It is well known that the inverse problem in optical tomography is highly ill-posed. The image reconstruction process is often unstable and nonunique, because the number of the boundary measurements data is far fewer than the number of the unknown parameters to be reconstructed. To overcome this problem, one can either increase the number of measurement data (e.g., multispectral or multifrequency methods), or reduce the number of unknowns (e.g., using prior structural information from other imaging modalities). We introduce a novel approach for reducing the unknown parameters in the reconstruction process. The discrete cosine transform (DCT), which has long been used in image compression, is here employed to parameterize the reconstructed image. In general, only a few DCT coefficients are needed to describe the main features in an optical tomographic image. Thus, the number of unknowns in the image reconstruction process can be drastically reduced. We show numerical and experimental examples that illustrate the performance of the new algorithm as compared to a standard model-based iterative image reconstructions scheme. We especially focus on the influence of initial guesses and noise levels on the reconstruction results.
Computational speed and available memory size on a single processor are two limiting factors when using the
frequency-domain equation of radiative transport (FD-ERT) as a forward and inverse model to reconstruct
three-dimensional (3D) tomographic images. In this work, we report on a parallel, multiprocessor reducedspace
sequential quadratic programming (RSQP) approach to improve computational speed and reduce memory
requirement. To evaluate and quantify the performance of the code, we performed simulation studies employing
a 3D numerical mouse model. Furthermore, we tested the algorithm with experimental data obtained from
tumor bearing mice.
We introduce in this work a PDE-constrained approach to optical tomography that makes use of an all-atonce
reduced Hessian Sequential Quadratic Programming (rSQP) scheme. The proposed scheme treats the
forward and inverse variables independently, which makes it possible to update the radiation intensities and
the optical coefficients simultaneously by solving the forward and inverse problems, all at once. We evaluate
the performance of the proposed scheme with numerical and experimental data, and find that the rSQP
scheme can reduce the computation time by a factor of 10 to 25, as compared to the commonly employed
limited memory BFGS method.
Optical tomography of small tissue volumes, as they are encountered in rodent or finger imaging, holds great promise as the signal-to-noise levels are usually high and the spatial resolutions are much better than that of large imaging domains. To accurately model the light propagation in these small domains, radiative transport equations have to be solved directly. In the study at hand, we use the frequency-domain equation of radiative transfer (ERT) to perform a sensitivity study. We determine optimal source-modulation frequencies for which amplitude and phase of the measured signal. These results will be useful in designed experiments and optical tomographic imaging system.
It is well know that the inverse problem in optical tomography is highly ill-posed. The image reconstruction
process is often unstable and non-unique, because the number of the boundary measurements data is far fewer
than the number of the unknown parameters (optical properties) to be reconstructed. To overcome this problem
one can either increase the number of measurement data (e.g. multi-spectral or multi-frequency methods), or
reduce the number of unknows (e.g. using prior structural information from other imaging modalities). In
this paper, we introduce a novel approach for reducing the unknown parameters in the reconstruction process.
The discrete cosine transform (DCT), which has long been used in image compression, is here employed to
parameterize the reconstructed image. In general, only a few DCT coefficient are needed to describe the main
features in an image, and the number of unknowns in the image reconstruction process can be drastically
reduced. Numerical as well as experimental examples are shown that illustrate the performance of the new
Small animal models are employed to simulate disease in humans and to study its progression, what factors are
important to the disease process, and to study the disease treatment. Biomedical imaging modalities such as magnetic
resonance imaging (MRI) and Optical Tomography make it possible to non-invasively monitor the progression of
diseases in living small animals and study the efficacy of drugs and treatment protocols. MRI is an established imaging
modality capable of obtaining high resolution anatomical images and along with contrast agents allow the studying of
blood volume. Optical tomography, on the other hand, is an emerging imaging modality, which, while much lower in
spatial resolution, can separate the effects of oxyhemoglobin, deoxyhemoglobin, and blood volume with high temporal
resolution. In this study we apply these modalities to imaging the growth of kidney tumors and then there treatment by
an anti-VEGF agent. We illustrate how these imaging modalities have their individual uses, but can still supplement
each other and cross validation can be performed.
We have developed a model-based iterative image reconstruction scheme based on the equation of radiative transfer in the frequency domain for the applications in small animal optical tomographic imaging. To test the utility of such a code in small animal imaging we have furthermore developed a numerical phantom of a mouse. In simulation studies using this and other phantoms, we found that to make truly use of phase information in the reconstruction process modulation frequencies well above 100 MHz are necessary. Only at these higher frequencies the phase shifts introduced by the lesions of interest are large enough to be measured. For smaller frequencies no substantial improvements over steady-state systems are achieved in small geometries typical for small animal imaging.