Convex Sets Approach Research Articles

Dual-excitation flip-angle simultaneous cine and T1 mapping using spiral acquisition with respiratory and cardiac self-gating.

To develop a free-breathing cardiac self-gated technique that provides cine images and slice profile-corrected T1 maps from a single acquisition. Without breath-holding or electrocardiogram gating, data were acquired continuously on a 3T scanner using a golden-angle gradient-echo spiral pulse sequence, with an inversion RF pulse applied every 4 seconds. Flip angles of 3° and 15° were used for readouts after the first four and second four inversions. Self-gating cardiac triggers were extracted from heart image navigators, and respiratory motion was corrected by rigid registration on each heartbeat. Cine images were reconstructed from the steady-state portion of 15° readouts using a low-rank plus sparse reconstruction. The T1 maps were fit using a projection onto convex sets approach from images reconstructed using slice profile-corrected dictionary learning. This strategy was evaluated in a phantom and 14 human subjects. The self-gated signal demonstrated close agreement with the acquired electrocardiogram signal. The image quality for the proposed cine images and standard clinical balanced SSFP images were 4.31 (±0.50) and 4.65 (±0.30), respectively. The slice profile-corrected T1 values were similar to those of the inversion-recovery spin-echo technique in phantom, and had a higher global T1 value than that of MOLLI in human subjects. Cine and T1 mapping using spiral acquisition with respiratory and cardiac self-gating successfully acquired T1 maps and cine images in a single acquisition without the need for electrocardiogram gating or breath-holding. This dual-excitation flip-angle approach provides a novel approach for measuring T1 while accounting for and slice profile effect on the apparent .

Topology Optimization of Dynamic Systems Under Uncertain Loads: An H∞-Norm-Based Approach

An innovative approach to topology optimization of dynamic system is introduced that is based on the system transfer-function H∞-norm. As for the structure, the proposed strategy allows to determine the optimal material distribution that ensures the minimization of a suitable goal function, such as (an original definition of) the dynamic compliance. Load uncertainty is accounted for by means of a nonprobabilistic convex-set approach (Ben-Haim and Elishakoff, 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science, Amsterdam). At each iteration, the worst load is determined as the one that maximizes the current dynamic compliance so that the proposed strategy fits the so-called worst case scenario (WCS) approach. The overall approach consists of the repeated solution of the two steps (minimization of the dynamic compliance with respect to structural parameters and maximization of the dynamic compliance with respect to the acting load) until convergence is achieved. Results from representative numerical studies are eventually presented along with extensions to the proposed approach that are currently under development.

High-resolution reconstruction for terahertz imaging.

We present a high-resolution (HR) reconstruction model and algorithms for terahertz imaging, taking advantage of super-resolution methodology and algorithms. The algorithms used include projection onto a convex sets approach, iterative backprojection approach, Lucy-Richardson iteration, and 2D wavelet decomposition reconstruction. Using the first two HR reconstruction methods, we successfully obtain HR terahertz images with improved definition and lower noise from four low-resolution (LR) 22×24 terahertz images taken from our homemade THz-TDS system at the same experimental conditions with 1.0mm pixel. Using the last two HR reconstruction methods, we transform one relatively LR terahertz image to a HR terahertz image with decreased noise. This indicates potential application of HR reconstruction methods in terahertz imaging with pulsed and continuous wave terahertz sources.

Super-resolution reconstruction for 4D computed tomography of the lung via the projections onto convex sets approach.

The use of 4D computed tomography (4D-CT) of the lung is important in lung cancer radiotherapy for tumor localization and treatment planning. Sometimes, dense sampling is not acquired along the superior-inferior direction. This disadvantage results in an interslice thickness that is much greater than in-plane voxel resolutions. Isotropic resolution is necessary for multiplanar display, but the commonly used interpolation operation blurs images. This paper presents a super-resolution (SR) reconstruction method to enhance 4D-CT resolution. The authors assume that the low-resolution images of different phases at the same position can be regarded as input "frames" to reconstruct high-resolution images. The SR technique is used to recover high-resolution images. Specifically, the Demons deformable registration algorithm is used to estimate the motion field between different "frames." Then, the projection onto convex sets approach is implemented to reconstruct high-resolution lung images. The performance of the SR algorithm is evaluated using both simulated and real datasets. Their method can generate clearer lung images and enhance image structure compared with cubic spline interpolation and back projection (BP) method. Quantitative analysis shows that the proposed algorithm decreases the root mean square error by 40.8% relative to cubic spline interpolation and 10.2% versus BP. A new algorithm has been developed to improve the resolution of 4D-CT. The algorithm outperforms the cubic spline interpolation and BP approaches by producing images with markedly improved structural clarity and greatly reduced artifacts.

Cooperative Wireless Sensor Network Positioning via Implicit Convex Feasibility

We propose a distributed positioning algorithm to estimate the unknown positions of a number of target nodes, given distance measurements between target nodes and between target nodes and a number of reference nodes at known positions. Based on a geometric interpretation, we formulate the positioning problem as an implicit convex feasibility problem in which some of the sets depend on the unknown target positions, and apply a parallel projection onto convex sets approach to estimate the unknown target node positions. The proposed technique is suitable for parallel implementation in which every target node in parallel can update its position and share the estimate of its location with other targets. We mathematically prove convergence of the proposed algorithm. Simulation results reveal enhanced performance for the proposed approach compared to available techniques based on projections, especially for sparse networks.

Estimation of an Initial Condition of Sigma–Delta Modulators via Projection Onto Convex Sets

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, an initial condition of strictly causal rational interpolative sigma–delta modulators (SDMs) is estimated based on quantizer output bit streams and an input signal. A set of initial conditions generating bounded trajectories is characterized. It is found that a set of initial conditions generating bounded trajectories but not necessarily corresponding to quantizer output bit streams is convex. Also, it is found that a set of initial conditions corresponding to quantizer output bit streams but not necessarily generating bounded trajectories is convex too. Moreover, it is found that an initial condition both corresponding to quantizer output bit streams and generating bounded trajectories is uniquely defined if the loop filter is unstable (Here, an unstable loop filter refers to that with at least one of its poles being strictly outside the unit circle). To estimate that unique initial condition, a projection onto convex set approach is employed. Numerical computer simulations show that the employed method can estimate the initial condition effectively. </para>

Shape/size Optimization Of Truss Structures UsingNon-probabilistic Description Of Uncertainty

In the present work an optimal solution for the well studied problem of truss shape/size optimization will be pursued when a certain level of uncertainty in the material constants is considered. This uncertain optimization will then give optimal structures which can be considered robust with respect to material constants variation. To this goal the convex set approach, and anti-optimization will be used to find the worst effect of the uncertainty on the structural response. The method consists in alternating between the main optimization problem and the maximization of constraints with respect to the variation of the uncertain variables. The main optimization is carried out using the Diagonal Quadratic Approximation of Zhang and Fleury. Numerical examples will be given using some simple classical cases of truss optimization.