PET regularization by envelope guided conjugate gradients

Enhanced Resolution Analysis for Water Molecules in MCM-41 and SBA-15 in Low-Field T2 Relaxometric Spectra

Mesoporous silica materials are the subjects for relaxometric NMR studies in which we obtain information on the properties of molecules in confined geometries. The signal analysis in such investigations is generally carried out with the help of the Inverse Laplace Transform (ILT), which is accompanied by a regularization procedure. The appropriate selection of the regularization method may positively affect the resolution of the spectrum and the essence of the final conclusions. In this work, we examined the MCM-41 and SBA-15 model systems in various saturation states, using L-Curve regularization for relaxation spectra based on our own version of the fast fast ILT implementation. In a single relaxometric spectrum, the water contributions from the internal volume in the pores and between the silica particles were identified, which allowed us to trace the dynamics of the corresponding drying trends during the removal of water from the sample as a function of total water saturation.

Reconstruction for 3D PET Based on Total Variation Constrained Direct Fourier Method

This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).

Optical mammography: Diffuse optical imaging of breast cancer

Existing imaging modalities for breast cancer screening, diagnosis and therapy monitoring, namely X-ray mammography and magnetic resonance imaging, have been proven to have limitations. Diffuse optical imaging is a set of non-invasive imaging modalities that use near-infrared light, which can be an alternative, if not replacement, to those existing modalities. This review covers the background knowledge, recent clinical outcome, and future outlook of this newly emerging medical imaging modality.

Differentiation of benign and malignant breast tumors by in-vivo three-dimensional parallel-plate diffuse optical tomography

We have developed a novel parallel-plate diffuse optical tomography (DOT) system for three-dimensional in vivo imaging of human breast tumor based on large optical data sets. Images of oxy-, deoxy-, and total hemoglobin concentration as well as blood oxygen saturation and tissue scattering were reconstructed. Tumor margins were derived using the optical data with guidance from radiology reports and magnetic resonance imaging. Tumor-to-normal ratios of these endogenous physiological parameters and an optical index were computed for 51 biopsy-proven lesions from 47 subjects. Malignant cancers (N=41) showed statistically significant higher total hemoglobin, oxy-hemoglobin concentration, and scattering compared to normal tissue. Furthermore, malignant lesions exhibited a twofold average increase in optical index. The influence of core biopsy on DOT results was also explored; the difference between the malignant group measured before core biopsy and the group measured more than 1 week after core biopsy was not significant. Benign tumors (N=10) did not exhibit statistical significance in the tumor-to-normal ratios of any parameter. Optical index and tumor-to-normal ratios of total hemoglobin, oxy-hemoglobin concentration, and scattering exhibited high area under the receiver operating characteristic curve values from 0.90 to 0.99, suggesting good discriminatory power. The data demonstrate that benign and malignant lesions can be distinguished by quantitative three-dimensional DOT.

Comparison of methods for optimal choice of the regularization parameter for linear electrical impedance tomography of brain function

Electrical impedance tomography has the potential to provide a portable non-invasive method for imaging brain function. Clinical data collection has largely been undertaken with time difference data and linear image reconstruction methods. The purpose of this work was to determine the best method for selecting the regularization parameter of the inverse procedure, using the specific application of evoked brain activity in neonatal babies as an exemplar. The solution error norm and image SNR for the L-curve (LC), discrepancy principle (DP), generalized cross validation (GCV) and unbiased predictive risk estimator (UPRE) selection methods were evaluated in simulated data using an anatomically accurate finite element method (FEM) of the neonatal head and impedance changes due to blood flow in the visual cortex recorded in vivo. For simulated data, LC, GCV and UPRE were equally best. In human data in four neonatal infants, no significant differences were found among selection methods. We recommend that GCV or LC be employed for reconstruction of human neonatal images, as UPRE requires an empirical estimate of the noise variance.

Advances in PET Image Reconstruction

Until recently, the most widely used methods for image reconstruction were direct analytic techniques. Iterative techniques, although computationally much more intensive, produce improved images (principally arising from more accurate modeling of the acquired projection data), enabling these techniques to replace analytic techniques not only in research settings but also in the clinic. This article offers an overview of image reconstruction theory and algorithms for PET, with a particular emphasis on statistical iterative reconstruction techniques. Future directions for image reconstruction in PET are considered, which concern mainly improving the modeling of the data acquisition process and task-specific specification of the parameters to be estimated in image reconstruction.

A priori selection of the regularization parameters in emission tomography by Fourier synthesis

This paper describes how the stability of the inverse problem underlying emission tomography can be measured and controlled in clinical settings. We show how the Lanczos approximation provides a way to regularize a certain class of iterative reconstruction algorithms through a given level of noise or resolution in the slices and for a given acquisition protocol. Moreover, we show how the same Lanczos approximation can be used to decide when the iterative reconstruction algorithm actually converges for a given machine precision. These ideas are illustrated by means of reconstructions of simulated and actual emission datasets.

Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI

We employ diffuse optical tomography (DOT) to track treatment progress in a female subject presenting with locally advanced invasive carcinoma of the breast during neoadjuvant chemotherapy. Three-dimensional images of total hemoglobin concentration and scattering identified the tumor. Our measurements reveal tumor shrinkage during the course of chemotherapy, in reasonable agreement with magnetic resonance images of the same subject. A decrease in total hemoglobin concentration contrast between tumor and normal tissue was also observed over time. The results demonstrate the potential of DOT for measuring physiological parameters of breast lesions during chemotherapy.

Experimental study of stochastic noise propagation in SPECT images reconstructed using the conjugate gradient algorithm

Thanks to an experimental study based on simulated and physical phantoms, the propagation of the stochastic noise in slices reconstructed using the conjugate gradient algorithm has been analysed versus iterations. After a first increase corresponding to the reconstruction of the signal, the noise stabilises before increasing linearly with iterations. The level of the plateau as well as the slope of the subsequent linear increase depends on the noise in the projection data.

A numerical method for estimating blood flow by dynamic functional imaging

We present a numerical deconvolution scheme for estimating regional blood flow and tissue retention functions by dynamic functional imaging. The present approach implements the Tikhonov-Miller regularization in general form, which allows for prior knowledge or assumptions to be incorporated during the deconvolution process, so as to stabilize the solution against variations due to noise. Appropriate approximations and simplifications in the context of functional imaging, were also introduced to ease numerical computations. Monte Carlo simulation experiments were carried out to study the applicability of the present approach and to compare with other deconvolution techniques previously studied.