Yiheng Zhang

Eigenvector-based spatial filtering for reduction of physiological interference in diffuse optical imaging

Diffuse optical imaging is an effective technique for noninvasive functional brain imaging. However, the measurements respond to systemic hemodynamic fluctuations caused by the cardiac cycle, respiration, and blood pressure, which may obscure or overwhelm the desired stimulus-evoked response. Previous work on this problem employed temporal filtering, estimation of systemic effects from background pixels, or modeling of interference signals with predefined basis functions, with some success. However, weak signals are still lost in the interference, and other complementary methods are desirable. We use the spatial behavior of measured baseline signals to identify the interference subspaces. We then project signals components in this subspace out of the stimulation data. In doing so, we assume that systemic interference components will be more global spatially, with higher energy, than the stimulus-evoked signals of interest. Thus, the eigenvectors corresponding to the largest eigenvalues of an appropriate correlation matrix form the basis for an interference subspace. By projecting the data onto the orthogonal nullspace of these eigenvectors, we can obtain more localized response, as reflected in improved contrast-to-noise ratio and correlation coefficient maps.

Optimal linear inverse solution with multiple priors in diffuse optical tomography

A general framework for incorporating single and multiple priors in diffuse optical tomography is described. We explore the use of this framework for simultaneously utilizing spatial and spectral priors in the context of imaging breast cancer. The utilization of magnetic resonance images of water and lipid content as a statistical spatial prior for the diffuse optical image reconstructions is also discussed. Simulations are performed to demonstrate the significant improvement in image quality afforded by combining spatial and spectral priors.

An analytical comparison of three spatio-temporal regularization methods for dynamic linear inverse problems in a common statistical framework

Dynamic inverse problems, which occur in medical imaging and other fields, are inverse problems in which the quantities to be reconstructed vary in time, although they are related to the measurements through spatial operators only. Traditional methods solve these problems by frame-by-frame reconstruction, then extract temporal behaviour of the objects or regions of interest through curve fitting and other image-based processing. These approaches solve the inverse problem while exploiting only the spatial relationship between the object and the measurement data at each time instant, without using any temporal dynamics of the underlying process, and thus are not optimal unless the solution is temporally uncorrelated. If the spatial operators are linear, and if one, by contrast, solves the whole spatio-temporal process jointly, it falls into the category of general linear least-squares problems. Such approaches are generally difficult, both due to the challenge of modelling the temporal dynamics appropriately as well as to the high dimensionality of the associated large linear system. Several recent reports have approached this problem in different ways, making different prior assumptions on the spatial and temporal behaviour. In this paper we discuss three such approaches, which have been introduced from different points of view, in a common statistical regularization framework, and illuminate their relationships. The three methods are a state-space model, the separability condition and a multiple constraints model. The key result is that there is a clear relationship among the three methods; specifically, the inverse of the spatio-temporal autocovariance matrix has a block tri-diagonal form, a Kronecker product form or a Kronecker sum form, respectively. Some simple simulation examples are presented to illustrate the theoretical analysis.

A haemodynamic response function model in spatio-temporal diffuse optical tomography

Diffuse optical tomography (DOT) is a new and effective technique for functional brain imaging. It can detect local changes in both oxygenated and deoxygenated haemoglobin concentrations in tissue based on differential absorption at multiple wavelengths. Traditional methods in spatio-temporal analysis of haemoglobin concentrations in diffuse optical tomography first reconstruct the spatial distribution at different time instants independently, then look at the temporal dynamics on each pixel, without incorporating any temporal information as a prior in the image reconstruction. In this work, we present a temporal haemodynamic response function model described by a basis function expansion, in a joint spatio-temporal DOT reconstruction of haemoglobin concentration changes during simulated brain activation. In this joint framework, we simultaneously employ spatial regularization, spectral information and temporal assumptions. We also present an efficient algorithm for solving the associated large-scale systems. The expected improvements in spatial resolution and contrast-to-noise ratio are illustrated with simulations of human brain activation.

Analysis of spatial-temporal regularization methods for linear inverse problems from a common statistical framework

In some medical imaging problems, the quantity to image is time-varying but related to the measurements by spatial dynamics only. Traditional methods solve the associated inverse problem separately at each time instant. Several recent reports take advantage of prior knowledge and/or measurement temporal behavior to solve jointly in space and time. In this paper we discuss three such approaches, which have been introduced in distinct mathematical contexts, from a common statistical regularization framework, and illuminate their relationships, advantages and disadvantages.

A multi-resolution admissible solution approach for diffuse optical tomography

We address the use of diffuse light to characterize the space-varying absorption coefficient in tissue, posed as an inverse problem, ill-posed due to the physics and limitations on source-detector location. Accurate reliable solutions require a priori constraints. We extend our previously utilized admissible solution approach, with convex constraint functions defining admissibility conditions, by using the deep-cut ellipsoid algorithm, iteratively choosing the most important constraint value, and introducing a multi-resolution grid method to decrease the computational burden. Simulations in representative 2-D scenarios indicate that we successfully reconstruct relatively deep anomalies while reducing the computational time more than 95%.

Inverse electrocardiography in the framework of dynamic imaging problems

We describe several current approaches which include temporal information into the inverse problem of electrocardiography. Some of these approaches operate directly on potential-based source models, and we show how three recent methods, introduced with rather distinct assumptions, can be placed in a common framework and compared. Others operate on parameterized models of the cardiac sources, and we discuss briefly how recent developments in curve evolution methods for inverse problems may allow more physiologically complex parametric models to be employed.

High-order state space models in dynamic linear inverse problems

For dynamic linear inverse problems, where the quantity to be imaged is time-varying, joint spatio-temporal regularization methods are useful to improve reconstructions. State space models, with first-order Markov temporal dynamics, have been used to directly model the temporal evolution, and can be efficiently solved by the Kalman filter and fixed-interval smoother. Here we discuss higher-order state space models in this framework, present a decomposition structure of the decomposition, and show how, if the temporal model is a corresponding regularization matrix, and describe a Kronecker product based efficient algorithm in the case in the case of a scalar AR model.

A spatio-temporal reconstruction algorithm for diffuse optical tomography based on a hemodynamic response function model

Diffuse optical tomography (DOT) can reconstruct localized changes in oxy- and deoxygenated hemoglobin concentrations in tissue, and is an effective technique for functional brain imaging. To recover the spatial distribution and temporal variation of changes evoked by brain activation, an inverse solution for a joint spatio-temporal reconstruction is proposed, in contrast to traditional methods which treat the problem independently at each time instant. We use a hemodynamic response function model patterned after fMRI. The DOT setting is more complicated than fMRI however, and we describe required extensions of this model. Simulation results show improvement in spatial resolution and contrast-to-noise ratio over traditional frame-by-frame reconstruction even after posterior fitting with same temporal prior

Reduction of physiological interference in optical functional neuroimaging using eigenvector-based spatial filtering

Diffuse optical imaging is an effective technique for noninvasive functional brain imaging. However these measurements also respond to systemic hemodynamic fluctuations which may obscure or overwhelm the desired stimulus-evoked response. In this paper, we use the spatial behavior of measured baseline signals to identify interference subspaces and project out components of the data which lie in this subspace. We assume that systemic components will be more global spatially, with higher energy than the signals of interest. Through this spatial filtering, we can obtain a more localized response, and improved correlation coefficient (CC) maps. We report tests in data from 2 human subjects.