Construction of wavelet decompositions for tomographic images

Peyrin, Françoise; Zaim, Mounia; Goutte, R.

doi:10.1007/bf01248406

Cited by 17 publications

(5 citation statements)

References 6 publications

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“…reconstruction [6], [7], and in the design of new acquisition schemes for magnetic resonance imaging (MRI) [8]- [11]. Wavelet representations are also well suited for a variety of data processing tasks.…”

mentioning

confidence: 99%

Statistical analysis of functional MRI data in the wavelet domain

Ruttimann

Unser

Rawlings

et al. 1998

IEEE Trans. Med. Imaging

135

110

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Abstract-The use of the wavelet transform is explored for the detection of differences between brain functional magnetic resonance images (fMRI's) acquired under two different experimental conditions. The method benefits from the fact that a smooth and spatially localized signal can be represented by a small set of localized wavelet coefficients, while the power of white noise is uniformly spread throughout the wavelet space. Hence, a statistical procedure is developed that uses the imposed decomposition orthogonality to locate wavelet-space partitions with large signal-to-noise ratio (SNR), and subsequently restricts the testing for significant wavelet coefficients to these partitions. This results in a higher SNR and a smaller number of statistical tests, yielding a lower detection threshold compared to spatial-domain testing and, thus, a higher detection sensitivity without increasing type I errors. The multiresolution approach of the wavelet method is particularly suited to applications where the signal bandwidth and/or the characteristics of an imaging modality cannot be well specified. The proposed method was applied to compare two different fMRI acquisition modalities. Differences of the respective useful signal bandwidths could be clearly demonstrated; the estimated signal, due to the smoothness of the wavelet representation, yielded more compact regions of neuroactivity than standard spatial-domain testing.

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mentioning

confidence: 99%

Statistical analysis of functional MRI data in the wavelet domain

Ruttimann

Unser

Rawlings

et al. 1998

IEEE Trans. Med. Imaging

135

110

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“…Wavelets approaches have already been proposed in tomographic reconstruction and especially in the context of local tomography [4][5][6]. Knowledge of two data sets respectively at LR and HR fits well in the framework Fig.…”

Section: Introductionmentioning

confidence: 93%

“…In this case there is no unique solution to the problem [1]. However if some measurements in the external region are possible, different solutions have been proposed in literature, ranging from introduction of a priori knowledge [2], use of iterative algorithms [3], or wavelets [4][5][6]. In this paper, we focus on the problem of the reconstruction of a ROI from high resolution (HR) truncated projections knowing a set of low resolution (LR) non truncated projections.…”

Section: Introductionmentioning

confidence: 99%

A wavelet algorithm for zoom-in tomography

Langer

Peyrin

2010

2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro

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In zoom-in tomography, the aim is to image a region of interest lying partially or fully within the imaged object, using a high resolution tomographic scan covering only the ROI, and a low resolution scan covering the whole object. We analyze the problem from a multiresolution point of view and propose an algorithm for combining the two data sets using the discrete wavelet transform and the Haar wavelet. We compare the proposed algorithm to a previously reported method that involves padding of the high resolution data with a supersampled version of the low resolution data, to zero padding and edge extension, using synthetic data sets. We show that the proposed algorithm is insensitive to offsets between the two data sets, but that it is slightly more sensitive to noise.

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“…Sym ab implies the new wavelet to be symmetric i.e. sym_ab=a=b (10) The th vanishing moment, denoted by momp is defined as momp Jx'7(x) =0 (11) momO for Eq. (11) leads to the symmetry condition.…”

Section: Design Of Biorthogonal Wavelet Filters Using Liftingmentioning

confidence: 99%

<title>Evaluation of various wavelet bases for use in wavelet-based multiresolution expectation maximization image reconstruction algorithm for PET</title>

Raheja¹,

Dhawan

2000

SPIE Proceedings

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Maximum Likelihood (ML) estimation based Expectation Maximization' (EM) reconstruction algorithm has shown to provide good quality reconstruction for PET. Our previous work23' introduced the multigrid EM (MGEM) and multiresolution (MREM) and Wavelet based Multiresolution EM (WMREM) algorithm26 for PET image reconstruction. This paper investigates the use of various wavelets in the new Wavelet based Multiresolution EM (WMREM) algorithm. The wavelets are used to construct a multiresolution data space, which is then used in the estimation process. The beauty of the wavelet transform to provide localized frequency-space representation of the data allows us to perform the estimation using these decomposed components. The advantage of this method lies with the fact that the noise in the acquired data becomes localized in the high-high or diagonal frequency bands and not using these bands for estimation at coarser resolution helps speed up the recovery of various frequency components with reduced noise estimation. Different wavelet bases result in different reconstructions. Custom wavelets are designed for the reconstruction process and these wavelets provide better results than the commonly known wavelets. The WMREM reconstruction algorithm is implemented to reconstruct simulated phantom data and real data.

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Construction of wavelet decompositions for tomographic images

Cited by 17 publications

References 6 publications

Statistical analysis of functional MRI data in the wavelet domain

Statistical analysis of functional MRI data in the wavelet domain

A wavelet algorithm for zoom-in tomography

<title>Evaluation of various wavelet bases for use in wavelet-based multiresolution expectation maximization image reconstruction algorithm for PET</title>

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