Convergence Studies on Iterative Algorithms for Image Reconstruction
We introduce a general iterative scheme for image reconstruction based on Landweber's method. In our configuration, a sequential block-iterative (SeqBI) version can be readily formulated from a simultaneous block-iterative (SimBI) version, and vice versa. This provides a mechanism to derive new algorithms from known ones. It is shown that some widely used iterative algorithms, such as the algebraic reconstruction technique (ART), simultaneous ART (SART), Cimmino's, and the recently designed diagonal weighting and component averaging algorithms, are special examples of the general scheme. We prove convergence of the general scheme under conditions more general than assumed in earlier studies, for its SeqBI and SimBI versions in the consistent and inconsistent cases, respectively. Our results suggest automatic relaxation strategies for the SeqBI and SimBI versions and characterize the dependence of the limit image on the initial guess. It is found that in all cases the limit is the sum of the minimum norm solution of a weighted least-squares problem and an oblique projection of the initial image onto the null space of the system matrix.

title: Convergence of the simultaneous algebraic reconstruction technique (SART)
abstract: In 1984, the simultaneous algebraic reconstruction technique (SART) was developed as a major refinement of the algebraic construction technique (ART). Since then, the SART approach remains a powerful tool for iterative image reconstruction. However, the convergence of the SART has never been established. This long-standing conjecture is proven under the condition that coefficients of the linear imaging system are non-negative. It is shown that from any initial value the sequence generated by the SART converges to a weighted least square solution. The importance of the SART and several relevant issues are also discussed.

title: Convergence of iterative algorithms for image reconstruction
abstract: We introduce a general iterative scheme for image reconstruction based on Landweber's method. Within our configuration, the block-iterative (BI) version can be formulated from its simultaneous version easily, and vice versa. This provides the mechanism to formulate new algorithms from known algorithms. It can be shown that some of the widely used iterative algorithms, such as the ART, SART, Cimmino's Algorithm and recently designed DWE and CAV, are special examples of the general scheme or its BI version. By applying the convergence results of the general scheme, the corresponding convergence in the consistent or inconsistent cases, for the block-iterative or simultaneous versions, of those specific algorithms can be established under mild conditions on the relaxation parameters.

title: Cone-beam reconstruction for Micro-CT
abstract: X-ray micro-CT has been a focus in the CT/Micro-CT Lab, the University of Iowa. In this paper, some recent progress we made on cone-beam micro-CT is described. First, we address approximation reconstruction using Feldkamp-type algorithms with multiple X-ray sources and displaced detector configurations. Then, we explain three types of artifacts associated with exact reconstruction in the Grangeat framework. Finally, we report the convergence of a generalized block-iterative Landweber scheme. Representative images from simulation and experiments are also given.

title: Blind deblurring of spiral CT images
abstract: To discriminate fine anatomical features in the inner ear, it has been desirable that spiral computed tomography (CT) may perform beyond their current resolution limits with the aid of digital image processing techniques. In this paper, we develop a blind deblurring approach to enhance image resolution retrospectively without complete knowledge of the underlying point spread function (PSF). An oblique CT image can be approximated as the convolution of an isotropic Gaussian PSF and the actual cross section. Practically, the parameter of the PSF is often unavailable. Hence, estimation of the parameter for the underlying PSF is crucially important for blind image deblurring. Based on the iterative deblurring theory, we formulate an edge-to-noise ratio (ENR) to characterize the image quality change due to deblurring. Our blind deblurring algorithm estimates the parameter of the PSF by maximizing the ENR, and deblurs images. In the phantom studies, the blind deblurring algorithm reduces image blurring by about 24%, according to our blurring residual measure. Also, the blind deblurring algorithm works well in patient studies. After fully automatic blind deblurring, the conspicuity of the submillimeter features of the cochlea is substantially improved.

title: A Surface Reconstruction Method for Highly Noisy Point Clouds
abstract: In this paper we propose a surface reconstruction method for highly noisy and non-uniform data based on minimal surface model and tensor voting method. To deal with ill-posedness, noise and/or other uncertainties in the data we processes the raw data first using tensor voting before we do surface reconstruction. The tensor voting procedure allows more global and robust communications among the data to extract coherent geometric features and saliency independent of the surface reconstruction. These extracted information will be used to preprocess the data and to guide the final surface reconstruction. Numerically the level set method is used for surface reconstruction. Our method can handle complicated topology as well as highly noisy and/or non-uniform data set. Moreover, improvements of efficiency in implementing the tensor voting method are also proposed. We demonstrate the ability of our method using synthetic and real data.

