Jong Chul Ye

Optical diffusion tomography by iterative-coordinate-descent optimization in a Bayesian framework

Frequency-domain diffusion imaging uses the magnitude and phase of modulated light propagating through a highly scattering medium to reconstruct an image of the spatially dependent scattering or absorption coefficients in the medium. An inversion algorithm is formulated in a Bayesian framework and an efficient optimization technique is presented for calculating the maximum a posteriori image. In this framework the data are modeled as a complex Gaussian random vector with shot-noise statistics, and the unknown image is modeled as a generalized Gaussian Markov random field. The shot-noise statistics provide correct weighting for the measurement, and the generalized Gaussian Markov random field prior enhances the reconstruction quality and retains edges in the reconstruction. A localized relaxation algorithm, the iterative-coordinate-descent algorithm, is employed as a computationally efficient optimization technique. Numerical results for two-dimensional images show that the Bayesian framework with the new optimization scheme outperforms conventional approaches in both speed and reconstruction quality.

Nonlinear multigrid algorithms for Bayesian optical diffusion tomography

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.

A Self-Referencing Level-Set Method for Image Reconstruction from Sparse Fourier Samples

We address an ill-posed inverse problem of image estimation from sparse samples of its Fourier transform. The problem is formulated as joint estimation of the supports of unknown sparse objects in the image, and pixel values on these supports. The domain and the pixel values are alternately estimated using the level-set method and the conjugate gradient method, respectively. Our level-set evolution shows a unique switching behavior, which stabilizes the level-set evolution. Furthermore, the trade-off between the stability and the speed of evolution can be easily controlled by the number of the conjugate gradient steps, thus avoiding the re-initialization steps in conventional level set approaches.

Modified distorted Born iterative method with an approximate Fréchet derivative for optical diffusion tomography

In frequency-domain optical diffusion imaging, the magnitude and the phase of modulated light propagated through a highly scattering medium are used to reconstruct an image of the scattering and absorption coefficients in the medium. Although current reconstruction algorithms have been applied with some success, there are opportunities for improving both the accuracy of the reconstructions and the speed of convergence. In particular, conventional integral equation approaches such as the Born iterative method and the distorted Born iterative method can suffer from slow convergence, especially for large spatial variations in the constitutive parameters. We show that slow convergence of conventional algorithms is due to the linearized integral equations’ not being the correct Frechet derivative with respect to the absorption and scattering coefficients. The correct Frechet derivative operator is derived here. However, the Frechet derivative suffers from numerical instability because it involves gradients of both the Green’s function and the optical flux near singularities, a result of the use of near-field imaging data. To ameliorate these effects we derive an approximation to the Frechet derivative and implement it in an inversion algorithm. Simulation results show that this inversion algorithm outperforms conventional iterative methods.

Lost motion vector recovery algorithm

In motion compensated video coding, if motion vectors are lost or received with errors, not only will the current frame be corrupted, but also the errors will propagate to succeeding frames. The effects of errors can be further magnified by the fact that motion vectors are usually coded differentially. In this paper, we propose a technique using motion vector smoothing in the encoder and both boundary matching and motion vector consistency check in the decoder to compensate for lost or erroneously received motion vectors. The proposed technique produces noticeably better results than those reported previously. And the proposed motion vector smoothing algorithm causes virtually no degradation in the decoded image quality when motion vectors have no errors.<<ETX>>

Asymptotic global confidence regions in parametric shape estimation problems

We introduce confidence region techniques for analyzing and visualizing the performance of two-dimensional parametric shape estimators. Assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary, Cramer-Rao bounds are used to define an asymptotic confidence region, centered around the true boundary. Computation of the probability that an entire boundary estimate lies within the confidence region is a challenging problem, because the estimate is a two-dimensional nonstationary random process. We derive lower bounds on this probability using level crossing statistics. The same bounds also apply to asymptotic confidence regions formed around the estimated boundaries, lower-bounding the probability that the entire true boundary lies within the confidence region. The results make it possible to generate asymptotic confidence regions for arbitrary prescribed probabilities. These asymptotic global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated object, and facilitate geometric inferences. Numerical simulations suggest that the new bounds are quite tight.

Cramer-Rao bounds for parametric shape estimation in inverse problems

We address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems, when the boundaries are parameterized by a finite number of unknown variables. Our model applies to multiple unknown objects, each with its own unknown gray level, or color, and boundary parameterization, on an arbitrary known background. While such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the Cramér-Rao lower bounds, very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation. We provide a general formula for computing Cramér-Rao lower bounds in inverse problems where the observations are related to the object by a general linear transform, followed by a possibly nonlinear and noisy measurement system. As an illustration, we derive explicit formulas for computed tomography, Fourier imaging, and deconvolution problems. The bounds reveal that highly accurate parametric reconstructions are possible in these examples, using severely limited and noisy data.

Video streaming over wireless LAN with efficient scalable coding and prioritized adaptive transmission

We propose a video streaming scheme over wireless LAN using novel rate-distortion optimized data partitioning scheme and prioritized adaptive packet transmission. The new algorithm enables DCT data partitioning up to the DCT block level without rate overhead using backward adaptation. For channel adaptation, we selectively drop enhancement layer packets when the channel throughput is not sufficient. Real video streaming experiments with 802.11b testbed have demonstrated excellent performance of the algorithm under severe interference such as microwave oven.

Importance of the ?D term in frequency-resolved optical diffusion imaging

The effects of the approximation ?D=0 that is often used in frequency-resolved optical diffusion imaging are examined. It is shown that this approximation can affect the performance of integral-equation-based approaches to optical diffusion imaging, such as the Born iterative method and the distorted Born iterative method. The approximation introduces errors into the calculation of data used in simulations, which can lead to misleading evaluations of reconstruction algorithms. Numerical calculations show the magnitude of these effects and the appearance of artifacts in reconstructed images when conventional inversion algorithms are applied to more accurately calculated data.

Rate-distortion optimized data partitioning for video using backward adaptation

While data partitioning, in conjunction with unequal error protection, provides superb error resiliency, insufficient video quality when only the base partition is available prevents its wide deployment in high-quality video applications. We develop a new scheme for data partitioning of motion-compensated DCT coded video in an operational rate-distortion context. Unlike the conventional data partitioning scheme, which adapts the DCT break points at slice or video packet level, our new partitioning algorithm adapts the partitioning points at as low as the DCT block level with virtually no overhead using backward adaptation; hence it produces superior video quality over the conventional data partitioning scheme. Simulation results show that significant PSNR gain can be achieved using the new algorithm.