Diffuse optical tomography in the presence of a chest wall

Abstract

Diffuse optical tomography (DOT) has been employed to derive spatial maps of physiologically important chromophores in the human breast, but the fidelity of these images is often compromised by boundary effects such as those due to the chest wall. We explore the image quality in fast, data-intensive analytic and algebraic linear DOT reconstructions of phantoms with subcentimeter target features and large absorptive regions mimicking the chest wall. Experiments demonstrate that the chest wall phantom can introduce severe image artifacts. We then show how these artifacts can be mitigated by exclusion of data affected by the chest wall. We also introduce and demonstrate a linear algebraic reconstruction method well suited for very large data sets in the presence of a chest wall.

Solution of the nonlinear inverse scattering problem byT-matrix completion. I. Theory

“…(39) Since M a , M b ≤ N v , x|W |x ≤ x|x and we have proved(36). The equality x|W |x = x|x holds only in the case M A = M B = N v , in which case W = I and the iteration(33) trivially converges to its fixed point right upon making the initial guess.…”

“…Therefore, the optimal size of the data set is determined by a complex interplay between the ill-posedness of the inverse problem and the statistical properties of the noise. Experimental DOT reconstruction with large data sets was demonstrated in [34], experimental determination of the optimal size of the data set was in [34,35] and further insights on selection of useful data points in the presence of strong nonlinearity were provided in [36]. However, all references just quoted used linearized image reconstruction.…”

Solution of the nonlinear inverse scattering problem byT-matrix completion. II. Simulations

“…Storing a matrix of this size in computer memory requires at least 112Gb of RAM (in single precision). One can follow the approach of [24] where we have computed the product K * K iteratively by storing only sufficiently small blocks of K in computer memory. Then the product K * K was Tikhonov-regularized by applying the operation K * K → K * K + λ 2 I and the resultant system of equations was solved by the conjugate gradient descent.…”

“…In the simulations shown below, such incorrect assignment occurred in the strong nonlinearity regime. We note that such occurrences can be easily "diagnosed" by monitoring the error of the matrix equation (24) as is explained below. If an incorrect assignment does occur, one can potentially alleviate the problem by adjusting the constants used by the algorithm or by not using sparsity checks at all.…”

Image reconstruction optimization and quantification for image-guided luminescent tomography

“…DOT imaging seeks to recover intrinsic optical absorption and scattering maps by tomographic imaging using transmitted light signals through the tissue. DOT has been extensively used for breast imaging (28,(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47)(48), prostate imaging (49)(50)(51)(52), small animal imaging (53)(54)(55)(56)(57)(58), and is widely used for clinical brain imaging(59-65). As we shall see, the addition of fluorescence can be a powerful tool in medical imaging.…”