title: Uplink Multi-User MIMO OFDM Enhancement Using Genetically Improved Turbo Receiver
abstract: Despite the assistance of well-recognized hot technologies such as Multiple-Input Multiple-Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM), cell-edge mobile users still suffer significant performance degradation in uplink, thus restricting the system coverage. In the context of the European B3G/4G WINNER system, we propose a hybrid solution which takes the advantages of both Genetic Algorithm (GA) and turbo processing, resulting in an enhanced MIMO OFDM receiver. Simulation results show that the proposed scheme is capable of achieving a good link performance, whilst improving the robustness of the multi-links and thus the cell coverage.

title: Positive Periodic Solutions of Nonautonomous Lotka-Volterra Dispersal System with Delays
abstract: In this paper, a general class of nonautonomous Lotka-Volterra dispersal system with discrete and continuous infinite delays is investigated. This class of Lotka-Volterra systems model the diffusion of a single species into n patches by discrete dispersal. By using Schauder's fixed point theorem, we prove the existence of positive periodic solutions of system. The global asymptotical stability of positive periodic solution is discussed and the sufficient conditions for exponential stability are also given. we give an example to illustrate the validity of the results in the end. The conditions we obtained are more general and it can be extended to several special systems.

title: Iterative Joint Channel Estimation and Multi-User Detection for Multiple-Antenna Aided OFDM Systems
abstract: Multiple-input-multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems have recently attracted substantial research interest. However, compared to single-input-single-output (SISO) systems, channel estimation in the MIMO scenario becomes more challenging, owing to the increased number of independent transmitter-receiver links to be estimated. In the context of the Bell layered space-time architecture (BLAST) or space division multiple access (SDMA) multi-user MIMO OFDM systems, none of the known channel estimation techniques allows the number of users to be higher than the number of receiver antennas, which is often referred to as a "rank-deficient" scenario, owing to the constraint imposed by the rank of the MIMO channel matrix. Against this background, in this paper we propose a new genetic algorithm (GA) assisted iterative joint channel estimation and multi-user detection (GA-JCEMUD) approach for multi-user MIMO SDMA-OFDM systems, which provides an effective solution to the multi-user MIMO channel estimation problem in the above-mentioned rank-deficient scenario. Furthermore, the GAs invoked in the data detection literature can only provide a hard-decision output for the forward error correction (FEC) or channel decoder, which inevitably limits the system's achievable performance. By contrast, our proposed GA is capable of providing "soft" outputs and hence it becomes capable of achieving an improved performance with the aid of FEC decoders. A range of simulation results are provided to demonstrate the superiority of the proposed scheme.

title: Spatial domain wavelet design for feature preservation in computational data sets
abstract: High-fidelity wavelet transforms can facilitate visualization and analysis of large scientific data sets. However, it is important that salient characteristics of the original features be preserved under the transformation. We present a set of filter design axioms in the spatial domain which ensure that certain feature characteristics are preserved from scale to scale and that the resulting filters correspond to wavelet transforms admitting in-place implementation. We demonstrate how the axioms can be used to design linear feature-preserving filters that are optimal in the sense that they are closest in L2 to the ideal low pass filter. We are particularly interested in linear wavelet transforms for large data sets generated by computational fluid dynamics simulations. Our effort is different from classical filter design approaches which focus solely on performance in the frequency domain. Results are included that demonstrate the feature-preservation characteristics of our filters

title: Finite-Time Boundedness Analysis of Uncertain CGNNs with Multiple Delays
abstract: The problem of finite-time boundedness(FTB) for a class of Cohen-Grossberg neural networks(CGNNs) with multiple delays and parameter perturbations is analyzed in this paper By way of extending the concept of FTB for time delay system and constructing a suitable Lyapunov function and using linear matrix inequality(LMI) technique, some delay-dependent criteria are derived to guarantee FTB for uncertain and certain CGNNs with multiple delays Meanwhile, an algorithm is also presented Finally, simulation examples are given to demonstrate the effectiveness of the conclusion.