Analysis/synthesis techniques for subband image coding

Smith, M.J.T.; Eddins, S.L.

doi:10.1109/29.57579

Cited by 316 publications

(117 citation statements)

References 17 publications

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“…However, it requires that the number of data points is a power of two, and the time points must be spaced equally t i = i=n. The first requirement is often met by extending the given data set to length 2 J using for example periodic extension or symmetric reflection (Smith and Eddins 1990). At first sight, this looks a little bit artificial, but we have seen that the DWT itself makes use of boundary conditions.…”

Section: 4mentioning

confidence: 99%

Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding

Kovac¹,

Silverman

2000

Journal of the American Statistical Association

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ABSTRACT. Various aspects of the wavelet approach to nonparametric regression are considered, with the overall aim of extending the scope of wavelet techniques, to irregularlyspaced data, to regularly-spaced data sets of arbitrary size, to heteroscedastic and correlated data, and to data some of which may be downweighted or omitted as outliers.At the core of the methodology discussed is the following problem: if a sequence has a given covariance structure, what is the variance and covariance structure of its discrete wavelet transform? For sequences whose length is a power of 2, an algorithm for finding all the variances and within-level covariances in the wavelet table is developed and investigated in detail. In particular, it is shown that if the original sequence has band-limited covariance matrix, then the time required by the algorithm is linear in the length of the sequence.Up to now, most statistical work on wavelet methods presumes that the number of observations is a power of 2 and that the independent variable takes values on a regular grid. The variance-calculation algorithm allows data on any set of independent variable values to be treated, by first interpolating to a fine regular grid of suitable length, and then constructing a wavelet expansion of the gridded data. The gridded data will, in general, have a band-limited covariance matrix, and the algorithm therefore allows the elements of the wavelet transform to be thresholded individually using thresholds proportional to their standard deviation.Various thresholding methods are discussed and investigated. Exact risk formulae for the mean square error of the methodology for given design are derived and used, to avoid, as far as possible, the need for simulation in assessing performance. Both for regular and irregular data, good performance is obtained by noise-proportional thresholding, with thresholds somewhat smaller than the classical universal threshold.The general approach allows outliers in the data to be removed or downweighted, and aspects of such robust techniques are developed and demonstrated in an example. Another natural application is to data that are themselves correlated, where the covariance of the wavelet coefficients is not due to an initial grid transform but is an intrinsic feature of the data. The use of the method in these circumstances is demonstrated by an application to data synthesized in the study of ion channel gating. The basic approach of the paper has many other potential applications, and some of these are discussed briefly.Arne Kovac is wissenschaftlicher Mitarbeiter,

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Section: 4mentioning

confidence: 99%

Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding

Kovac¹,

Silverman

2000

Journal of the American Statistical Association

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“…For example, [3] proposed using all pass filters instead of delays in lossless matrices to design IIR PRFB, approximately linearphase filters using complex all pass sections is proposed in [4], and orthogonal IIR 2-channel PRFBs are designed using all pass filters in [5]. For such FBs, synthesis filtering needs to be performed in anti-causal fashion by introducing time reversal [6], which increases the storage cost of the system and may only be acceptable for image processing applications.…”

Section: Introductionmentioning

confidence: 99%

“…Although some design methods have been proposed for the causal and stable case [7], they mostly treated the 2-channel FB cases. Recently, an M-channel real IIR FB [8] was presented, but the design method includes a complicated stabilization procedure of the synthesis filters.…”

Section: Introductionmentioning

confidence: 99%

Design of M-Channel Perfect Reconstruction Filter Banks with IIR-FIR Hybrid Building Blocks

Iwamura¹,

Suzuki

Tanaka³

et al. 2007

IEICE Transactions on Fundamentals of Electronics, Communicatio

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This paper discusses a new structure of M-channel IIR perfect reconstruction filterbanks. A novel design implementation for the new building block defined as a product of an IIR building block and an FIR building block is presented. The IIR building blocks are written by state space representation, in which we can easily obtain a stability of the filterbank by placing its eigen values inside the unit circle. Due to cascading of building blocks, we can get more free parameters. We introduce the condition how we obtain the new building blocks without increasing of the filter order. Additionally, by showing the simulation results, we show that our proposed FBs have better stopband attenuation than a conventional method.

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“…He noted that the solution required more effort than the actual filtering. Smith and Eddins [5] suggest explicitly computing the impulse response of the recursive filter and using this to compute the initial values. As given, their solution is restricted to filters that have only single poles.…”

Section: Introductionmentioning

confidence: 99%

Efficient and Consistent Recursive Filtering of Images with Reflective Extension

Appleton

Talbot

2003

Scale Space Methods in Computer Vision

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Abstract. Recursive filters are commonly used in scale space construction for their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of reflectively extended images for filters with symmetric denominator. We begin with an analysis of reflective extensions and their effect on nonrecursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on reflective domains as a linear but time-varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring the same order of computation as the standard recursive filtering. We give experimental evidence to verify these claims.

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Analysis/synthesis techniques for subband image coding

Cited by 316 publications

References 17 publications

Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding

Extending the Scope of Wavelet Regression Methods by Coefficient-Dependent Thresholding

Design of M-Channel Perfect Reconstruction Filter Banks with IIR-FIR Hybrid Building Blocks

Efficient and Consistent Recursive Filtering of Images with Reflective Extension

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