Noise sensitivity of sparse signal representations: reconstruction error bounds for the inverse problem

Certain sparse signal reconstruction problems have been shown to have unique solutions when the signal is known to have an exact sparse representation. This result is extended to provide bounds on the reconstruction error when the signal has been corrupted by noise or is not exactly sparse for some other reason. Uniqueness is found to be extremely unstable for a number of common dictionaries.     

Outcome of severe brain injury: a multimodality neurophysiologic study

We screened all head-injured trauma patients admitted to Lehigh Valley Hospital during a 2-year period. From 725 screened patients, 69 patients in a coma on the second day after trauma were entered into this study. During the first week, these patients underwent electroencephalography (EEG), evoked potentials, ocular pneumoplethysmography, and transcranial Doppler (TCD) sonography. Clinical examinations were undertaken 2 and 7 days after trauma. Test results were correlated with functional clinical outcome at 6 months. In a multiple regression analysis, EEG was the major independent variable that significantly predicted 6-month outcome based on Glasgow Outcome Scale score. Transcranial Doppler sonography contributed a small additional component. Though EEG was the most significant predictive factor in this neurophysiological battery, it did not add significantly to the predictive power of Glasgow Coma Scale score determined at day 7. These findings suggest that in neurophysiologic testing in this type of patient is not useful in improving predictive outcome data.     

Subsurface characterization with support vector machines

A typical subsurface environment is heterogeneous, consists of multiple materials (geologic facies), and is often insufficiently characterized by data. The ability to delineate geologic facies and to estimate their properties from sparse data is essential for modeling physical and biochemical processes occurring in the subsurface. We demonstrate that the support vector machine is a viable and efficient tool for lithofacies delineation, and we compare it with a geostatistical approach. To illustrate our approach, and to demonstrate its advantages, we construct a synthetic porous medium consisting of two heterogeneous materials and then estimate boundaries between these materials from a few selected data points. Our analysis shows that the error in facies delineation by means of support vector machines decreases logarithmically with increasing sampling density. We also introduce and analyze the use of regression support vector machines to estimate the parameter values between points where the parameter is sampled.     

Efficient Minimization Method for a Generalized Total Variation Functional

Replacing the lscr² data fidelity term of the standard total variation (TV) functional with an lscr¹ data fidelity term has been found to offer a number of theoretical and practical benefits. Efficient algorithms for minimizing this lscr¹-TV functional have only recently begun to be developed, the fastest of which exploit graph representations, and are restricted to the denoising problem. We describe an alternative approach that minimizes a generalized TV functional, including both lscr²-TV and lscr¹-TV as special cases, and is capable of solving more general inverse problems than denoising (e.g., deconvolution). This algorithm is competitive with the graph-based methods in the denoising case, and is the fastest algorithm of which we are aware for general inverse problems involving a nontrivial forward linear operator.     

A review of the fractal image coding literature

Fractal image compression is a technique based on the representation of an image by a contractive transform, on the space of images, for which the fixed point is close to the original image. This broad principle encompasses a very wide variety of coding schemes, many of which have been explored in the rapidly growing body of published research. While certain theoretical aspects of this representation are well established, relatively little attention has been given to the construction of a coherent underlying image model that would justify its use. Most purely fractal-based schemes are not competitive with the current state of the art, but hybrid schemes incorporating fractal compression and alternative techniques have achieved considerably greater success. This review represents a survey of the most significant advances, both practical and theoretical, since the publication of Jacquin's (1990) original fractal coding scheme.     

Error Tolerant Adaptive Algorithms for Delta-Modulation Coding

This paper investigates the adaption of qnantizer step size in voice coding circuits. Techniques which maintain the decoder step size in the presence of channel errors have been evaluated. Graphs are presented for the comparison of error recovery performance. Practical considerations favor one algorithm, and its digital implementation has been described in the paper. Laboratory measurements of step-size error recovery and SNR performance have been included to verify the theory.