measures
cites work: Wavelets on fractals
cites work: Hilbert spaces built on a similarity and on dynamical renormalization
cites work: On nonexistence of non-constant volatility in the Black-Scholes formula
cites work: Frames, bases and group representations
cites work: FEYNMAN–KAC FORMULAS FOR BLACK–SCHOLES-TYPE OPERATORS
cites work: Q3408823
cites work: Orthogonal harmonie analysis and scaling of fractal measures
cites work: Dense analytic subspaces in fractal \(L^2\)-spaces
cites work: Q4941120
cites work: Entropy encoding, Hilbert space, and Karhunen-Loève transforms
cites work: Merton's model of optimal portfolio in a Black-Scholes market driven by a fractional Brownian motion with short-range dependence
cites work: Extensions of Pure States
cites work: Regression in random design and warped wavelets
cites work: Analysis on fractals
cites work: Harmonic analysis for resistance forms.
cites work: Fusion frames and distributed processing
cites work: A TUBE FORMULA FOR THE KOCH SNOWFLAKE CURVE, WITH APPLICATIONS TO COMPLEX DIMENSIONS
cites work: Q3436885
cites work: Q5493731
cites work: Q3414367
cites work: THE BLACK SCHOLES BARENBLATT EQUATION FOR OPTIONS WITH UNCERTAIN VOLATILITY AND ITS APPLICATION TO STATIC HEDGING
cites work: Wavelets, generalized white noise and fractional integration: The synthesis of fractional Brownian motion
cites work: Pasting Together Julia Sets: A Worked Out Example of Mating
cites work: Asymptotics of eigenvalue clusters for Schrödinger operators on the Sierpiński gasket
cites work: On the Julia set of a typical quadratic polynomial with a Siegel disk
cites work: An alternative approach to solving the Black-Scholes equation with time-varying parameters
cites work: Optical von Neumann measurement.
cites work: JPEG2000: The upcoming still image compression standard

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (cites work)
cites work: Convergence of mock Fourier series

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (cites work)
cites work: Q5491075

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (cites work)
cites work: Q4264758

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (cites work)
cites work: Adaptive text mining: inferring structure from sequences

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (DOI)
DOI: 10.1007/S10440-009-9529-Y

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: Multiresolution Analysis of Fractal Image Compression
Similarity Score: 0.91986006
Recommender Run: Recommender Run 3

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: Q4321932
Similarity Score: 0.9177901
Recommender Run: Recommender Run 3

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: A wavelet-based analysis of fractal image compression
Similarity Score: 0.91625917
Recommender Run: Recommender Run 3

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: Q4431960
Similarity Score: 0.9116661
Recommender Run: Recommender Run 3

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: RATE/DISTORTION PERFORMANCE OF FRACTAL TRANSFORMS FOR IMAGE COMPRESSION
Similarity Score: 0.8960373
Recommender Run: Recommender Run 3

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: FRACTAL IMAGE COMPRESSION ALGORITHMS BASED ON POSSIBILITY THEORY
Similarity Score: 0.8926614
Recommender Run: Recommender Run 3

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: Q4893161
Similarity Score: 0.89197826
Recommender Run: Recommender Run 3

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: Q3123057
Similarity Score: 0.89159894
Recommender Run: Recommender Run 3

Analysis of fractals, image compression, entropy encoding, Karhunen-Loève transforms (Recommended article)
Recommended article: Q4251628
Similarity Score: 0.8913312
Recommender Run: Recommender Run 3