A super-resolution optical imaging method is presented that relies on the distinct temporal information associated with each fluorescent optical reporter to determine its spatial position to high precision with measurements of heavily scattered light. This multiple-emitter localization approach uses a diffusion equation forward model in a cost function, and has the potential to achieve micron-scale spatial resolution through centimeters of tissue. Utilizing some degree of temporal separation for the reporter emissions, position and emission strength are determined using a computationally efficient time stripping multiresolution algorithm. The approach circumvents the spatial resolution challenges faced by earlier optical imaging approaches using a diffusion equation forward model, and is promising for in vivo applications. For example, in principle, the method could be used to localize individual neurons firing throughout a rodent brain, enabling direct imaging of neural network activity.

Imaging fluorescence through millimeters or centimeters of tissue has important in vivo applications, such as guiding surgery and studying the brain. Often, the important information is the location of one of more optical reporters, rather than the specifics of the local geometry, motivating the need for a localization method that provides this information. We present an optimization approach based on a diffusion model for the fast localization of fluorescent inhomogeneities in deep tissue with expanded beam illumination that simplifies the experiment and the reconstruction. We show that the position of a fluorescent inhomogeneity can be estimated while assuming homogeneous tissue parameters and without having to model the excitation profile, reducing the computational burden and improving the utility of the method. We perform two experiments as a demonstration. First, a tumor in a mouse is localized using a near infrared folate-targeted fluorescent agent (OTL38). This result shows that localization can quickly provide tumor depth information, which could reduce damage to healthy tissue during fluorescence-guided surgery. Second, another near infrared fluorescent agent (ATTO647N) is injected into the brain of a rat, and localized through the intact skull and surface tissue. This result will enable studies of protein aggregation and neuron signaling.

We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.

A numerical approach to simulate the intrinsic noise sources within transistors is described, and the impact of spatial correlation between local fluctuations is investigated. Using a 2-D numerical device solver, spectral densities for the gate and drain noise current sources and their correlation are evaluated using a Green's function approach, which is an equivalent of Shockley's impedance field method. Case studies with an AlGaN/GaN high electron mobility transistor are supported by measurement data. Using a spatial noise source correlation model, similar terminal noise is found to the case of an uncorrelated diffusion noise source. Therefore, using uncorrelated local noise sources to calculate the intrinsic terminal noise is found to be valid even for the submicrometer gate length field-effect transistor studied.

A multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed. Since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements, the proposed algorithm further reduces the computation relative to conventional multigrid approaches, which change only the image space resolution at coarse scales. The advantage is particularly important for data-rich applications, where data resolutions may differ for different scales. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography with a generalized Gaussian Markov random field image prior are presented, both with a Poisson noise model and with a quadratic data term. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent method and a multigrid method with fixed-data resolution.

In vivo optical molecular imaging involves the use of light emitting tracers combined with sophisticated sensing modalities to perform in vivo imaging of genetic and molecular information. In contrast to the classical diagnostic imaging tools which image the end effects of the diseases, optical molecular imaging could enhance our knowledge of biological phenomena, monitor genetic expression and the alteration of cells, and lead to earlier detection of diseases. With the development of exotic molecular probes with easily detectable bioluminescence and fluorescence labels, optical molecular imaging has emerged as an important new field within biomedical imaging. This paper reviews this state-of-the-art imaging technology and signal processing issues to monitor molecular and cellular events in living organisms.

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction is particularly difficult because the forward problem is both nonlinear and computationally expensive to evaluate. In this paper, we propose a general framework for nonlinear multigrid inversion that is applicable to a wide variety of inverse problems. The multigrid inversion algorithm results from the application of recursive multigrid techniques to the solution of optimization problems arising from inverse problems. The method works by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid inversion algorithm efficiently computes the solution to the desired fine-scale inversion problem. Importantly, the new algorithm can greatly reduce computation because both the forward and inverse problems are more coarsely discretized at lower resolutions. An application of our method to Bayesian optical diffusion tomography with a generalized Gaussian Markov random-field image prior model shows the potential for very large computational savings. Numerical data also indicates robust convergence with a range of initialization conditions for this nonconvex optimization problem.

In this paper, we propose a general framework for nonlinear multigrid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. In multigrid inversion, the problem is adjusted to be solved at each resolution by using the solutions at both finer and coarser resolutions. To do this, we formulate a consistent set of coarse scale cost functionals to ultimately reduce the finest scale one. At each resolution, both the forward model and inverse problems are discretized at the lower resolution; thus reducing computation. Our simulation results for the application of optical diffusion tomography indicate the potential for fast and robust convergence.

Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem. Bayesian approaches are effective, but are computationally expensive, especially for three-dimensional (3-D) imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical diffusion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality.

Optical diffusion tomography attempts to reconstruct an object cross section (a highly scattering media such as tissue) from measurements of scattered and attenuated light. While Bayesian approaches are well suited to this difficult nonlinear inverse problem, the resulting optimization problem is very computationally expensive. In this paper, we propose a nonlinear multigrid technique for computing the maximum a posteriori (MAP) reconstruction in the optical diffusion tomography problem. The multigrid approach improves reconstruction quality by avoiding a local minimum. In addition, it dramatically reduces computation. Each iteration of the algorithm alternates a Born approximation step with a single cycle of a nonlinear multigrid algorithm.

By considering electromagnetic scattering problems as examples, a study of the performance and scalability of the conjugate gradient squared (CGS) algorithm on two MIMD machines is presented. A modified CGS (MCGS) algorithm, where the synchronization overhead is effectively reduced by a factor of two, is proposed in this paper. This is achieved by changing the computation sequence in the CGS algorithm. Both experimental and theoretical analyses were performed to investigate the impact of this modification on the overall execution time.