An ideal-observer framework to investigate signal detectability in diffuse optical imaging

Abstract

With the emergence of diffuse optical tomography (DOT) as a non-invasive imaging modality, there is a requirement to evaluate the performance of the developed DOT systems on clinically relevant tasks. One such important task is the detection of high-absorption signals in the tissue. To investigate signal detectability in DOT systems for system optimization, an appropriate approach is to use the Bayesian ideal observer, but this observer is computationally very intensive. It has been shown that the Fisher information can be used as a surrogate figure of merit (SFoM) that approximates the ideal observer performance. In this paper, we present a theoretical framework to use the Fisher information for investigating signal detectability in DOT systems. The usage of Fisher information requires evaluating the gradient of the photon distribution function with respect to the absorption coefficients. We derive the expressions to compute the gradient of the photon distribution function with respect to the scattering and absorption coefficients. We find that computing these gradients simply requires executing the radiative transport equation with a different source term. We then demonstrate the application of the SFoM to investigate signal detectability in DOT by performing various simulation studies, which help to validate the proposed framework and also present some insights on signal detectability in DOT. In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction," Acad. Radiol. 13, 195-202 (2006).

A three-step reconstruction method for fluorescence molecular tomography based on compressive sensing

“…Our ongoing work involves digital animal phantom, in-vivo animal experiment for further validation. Further, based on some of our previous work, 17–19 we are investigating the idea of objective evaluation to optimize fluorescence imaging systems.…”

A radiative transfer equation-based image-reconstruction method incorporating boundary conditions for diffuse optical imaging

“…Then, the m th component of $\overline{\mathbf{g}}false(\mathrm{bold-italic\mu }false)$, denoted by ${\overline{g}}_m$, is given by $${\overline{g}}_m=false(h_m,wfalse),$$ where (,) denotes the inner product of two vectors. Taking the derivative on both sides yields $$\frac{\partial {\overline{g}}_m}{\partial \mu }=\left(h_m,\frac{\partial w}{\partial \mu }\right)$$It can be shown, by taking an approach similar to that proposed in Jha et al ., 30 that the derivative of the gradient of w with respect to μ is given by: $$\frac{\partial w}{\partial \mu }=\mathrm{scriptX}\mathrm{scriptS}+\mathrm{scriptX}ℛ\frac{\partial w}{\partial \mu }+\mathrm{scriptX}\mathrm{scriptK}\frac{\partial w}{\partial \mu },$$ where $$\mathrm{scriptS}=-c_m{\varphi }_{n}w+\epsilon {\varphi }_n{\mathcal{K}}_{1}w$$ where ϕ n is a spatial basis function for the n th voxel, ε = 1 for μ = μ a and ε = 0 for μ = μ s , and the effect of operator ${\mathcal{K}}_1$ is: $$false[{\mathcal{K}}_{1}wfalse]false(\mathrm{bold-italicr},\hat{\mathit{s}}false)=c_{m}true\int d{\mathrm{normal\Omega }}^{\prime }ffalse(\hat{\mathit{s}},{\widehat{\mathrm{bold-italics}}}^{\prime }false)wfalse(\mathrm{bold-italicr},{\widehat{\mathrm{bold-italics}}}^{\prime }false).$$By comparing Eq. 11 to Eq.…”

Radiance and photon noise: imaging in geometrical optics, physical optics, quantum optics and radiology

“…5. For an example of this approach as applied to diffuse optical imaging, see Jha et al [20][21][22] When analytical solutions are not readily available, we can use Monte-Carlo simulation to estimate the spectral photon radiance. There is even a version of Monte-Carlo simulation, called adjoint Monte Carlo, 1 that allows direct estimation of the spectral photon radiance blurred by the estimation errors.…”