| This thesis is divided into 2 parts. In the first part of the thesis, we describe a software based approach to speeding up the Magnetic Resonance Imaging modality. In the second part of the thesis, we describe Significance Tree Quantization, which is a new framework for coding images. We now describe each of these parts in detail.; Magnetic Resonance Imaging (MRI) has become an essential tool in clinical medicine, producing exquisite contrast in images of soft tissue structures without the introduction of artificial contrast agents. However, it can be limited in the speed of image acquisition; imaging time can range from a second to as long as thirty minutes depending on the desired contrast. People have used expensive hardware to alleviate this problem. We present a software based approach using prior knowledge of the class being imaged. Our approach uses wavelets during the imaging process and greatly reduces imaging time without compromising image quality. Our results indicate that this procedure yields substantial improvements over the conventional Fourier basis techniques. We have also developed clustering algorithms using wavelets for this purpose, and here the results are somewhat mixed. Also, our theory extends to compressing images, and we describe this extension.; In recent years the Embedded Zerotree Wavelet (EZW) coder and its successor the Set Partitioning in Hierarchical Trees (SPIHT) coder have had a profound impact on the field of image compression. While the results obtained by these coders are some of the best in literature, no optimality results exist. We introduce a framework that we call Significance Tree Quantization (STQ) to explain why these coders work so well. We will also describe a dynamic programming procedure that allows one to optimize the tree structure used by these coders for a given image or a given set of images. We will then describe a coder that employs our optimization procedure for 8 {dollar}times{dollar} 8 DCT blocks. The resulting coder is fully embedded, has low-complexity, and yields substantial improvements in PSNR over baseline JPEG. |
