Balanced nonseparable orthogonal multiwavelets with two and three vanishing moments on the quincunx grid

Ruedin, Ana M. C.

doi:10.1117/12.408639

Cited by 5 publications

(4 citation statements)

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“…In [21] the properties of orthogonality, accuracy and balancing were analyzed, and for each property were derived conditions for the matrix filter coefficients H (k) . The conditions for accuracy or polynomial approximation order were obtained from [22].…”

Section: Construction Of Multiwaveletsmentioning

confidence: 99%

“…Since there is one downsampling step in (20), the approximation coefficients c (−1) 1,• and c (−1) 2,• are obtained from a 2d convolution of the original image withF 1 andF 2 plus two downsampling steps. If we impose the lowpass propertŷ…”

Section: Construction Of Multiwaveletsmentioning

confidence: 99%

“…In an attempt to unify advances made in both directions: multiwavelets, and nonseparable bidimensional wavelets, examples were built of continuous, nonseparable, orthogonal multiscaling functions in [20]. They are compactly supported, have quincunx decimation, and have polynomial approximation orders (i.e., accuracy) 2 and 3.…”

Section: Introductionmentioning

confidence: 99%

“…Their corresponding multiwavelets were also found. In [21] other examples were given, with the additional property of being balanced.…”

Section: Introductionmentioning

confidence: 99%

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Construction of Nonseparable Multiwavelets for Nonlinear Image Compression

Ruedin

2002

EURASIP J. Adv. Signal Process.

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A procedure for the construction of balanced orthogonal nonseparable quincunx multiwavelets, having filters with good lowpass properties, is introduced. The matrix filter bank is viewed as the polyphase matrix of other filters, upon which the lowpass condition is imposed. The multiscaling functions obtained are plotted by means of the cascade algorithm. The process of transforming an image with these wavelets is outlined: formulae for analysis and synthesis are given, the first steps are illustrated with images, and the decomposition of the original image into two input images is addressed. Compression is achieved in a nonlinear process. Experimental results show that (i) the constructed multiwavelets having lowpass properties perform better than other nonseparable multiwavelets, (ii) the energy compaction in the fine detail subbands is greater for the multiwavelets than for the one-dimensional wavelets tried

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Section: Construction Of Multiwaveletsmentioning

confidence: 99%

Section: Construction Of Multiwaveletsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Their corresponding multiwavelets were also found. In [21] other examples were given, with the additional property of being balanced.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations