A new class of pair-wise regularizers is proposed for vector-valued signals, including several new regularizers that penalize the angular difference between neighboring vectors. The pair-wise model is a generalization of the conventional difference model that includes discretized Tikhonov, Li, and Total Variation (TV) as special cases. Whereas Tikhonov and TV regularization have become popular for encouraging signal values to be smooth or piecewise smooth, respectively, angular regularizers are pro posed to encourage vector directions to be smooth or piecewise smooth. The regularizers are simple, effective, and general, making them easily applicable to a wide array of problems. Experimental results demonstrate the method's effectiveness in denoising vector fields and color images.

Typical vector quantizer (VQ) design algorithms, such as generalized Lloyd methods, are susceptible to local minima. In addition, for entropy-constrained VQ, it is not obvious what the "right" number of codevectors is for any given source and target rate. One method that has shown promising results for solving both problems is deterministic annealing, where randomness is added to the encoding process, the uncertainty of which is gradually reduced until a deterministic coder is found. This method has been used for fixed-rate and entropy-constrained unstructured VQ, as well as for a variety of structurally constrained VQs. For the unstructured entropy-constrained case, we generalize the existing methods to include new cost functions, and we argue that, depending on the chosen cost function, some splitting criteria are more suitable than others. We give analytical advantages and disadvantages to several cost functions and several splitting criteria, then give performance evaluations by testing on synthetic and natural sources.

To achieve good image quality for computed tomography scans, it is important to accurately know the geometrical relationship between the x-ray source, detector, and axis of rotation. Conventional geometric calibration algorithms generally require particular calibration phantoms, such as a small pin or wire, which may not be practical for all scanner types, particularly for large industrial scanners. This paper presents an alternative framework to calibrate system geometry from scans of arbitrary objects, without prior knowledge of the object's form. This lessens physical construction requirements, and permits post-scan geometric calibration from any arbitrary scan data. Experimental results show that central ray calibration using this approach can give results accurate to 0.01 channels for low-noise conditions, or 0.1-0.45 channels under higher noise levels.

A new image coder is presented in which an image is divided into blocks, each block is quadtree segmented, and each segment is coded using a form of predictive coding. We provide nearly-optimal segmentation and quantization rules for this framework, as well as an iterative codebook design algorithm. In simulations, our new system comes within 1 dB of JPEG 2000 and outperforms JPEG by about 1.5 dB at moderate rates and up to 4.5 dB at low rates. Additionally, our method captures edges better and has potentially lower complexity than transform-based methods.

Typically, predictive vector quantization is performed by making a prediction of upcoming data based on previously coded samples, then, using a residual quantizer to code the prediction errors. We take in alternative approach, and introduce coding by selective prediction (CSP). In CSP, there is no residual quantizer - the codebook consists only of a collection of predictors. The encoder selects the predictor that best describes a source block, then transmits the index of that predictor. We give a framework for CSP, then propose a training method for codebook design, similar to the generalized Lloyd algorithm. Using fixed-rate coding, performance results for CSP as an image coder indicate a 0.5 dB improvement over conventional predictive vector quantization at equal rates.