A time‐domain wavelet‐based approach for fluorescence diffuse optical tomography

Abstract

Purpose: In the context of fluorescence diffuse optical tomography, determining the optimal way to exploit the time-resolved information has been receiving much attention and different features of the time-resolved signals have been introduced. In this article, the authors revisit and generalize the notion of feature, considering the projection of the measurements onto some basis functions. This leads the authors to propose a novel approach based on the wavelet transform of the measurements. Methods: A comparative study between the reconstructions obtained from the proposed waveletbased approach and the reconstructions obtained from the reference temporal moments is provided. An inhomogeneous cubic medium is considered. Reconstructions are performed from synthetic measurements assuming Poisson noise statistics. In order to provide fairly comparable reconstructions, the reconstruction scheme is associated with a particular procedure for selecting the regularization parameter. Results: In the noise-free case, the reconstruction quality is shown to be mainly driven by the number of selected features. In the presence of noise, however, the reconstruction quality depends on the type of the features. In this case, the wavelet approach is shown to outperform the moment approach. While the optimal time-resolved reconstruction quality, which is obtained considering the whole set of time samples, is recovered using only eight wavelet functions, it cannot be attained using moments. It is finally observed that the time-resolved information is of limited utility, in terms of reconstruction, when the maximum number of detected photons is lower than 10 5 . Conclusions: The wavelet approach allows for better exploiting the time-resolved information, especially when the number of detected photons is low. However, when the number of detected photons decreases below a certain threshold, the time-resolved information itself is shown to be of limited utility.

Full-wavelet approach for fluorescence diffuse optical tomography with structured illumination

“…Fast algorithms able to deal with very large datasets have been proposed for this modality [6,7], and it was observed that a limited number of patterns can be used in contrast to a large number of point-source illuminations. In parallel, the concept of data compression based on Fourier [8] or wavelet encoding [9,10] has been recently applied to CCD measurements acquired with point sources, in order to reduce the computational size of the problem. In this Letter, for the first time to our knowledge, we apply compression techniques to the measurements acquired with structured illuminations, implementing a simple approach that relies on the wavelet description of both source and detection spaces.…”

Fluorescence diffuse optical tomography: Time-resolved versus continuous-wave in the reflectance configuration

“…The larger N max is (in practice the longer the integration time) the better the signal-to-noise ratio. The influence of N max is of particular interest since the reconstruction quality mainly depends on this parameter [24].…”

“…Here, the multiplicative constant, noted κ, is chosen so as to set the maximum number of detected photons N max to a prescribed value [24]:…”

“…Although CW and TR are both long-standing approaches in FDOT, few studies have been dedicated to compare their reconstruction performances. In a recent work, we showed that the TR approach outperforms the CW approach in situations when a sufficient number of photons is collected [24]. However, this study was restricted to the transmittance configuration, i.e.…”

Image reconstruction of fluorescent molecular tomography based on the simplified matrix system

“…Some related research on wavelet-based image reconstruction has been conducted. In [18], a time-resolved forward model and its projection onto wavelet basis functions have been implemented. Ducros et al apply compression techniques to the measurements acquired with structured illuminations [19].…”