U-L block-triangular matrix and ladder realizations of subband coders

Marshall, T.G.

doi:10.1109/icassp.1993.319464

Cited by 12 publications

(5 citation statements)

References 17 publications

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“…FFT implementations [12] are useful for large filters (of length 64 or 128), but do not bring any improvement over a straightforward implementation for short and medium size filter [12]. Recently, several authors [13]- [16] have proposed efficient implementations of 1-D biorthogonal filters using a factorization of the filters into smaller filters. In [15], the authors show that all biorthogonal filters can be factored into a sequence of ladder steps.…”

Section: A Factoring the Biorthogonal Filtersmentioning

confidence: 99%

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Fast adaptive wavelet packet image compression

Meyer

Averbuch

Strömberg

2000

IEEE Trans. on Image Process.

118

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Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients, which are often quantized to zero, even at high bit rates. Our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis is placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four times faster than a standard convolution-decimation. An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly out performs one of the best wavelet coder on images such as Barbara and fingerprints, both visually and in term of PSNR.

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Section: A Factoring the Biorthogonal Filtersmentioning

confidence: 99%

“…In [13] the ladder step is a lifting step, and similar results were derived using the same methods. A more direct proof, based on matrix factorization, was obtained in [17], [16]. We now introduce the notations and recall the key results.…”

Section: A Factoring the Biorthogonal Filtersmentioning

confidence: 99%

Fast adaptive wavelet packet image compression

Meyer

Averbuch

Strömberg

2000

IEEE Trans. on Image Process.

118

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“…Lifting also leads to a filter bank implementation known as ladder structures [2]. Moreover, it is known that all 1-D FIR filter banks fit into lifting [15], [31], [43], [53].…”

Section: Introductionmentioning

confidence: 99%

Wavelet families of increasing order in arbitrary dimensions

Kovačević¹,

Sweldens²

2000

IEEE Trans. on Image Process.

168

133

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Abstract-We build discrete-time compactly supported biorthogonal wavelets and perfect reconstruction filter banks for any lattice in any dimension with any number of primal and dual vanishing moments. The associated scaling functions are interpolating. Our construction relies on the lifting scheme and inherits all of its advantages: fast transform, in-place calculation, and integer-to-integer transforms. We show that two lifting steps suffice: predict and update. The predict step can be built using multivariate polynomial interpolation, while update is a multiple of the adjoint of predict. While we concentrate on the discrete-time case, some discussion of convergence and stability issues together with examples is given.

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“…One of the signals is a direct copy of the input, the other one is a direct copy modified by addition of a filtered version of the other signal. In terms of matrices, a ladder step performs a linear operation described by a matrix of the form In literature matrices of this form are known as elementary matrices [2] [4] [ll]. We will also refer to these matrices as step matrices and to the filter F ( r ) as the step filter.…”

Section: General Ladder Structuresmentioning

confidence: 99%

On ladder structures and linear phase conditions for bi-orthogonal filter banks

Shah

Kalker²

Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing

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cosets X is eaual to Idet(LI1. The quotient map w-'' takes In this paper some new results for multidimensional m-band bi-orthogonal filter banks are presented. In the first part of the paper we introduce the ladder structure as a method for the design and implementation of aforementioned filter banks. The second part of the paper focuses upon enforcing linear phase (LP) conditions in the context of ladder structures. The formulation of the LP conditions is done with the help of a recently introduced, algebraicly oriented method for describing multidimensional filter banks. It is shown that in this notation, ladder structures allow a natural formulation of LP conditions.

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U-L block-triangular matrix and ladder realizations of subband coders

Cited by 12 publications

References 17 publications

Fast adaptive wavelet packet image compression

Fast adaptive wavelet packet image compression

Wavelet families of increasing order in arbitrary dimensions

On ladder structures and linear phase conditions for bi-orthogonal filter banks

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