EECS 755 Projects, Fall 2006 ** RADAR * Hyun Jeong Cho Optimization transfer method for minimum-entropy estimation of phase errors in SAR : Synthetic Aperture Radar(SAR) images suffer from defocusing problem due to the phase errors induced by unknown aircraft motion, terrain height variation, and other signal propagation delays. Since entropy is a sensitive measure of image focus quality, iterative algorithms for minimizing entropy are widely used to correct this problem, and they show promising results. However, iterative algorithms for minimizing entropy should satisfy certain conditions in order to guarantee convergence since the cost function is non-quadratic. In this project, we use optimization transfer method to guarantee monotonic convergence. We also introduce several modified versions of this method to improve computational efficiency. We present results using SAR imagery, and give assessments of the algorithms. ** MR maps / reconstruction * Amanda Funai Regularized B1+ map estimation with slice selection effects : A challenge in MR imaging is that RF transmit coils produce non-uniform field strengths, so an excitation pulse will produce tip angles that vary substantially from the desired tip angle over the field of view. For parallel transmit excitation (using a coil array), it is particularly important to have a map of the B1+ field strength (and phase) for RF pulse design. Standard B1+ map estimation methods perform poorly in image regions with low spin density. These methods also do not take into account other important factors, such as slice selection effects. This paper describes a regularized method for B1+ map estimation using MR scans for each coil and for two or more tip angles. Using these scans and known slice profile, the iterative algorithm estimates both the magnitude and phase of each coil's B1+ map by exploiting the fact that maps are generally smooth. Results from simulation show an improvement over conventional unregularized methods. * Yoon Chung (Christie) Kim Joint estimation of image and coil sensitivities with separation of real and imaginary part of sensitivity map for spiral MRI data : In this project, I will focus on the joint estimation of image and coil sensitivity map of non-Cartesian SENSE method with fMRI data. Determining the sensitivity maps is an important part of the SENSitivity Encoding (SENSE) method [1], since it forms unfolding matrix, that is used as a system matrix to estimate unaliased image from undersampled k-space data. For SENSE with non-Cartesian trajectories, iterative CG reconstruction can be used to estimate image and have shown good results [2][3]. However, since the result heavily relies on the sensitivity map estimation, we can jointly estimate image and sensitivity map to improve the result image quality. Ying[4] have shown the feasibility to use joint estimation technique by using polynomial fit of sensitivity map and using regularization on the image. However, we can separate the polynomial fit into the real and imaginary part so that we can constrain the coefficients of it to be only real/imaginary. We will evaluate our results in terms of image quality and the convergence rate. * Venky Balasubramanyam Penalized-Likelihood Relaxation Map Estimation in MRI : T2 weighted imaging in MRI is useful in imaging morphological changes in pathology. Radiologists can detect lesions, differentiate between benign and malicious lesions, determine musculoskeletal infections, perform perfusion studies in brain and a whole lot of pathological studies using T2 weighted imaging. Obtaining a high-resolution T2 weighted image is time consuming. A typical T2 weighted image acquisition done using conventional techniques takes at least 10 minutes. The slow acquisition time induces motion artifacts when imaging moving anatomy, for example, in cardiac lesion studies. Researchers are trying to come up with faster techniques for estimating the T2 relaxation map. Techniques such as single shot echo planar, single shot spin echo imaging help in fast acquisition, but affect spatial resolution. Some more techniques exist in the literature such as, FLASH, T2 FARM which reduces the acquisition time to less than 30 sec. This project implements a Penalized Likelihood estimation technique to estimate the T2 relaxation map from image domain data. Images are acquired at two different echo times and a Maximum Likelihood estimate of the relaxation map is used as the initial guess for the PL algorithm. If time permits, the project will also explore implementation of relaxation map estimation from k-space data and compare the results with image domain estimates. * Kim Khalsa Resolution properties in regularized dynamic MRI reconstruction : In dynamic MRI, one is constantly addressing the tradeoff between spatial and temporal resolution. Regularized reconstruction methods may offer benefits in terms of this tradeoff. However, selection of the