Graph- and finite element-based total variation models for the inverse problem in diffuse optical tomography

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and unstructured geometries, non-linearity of the data fitting and regularization terms, and non-differentiability of the regularization term. We develop several approaches to overcome these difficulties by: i) defining discrete differential operators for unstructured geometries using both finite element and graph representations; ii) developing an optimization algorithm based on the alternating direction method of multipliers (ADMM) for the non-differentiable and non-linear minimization problem; iii) investigating isotropic and anisotropic variants of TV regularization, and comparing their finite element- and graph-based implementations. These approaches are evaluated on experiments on simulated data and real data acquired from a tissue phantom. Our results show that both FEM and graph-based TV regularization is able to accurately reconstruct both sparse and non-sparse distributions without the over-smoothing effect of Tikhonov regularization and the over-sparsifying effect of L$_1$ regularization. The graph representation was found to out-perform the FEM method for low-resolution meshes, and the FEM method was found to be more accurate for high-resolution meshes.Comment: 24 pages, 11 figures. Reviced version includes revised figures and improved clarit

Application de la factorisation en matrices non-négatives à l'élimination de l'autofluorescence des tissus biologiques

National audienceFluorescent imaging in diffusive media is an emerging modality for medical applications. Here, we use spectrally resolved measurements in order to separate several fluorescence sources. As we want to examine deep (4 cm) fluorophores for human applications, a very weak optical signal is measured and any interference to it may limit the sensitivity of the system. It is thus useful to filter any parasite signal, such as the intrinsic biological tissues fluorescence, called autofluorescence, which mixes with the fluorophore-specific signal. A spectroscopic approach, based on the Non-negative Matrix Factorization (NMF) method, is explored to unmix overlapping spectra and thus isolate the specific fluorescence signals from the autofluorescence signal. This blind source separation method treats specific fluorescence and autofluorescence as different sources to separate; it only needs initial spectra, updated over iterations thanks to regularized multiplicative update rules. Fluorescence contributions of intrinsic fluorescence and specific fluorescence have been satisfactorily isolated on experimental data

Non-negative Matrix Factorization: a blind sources separation method applied to optical fluorescence spectroscopy and multiplexing

International audienceFluorescence optical imaging use one or several (in multiplexing) injected fluorescent markers which specifically bind to targeted compounds. Near infrared light illuminates the region of interest and the emitted fluorescence is analyzed to localize fluorescence sources. A spectroscopic approach and a separation source method (Nonnegative matrix factorization) are explored to separate di fferent fluorescence sources and remove the unwanted biological tissues autofluorescence. We present unmixing results on overlapping spectra of interest, and show that autofluorescence removal improves Fluorescent Diffuse Optical Tomograph

Nonnegative matrix factorization: a blind spectra separation method for in vivo fluorescent optical imaging

International audienceFluorescence imaging in diffusive media is an emerging imaging modality for medical applications that uses injected fluorescent markers that bind to specific targets, e.g., carcinoma. The region of interest is illuminated with near-IR light and the emitted back fluorescence is analyzed to localize the fluorescence sources. To investigate a thick medium, as the fluorescence signal decreases with the light travel distance, any disturbing signal, such as biological tissues intrinsic fluorescence (called autofluorescence) is a limiting factor. Several specific markers may also be simultaneously injected to bind to different molecules, and one may want to isolate each specific fluorescent signal from the others. To remove the unwanted fluorescence contributions or separate different specific markers, a spectroscopic approach is explored. The nonnegative matrix factorization (NMF) is the blind positive source separation method we chose. We run an original regularized NMF algorithm we developed on experimental data, and successfully obtain separated in vivo fluorescence spectra

Application de la Factorisation en Matrices Non-négatives pour l'amélioration de la localisation de tumeurs en tomographie optique diffusive de fluorescence

