Phaneendra K. Yalavarthy

Structural information within regularization matrices improves near infrared diffuse optical tomography

Near-Infrared (NIR) tomographic image reconstruction is a non-linear, ill-posed and ill-conditioned problem, and so in this study, different ways of penalizing the objective function with structural information were investigated. A simple framework to incorporate structural priors is presented, using simple weight matrices that have either Laplacian or Helmholtz-type structures. Using both MRI-derived breast geometry and phantom data, a systematic and quantitative comparison was performed with and without spatial priors. The Helmholtz-type structure can be seen as a more generalized approach for incorporating spatial priors into the reconstruction scheme. Moreover, parameter reduction (i.e. hard prior information) in the imaging field through the enforcement of spatially explicit regions may lead to erroneous results with imperfect spatial priors.

Weight‐matrix structured regularization provides optimal generalized least‐squares estimate in diffuse optical tomography

Diffuse optical tomography (DOT) involves estimation of tissue optical properties using noninvasive boundary measurements. The image reconstruction procedure is a nonlinear, ill-posed, and ill-determined problem, so overcoming these difficulties requires regularization of the solution. While the methods developed for solving the DOT image reconstruction procedure have a long history, there is less direct evidence on the optimal regularization methods, or exploring a common theoretical framework for techniques which uses least-squares (LS) minimization. A generalized least-squares (GLS) method is discussed here, which takes into account the variances and covariances among the individual data points and optical properties in the image into a structured weight matrix. It is shown that most of the least-squares techniques applied in DOT can be considered as special cases of this more generalized LS approach. The performance of three minimization techniques using the same implementation scheme is compared using test problems with increasing noise level and increasing complexity within the imaging field. Techniques that use spatial-prior information as constraints can be also incorporated into the GLS formalism. It is also illustrated that inclusion of spatial priors reduces the image error by at least a factor of 2. The improvement of GLS minimization is even more apparent when the noise level in the data is high (as high as 10%), indicating that the benefits of this approach are important for reconstruction of data in a routine setting where the data variance can be known based upon the signal to noise properties of the instruments.

Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis

The image resolution and contrast in Near-Infrared (NIR) tomographic image reconstruction are affected by parameters such as the number of boundary measurements, the mesh resolution in the forward calculation and the reconstruction basis. Increasing the number of measurements tends to make the sensitivity of the domain more uniform reducing the hypersensitivity at the boundary. Using singular-value decomposition (SVD) and reconstructed images, it is shown that the numbers of 16 or 24 fibers are sufficient for imaging the 2D circular domain for the case of 1% noise in the data. The number of useful singular values increases as the logarithm of the number of measurements. For this 2D reconstruction problem, given a computational limit of 10 sec per iteration, leads to choice of forward mesh with 1785 nodes and reconstruction basis of 30x30 elements. In a three-dimensional (3D) NIR imaging problem, using a single plane of data can provide useful images if the anomaly to be reconstructed is within the measurement plane. However, if the location of the anomaly is not known, 3D data collection strategies are very important. Further the quantitative accuracy of the reconstructed anomaly increased approximately from 15% to 89% as the anomaly is moved from the centre to boundary, respectively. The data supports the exclusion of out of plane measurements may be valid for 3D NIR imaging.

A boundary element approach for image-guided near-infrared absorption and scatter estimation

Multimodality NIR spectroscopy systems offer the possibility of region-based vascular and molecular characterization of tissue in vivo. However, computationally efficient 3D image reconstruction algorithms specific to these image-guided systems currently do not exist. Image reconstruction is often based on finite-element methods (FEMs), which require volume discretization. Here, a boundary element method (BEM) is presented using only surface discretization to recover the optical properties in an image-guided setting. The reconstruction of optical properties using BEM was evaluated in a domain containing a 30 mm inclusion embedded in two layer media with different noise levels and initial estimates. For 5% noise in measurements, and background starting values for reconstruction, the optical properties were recovered to within a mean error of 6.8%. When compared with FEM for this case, BEM showed a 28% improvement in computational time. BEM was also applied to experimental data collected from a gelatin phantom with a 25 mm inclusion and could recover the true absorption to within 6% of expected values using less time for computation compared with FEM. When applied to a patient-specific breast mesh generated using MRI, with a 2 cm ductal carcinoma, BEM showed successful recovery of optical properties with less than 5% error in absorption and 1% error in scattering, using measurements with 1% noise. With simpler and faster meshing schemes required for surface grids as compared with volume grids, BEM offers a powerful and potentially more feasible alternative for high-resolution 3D image-guided NIR spectroscopy.

