Development of Next Generation Image Reconstruction Algorithms for Diffuse Optical and Photoacoustic Tomography
Biomedical optical imaging is capable of providing functional information of the soft bi-ological tissues, whose applications include imaging large tissues, such breastand brain in-vivo. Biomedical optical imaging uses near infrared light (600nm-900nm) as the probing media, givin ganaddedadvantageofbeingnon-ionizingimagingmodality. The tomographic technologies for imaging large tissues encompasses diﬀuse optical tomogra-phyandphotoacoustictomography. Traditional image reconstruction methods indiﬀuse optical tomographyemploysa �2-norm based regularization, which is known to remove high frequency no is either econstructed images and make the mappearsmooth. Hence as parsity based image reconstruction has been deployed for diﬀuse optical tomography, these sparserecov-ery methods utilize the �p-norm based regularization in the estimation problem with 0≤ p<1. These sparse recovery methods, along with an approximation to utilizethe �0-norm, have been used forther econstruction of diﬀus eopticaltomographic images.The comparison of these methods was performed by increasing the sparsityinthesolu-tion. Further a model resolution matrix based framework was proposed and shown to in-duceblurinthe�2-norm based regularization framework for diﬀuse optical tomography. This model-resolution matrix framework was utilized in the optical imaged econvolution framework. A basis pursuitdeconvolution based on Split AugmentedLagrangianShrink-ageAlgorithm(SALSA)algorithm was used along with the Tikhonovregularization step making the image reconstruction into a two-step procedure. This new two-step approach was found to be robust with no iseandwasabletobetterdelineatethestructureswhichwasevaluatedusingnumericalandgelatinphantom experiments. Modern diﬀuse optical imaging systems are multi-modalin nature, where diﬀuse optical imaging is combined with traditional imaging modalitiessuc has Magnetic Res-onanceImaging(MRI),or Computed Tomography(CT). Image-guided diﬀuse optical tomography has the advantage of reducingthetota lnumber of optical parameters beingreconstructedtothenumber of distinct tissue types identiﬁed by the traditional imaging modality, converting the optical image-reconstruction problem fromunder-determined innaturetoover-determined. In such cases, the minimum required measurements might be farless compared to those of the traditional diﬀuse optical imaging. An approach to choose these measurements optimally based on a data-resolution matrix is proposed, and it is shown that it drastically reduces the minimum required measurements (typicalcaseof240to6) without compromising the image reconstruction performance. In the last part of the work , a model-based image reconstruction approaches in pho-toacoustic tomography (which combines light and ultra sound) arestudied as it is know that these methods have a distinct advantage compared to traditionalanalytical methods in limited datacase. These model-based methods deployTikhonovbasedregularizationschemetoreconstruct the initial pressure from the boundary acoustic data. Again a model-resolution for these cases tend to represent the blurinduced by the regularization scheme. A method that utilizes this blurringmodelandper forms the basis pursuit econ-volution to improve the quantitative accuracy of the reconstructed photoacoustic image is proposed and shown to be superior compared to other traditional methods. Moreover, this deconvolution including the building of model-resolution matrixis achievedvia the Lanczosbidiagonalization (least-squares QR) making this approach computationally ef-ﬁcient and deployable inreal-time. Keywords Medical imaging, biomedical optical imaging, diﬀuse optical tomography, photoacous-tictomography, multi-modalimaging, inverse problems,sparse recovery,computational methods inbiomedical optical imaging.
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