National audienceL'imagerie optique de fluorescence permet de localiser des marqueurs fluorescents spécifiques injectés au patient qui s'accumulent autour de tumeurs cancéreuses. Une fois les régions dŠintérêt illuminées, un signal de fluorescence est émis par les marqueurs mais également par les tissus sains environnants. Lors de l'analyse de tissus épais, alors que le signal de fluorescence décroit avec le parcours de la lumière, l'autofluorescence des tissus prévient la détection des marqueurs profonds. Un approche spectroscopique basée sur la Factorisation en Matrices Non-négatives (FMN) est proposée pour séparer les spectres de fluorescence et éliminer l'autofluorescence des tissus. Afin de limiter le problème de non-unicité de la décomposition, l'ajout d'a priori à la méthode classique développée par Lee et Seung est proposé; la pertinence de ces contraintes est illustrée sur des exemples d'acquisitions de fluorescence in vivo

In vivo fluorescence spectra unmixing and autofluorescence removal by sparse Non-negative Matrix Factorization

International audienceFluorescence imaging locates fluorescent markers that specifically bind to targets, as tumors: markers are injected to a patient, optimally excited with near infrared light, and located thanks to emitted back fluorescence analysis. To investigate thick and diffusive media, as the fluorescence signal decreases with the light travel distance, the autofluorescence of biological tissues comes to be a limiting factor. To remove autofluorescence and isolate specific fluorescence, a spectroscopic approach, based on Non-negative Matrix Factorization (NMF), is explored. To improve results on spatially sparse markers detection, we suggest a new constrained NMF algorithm which takes sparsity constraints into account. A comparative study between both algorithms is proposed on simulated and in vivo data

Non-negative Matrix Factorization under sparsity constraints to unmix in vivo spectrally resolved acquisitions

International audienceFluorescence imaging in diffusive media is an emerging imaging modality for medical applications which uses injected fluorescent markers (several ones may be simultaneously injected) that bind to specific targets, as tumors. The region of interest is illuminated with near infrared light and the emitted back fluorescence is analyzed to localize the fluorescence sources. To investigate thick medium, as the fluorescence signal decreases with the light travel distance, any disturbing signal, such as biological tissues intrinsic fluorescence - called autofluorescence -, is a limiting factor. To remove autofluorescence and isolate each specific fluorescent signal from the others, a spectroscopic approach, based on Non-negative Matrix Factorization, is explored. We ran an NMF algorithm with sparsity constraints on experimental data, and successfully obtained separated in vivo fluorescence spectra

Regularized non negative matrix factorization for autofluorescence removal in fluorescence optical imaging

International audienceFluorescence imaging in diffusive media locates cancers thanks to injected fluorescent markers specific to the tumors. The region of interest is illuminated with red light and the emitted back fluorescence is analyzed to locate the fluorescence sources. To detect accurately the markers signal and be able to explore thick media (breast, prostate), autofluorescence emitted by biological tissues has to be removed. We propose a spectroscopic approach, based on Non-negative Matrix Factorization (NMF) method, and present interest of regularized NMF algorithms on unmixing results. In vivo autofluorescence removal and tumor detection enhancement results on mice will be presented

Background fluorescence reduction and absorption correction for fluorescence reflectance imaging

International audienceIntraoperative fluorescence imaging in reflectance geometry (FRI) is an attractive imaging modality as it allows to noninvasively monitor the fluorescence targeted tumors located below the tissue surface. Some drawbacks of this technique are the background fluorescence decreasing the contrast and absorption heterogeneities leading to misinterpretations concerning fluorescence concentrations. We presented a FRI technique relying on a laser line scanning instead of a uniform illumination. Here, we propose a correction technique based on this illumination scheme. We scan the medium with the laser line and acquire at each position of the line both fluorescence and excitation images. We then use the finding that there is a relationship between the excitation intensity pro le and the background fluorescence one. This allows us to predict the amount of signal to subtract to the fluorescence images to get a better contrast. As the light absorption information is contained both in fluorescence and excitation images, this method also permits us to correct the eff ects of absorption heterogeneities, leading to a better accuracy for the detection. This technique has been validated on simulations (with a Monte-Carlo code and with the di usion approximation using NIRFAST) and experimentally with tissue-like liquid phantoms with di erent levels of background fluorescence. Fluorescent inclusions are observed in several con gurations at depths ranging from 1 mm to 1 cm. Results obtained with this technique are compared to those obtained with a more classical wide- field detection scheme for the contrast enhancement and to the fluorescence to excitation ratio approach for the absorption correction