Basis pursuit deconvolution for improving model-based reconstructed images in photoacoustic tomography

The model-based image reconstruction approaches in photoacoustic tomography have a distinct advantage compared to traditional analytical methods for cases where limited data is available. These methods typically deploy Tikhonov based regularization scheme to reconstruct the initial pressure from the boundary acoustic data. The model-resolution for these cases represents the blur induced by the regularization scheme. A method that utilizes this blurring model and performs the basis pursuit deconvolution to improve the quantitative accuracy of the reconstructed photoacoustic image is proposed and shown to be superior compared to other traditional methods via three numerical experiments. Moreover, this deconvolution including the building of an approximate blur matrix is achieved via the Lanczos bidagonalization (least-squares QR) making this approach attractive in real-time.

Accelerating frequency-domain diffuse optical tomographic image reconstruction using graphics processing units

Diffuse optical tomographic image reconstruction uses advanced numerical models that are computationally costly to be implemented in the real time. The graphics processing units (GPUs) offer desktop massive parallelization that can accelerate these computations. An open-source GPU-accelerated linear algebra library package is used to compute the most intensive matrix-matrix calculations and matrix decompositions that are used in solving the system of linear equations. These open-source functions were integrated into the existing frequency-domain diffuse optical image reconstruction algorithms to evaluate the acceleration capability of the GPUs (NVIDIA Tesla C 1060) with increasing reconstruction problem sizes. These studies indicate that single precision computations are sufficient for diffuse optical tomographic image reconstruction. The acceleration per iteration can be up to 40, using GPUs compared to traditional CPUs in case of three-dimensional reconstruction, where the reconstruction problem is more underdetermined, making the GPUs more attractive in the clinical settings. The current limitation of these GPUs in the available onboard memory (4 GB) that restricts the reconstruction of a large set of optical parameters, more than 13,377.

Toward Real-Time Availability of 3D Temperature Maps Created with Temporally Constrained Reconstruction

To extend the previously developed temporally constrained reconstruction (TCR) algorithm to allow for real‐time availability of three‐dimensional (3D) temperature maps capable of monitoring MR‐guided high intensity focused ultrasound applications.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

Abstract. A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison.

Sparse Recovery Methods Hold Promise for Diffuse Optical Tomographic Image Reconstruction

The sparse recovery methods utilize the ℓp-norm-based regularization in the estimation problem with 0 ≤ p ≤ 1. These methods have a better utility when the number of independent measurements are limited in nature, which is a typical case for diffuse optical tomographic image reconstruction problem. These sparse recovery methods, along with an approximation to utilize the ℓ0-norm, have been deployed for the reconstruction of diffuse optical images. Their performance was compared systematically using both numerical and gelatin phantom cases to show that these methods hold promise in improving the reconstructed image quality.

Helmholtz-Type Regularization Method for Permittivity Reconstruction Using Experimental Phantom Data of Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitance between sets of electrodes placed around its periphery. Image reconstruction in ECT is a nonlinear ill-posed inverse problem, and regularization methods are needed to stabilize this inverse problem. The reconstruction of complex shapes (sharp edges) and absolute permittivity values is a more difficult task in ECT, and the commonly used regularization methods in Tikhonov minimization are unable to solve these problems. In the standard Tikhonov regularization method, the regularization matrix has a Laplacian-type structure, which encourages smoothing reconstruction. A Helmholtz-type regularization scheme has been implemented to solve the inverse problem with complicated-shape objects and the absolute permittivity values. The Helmholtz-type regularization has a wavelike property and encourages variations of permittivity. The results from experimental data demonstrate the advantage of the Helmholtz-type regularization for recovering sharp edges over the popular Laplacian-type regularization in the framework of Tikhonov minimization. Furthermore, this paper presents examples of the reconstructed absolute value permittivity map in ECT using experimental phantom data.