regularization parameters is challenging. In this work we examine the spatial and temporal resolution of penalized-likelihood image reconstruction for dynamic MRI, and present an accelerated method for computing the local impulse response. This method may prove advantageous for regularization parameter selection. ** MR excitation * Will Grissom Quadratic surrogates for optimization of echo-planar phase encoding locations in the joint design of RF and gradient waveforms for small-tip-angle parallel excitation. : Traditionally, in the design of multi-dimensional RF pulses for parallel excitation, one pre-selects a k-space trajectory according to sampling requirements and acceleration factor. However, it has recently been shown that jointly designing RF waveforms and the k-space trajectory can result in improved excitation accuracy and reduced RF power deposition. In the small-tip-angle regime, one can formulate a pulse design cost function that is quadratic in RF pulse samples, and can be solved using conjugate gradient. However, the same type of cost function is non-quadratic in the k-space trajectory, and one must therefore use other methods to minimize it with respect to the trajectory, such as gradient descent. While gradient descent is theoretically and computationally simple, and lends itself well to a joint design framework, it requires the user to pre-select a step size, the best choice of which may change as a function of the target excitation pattern or sensitivity patterns. In this work, we demonstrate that optimization transfer principles may be applied to this problem, for the purpose of automatically choosing a step size that is guaranteed to monotonically decrease the cost function. * Daehyun Yoon The in-plane phase encoding in the MRI excitation pattern. : The slice selection techniques in the MR excitation has focused on creating a coherent through-plane phase to prevent a signal loss. However, there was not much research done to find the optimal phase distribution of the spins on the selected slice. In this project, we would explore several methods to generate in-plane phases of the initial magnetizations to reduce the peak power of the RF pulse and to minimize the discrepancy between the desired excitation pattern and it realization. Particularly, an iterative approach and a random-phase generation approach will be investigated and compared. ** Restoration * Xing Zhou Benefits of rotationally invariant penalty functions : A roughness penalty function and its rotationally invariant form are examined. Performance differences between the two are examined subjectively with simple examples. * Candice Gliniecki Vollweiler Super Resolution Regularization : Super resolution is a method of image reconstruction that uses multiple low resolution images to reconstruct one higher resolution image. The multiple low resolution images, obtained via microscanning, may be from different shots or looks from the same imaging system, or the images may come from multiple sensors. The sharper super resolution output is useful in various fields, including medical, defense, and entertainment. This project explores the application of different reconstruction penalties to current super resolution methods and compares the results with standard interpolation techniques. * John Valenzuela Model-Based Statistical Image Reconstruction--Applications to Polarimetric Imaging : Polarimetry is the measurement of the state of polarization of light and offers unique advantages over other imaging modalities. During the past several years there has been steady progress in the development of polarimetric sensors. Specifically, wire grid polarizers have become efficient and reliable. These small wire grid devices are placed in front of CCD cameras and absorb light that is parallel to the wires thereby passing a particular component of the electric field. By orienting the polarizers at different angles different components of the light are passed to the CCD and measured. In practice two configurations are popular: (1) (0,90,45,135) degrees, and (2) (0,60,120) degrees. In order to elucidate the polarimetric content of the imagery the data is typically linearly transformed into the Stokes (G.G. Stokes 1852) vectors (images) {S0,S1,S2}. Polarimeters are plagued with the typical degradations of optical imaging systems: optical blur, detector blur, aliasing, and noise; consequently, image restoration techniques are often employed. An open question is whether to restore the intensity images themselves or the Stokes images directly. In the case where there are more than three measurement angles estimating the Stokes vectors results in a parameter reduction and so seems like the natural space to work in. In this work we investigate this conjecture through simulation experiments. Image restoration is done for both the polarimetric data and the Stokes vectors for measurement angles of (0,90,45,135) and (0,60,120).