A multigrid inversion approach is proposed to solve Poisson noise model-based inverse problems. The algorithm works by moving up and down in resolution with a set of coarse scale cost functions, which incorporates a coarse scale Poisson mean defined in low resolution data and image spaces. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography are presented. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent (ICD) method.
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 can be formulated as the solution to a non-quadratic optimization problem.
In this paper, we discuss the use of nonlinear multigrid methods as both tools for optimization and algorithms for the solution of difficult inverse problems. In particular, we review some existing methods for directly formulating optimization algorithm in a multigrid framework, and we introduce a new method for the solution of general inverse problems which we call multigrid inversion. These methods work 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 optimization methods can efficiently compute the solution to a desired fine scale optimization problem. Importantly, the multigrid inversion algorithm can greatly reduce computation because both the forward and the inverse problems are more coarsely discretized at lower resolutions. An application of our method to optical diffusion tomography shows the potential for very large computational savings.
A Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the scattering coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and emission wavelengths for reconstructing all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing a fluorescent agent.
Optical diffusion tomography is a new imaging modality that offers significant potential in medical applications. The resulting nonlinear image reconstruction problem is further complicated by the fact that for practical imaging variable source excitation and detector coupling needs to be accounted for in order to obtain quantitative images. We formulated the joint problem of coupling coefficient estimation and three-dimensional image reconstruction in a Bayesian framework, and the resulting estimates are computed in an iterative coordinate-descent optimization scheme. Simulations show that this approach is an accurate and efficient method for simultaneous reconstruction of absorption and diffusion coefficients, as well as the coupling coefficients.
We demonstrate accurate and efficient three-dimensional optical diffusion imaging using simulated noisy data from a set of measurements at a single modulation frequency. A Bayesian framework provides for prior model conditioning, and a dual-step cost function optimization allows sequential estimation of the data noise variance and the image.
In this paper, the performance of the extrapolation block transform (EBT) and the shape-adaptive DCT (SA-DCT) for arbitrarily shaped image segment coding is theoretically compared. The comparison indicates that the EBT approach yields better performance than the SA-DCT on the highly correlated image at low bit rates. Since the correlation maximizing extrapolation (CME) algorithm proposed in maximizes the correlation of the extrapolated block, it is considered to be one of the EBT techniques that can achieve the performance expected by the theoretical performance. Thus, a novel object-oriented video coder employing the CME algorithm for the texture coding is proposed in this paper, and its performance is compared with that of the MPEG-4 VM through intensive computer simulations. In the proposed video coder, the contour coding technique employing the two- stage motion compensation is adopted for the shape coding, and the rate-constrained hierarchical grid interpolation is adopted for the object-based motion compensation. The simulation results show that the proposed coder outperforms the MPEG-4 VM by about 0.84 approximately 1.29 dB depending on the test sequences at the same bit rate.