Multichannel restoration of single channel images using a wavelet decomposition

Banham, M.R.; Gonzalez, Hernán; Galatsanos, N.P.; Katsaggelos, Aggelos K.

doi:10.1109/icassp.1993.319802

Cited by 11 publications

(3 citation statements)

References 8 publications

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“…The multiscale Kalman smoother in this figure is implemented with Eqs. (11)(12)(13) and (23-25) with D(s) _ 1, leading to a reduced state size at each node, and an observation z(s) instead of p(s).…”

Section: Model Order Reduction By Prefilteringmentioning

confidence: 98%

“…(13). Additional adaptivity to the characteristics of each tree of wavelet coefficients is provided through A(s) and B(s) as discussed in the next section.…”

Section: (34) J=1+imentioning

confidence: 99%

“…We have written this prefiltering operation in terms of the lexicographically stacked wavelet domain data. The implementation of this filter may be carried out with ease in the wavelet-frequency domain [13,14], or in the spatial frequency domain [6] if we do not wish to include further adaptivity of the regularization parameter to each wavelet domain subband. This prefiltering operation tends to decorrelate the data in the spatial direction (by removing the blur), but leaves the relationships between wavelet coefficients in scale unchanged.…”

Section: Model Order Reduction By Prefilteringmentioning

confidence: 99%

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<title>Spatially adaptive multiscale image restoration using the wavelet transform</title>

Banham¹,

Katsaggelos²

1994

Visual Communications and Image Processing '94

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In this paper, we present a new adaptive approach to the restoration of noisy blurred images which is particularly effective at producing sharp deconvolution while suppressing the noise in the flat regions of an image. This is accomplished through a multiscale Kalman smoothing filter applied to a prefiltered observed image in the discrete, separable, two dimensional wavelet domain. The prefiltering step involves a constrained least squares filter based on a very small choice for the regularization parameter, producing an under-regularized restored image. This leads to a reduction in the support of the required state vectors in the wavelet domain, and an improvement in the computational efficiency of the multiscale filter. The proposed method has the benefit that the majority of the regularization, or noise suppression, of the restoration is accomplished by the efficient multiscale filtering of wavelet detail coefficients ordered on quadtrees. Not only does this permit adaptivity to the local edge information in the image, but it leads to potential parallel implementation schemes. In particular, this method changes filter parameters depending on scale, local signal-to-noise ratio (SNR), and orientation. Because the wavelet detail coefficients are a manifestation of the multiscale edge information in an image, this algorithm may be viewed as an "edge-adaptive" multiscale restoration approach.

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Section: Model Order Reduction By Prefilteringmentioning

confidence: 98%

“…(13). Additional adaptivity to the characteristics of each tree of wavelet coefficients is provided through A(s) and B(s) as discussed in the next section.…”

Section: (34) J=1+imentioning

confidence: 99%

Section: Model Order Reduction By Prefilteringmentioning

confidence: 99%

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<title>Spatially adaptive multiscale image restoration using the wavelet transform</title>

Banham¹,

Katsaggelos²

1994

Visual Communications and Image Processing '94

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Wavelet-based neural network with fuzzy-logic adaptivity for nuclear image restoration

Qian

Clarke

1996

Proc. IEEE

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Multiresolution image restoration in the wavelet domain

Zervakis

Kwon

Yang

1995

IEEE Trans. Circuits Syst. II

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Abstruct-This paper proposes an image restoration approach in the wavelet domain that directly associates multiresolution with multichannel image processing. We express the formation of the multiresolution image as an operator on the image domain that transforms block-circulant structures into partially-blockcirculant structures. We prove that the stationarity assumption in the image domain leads to the suppression of cross-band correlation in the multiresolution domain. Moreover, the space invariance assumption leads to the loss of cross-band interference and interaction. In addition to the rigorous explanation of these effects, our formulation reveals new correlation schemes for the multiresolution signal in the wavelet domain. In essence, the proposed implementation relaxes the stationarity and spaceinvariance assumptions in the image domain and introduces new operator structures for the implementation of single-channel algorithms that take advantage of the correlation structure in the wavelet domain. We provide a rigorous study of these effects for both the equal-rate subband decomposition and the multiresolution pyramid decomposition. Several image restoration examples on the Wiener-filtering approach show significant improvement achieved by the proposed approach over the conventional discrete Fourier transform (DFT) implementation.

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Multichannel restoration of single channel images using a wavelet decomposition

Cited by 11 publications

References 8 publications

<title>Spatially adaptive multiscale image restoration using the wavelet transform</title>

<title>Spatially adaptive multiscale image restoration using the wavelet transform</title>

Wavelet-based neural network with fuzzy-logic adaptivity for nuclear image restoration

Multiresolution image restoration in the wavelet domain

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