Kenneth Kreutz-Delgado | PubMed Health

PubMed2003

Frequency characterization of blood glucose dynamics.

Examples of the frequency range of blood glucose dynamics of normal subjects and subjects with diabetes are reported here, based on data from the literature. The frequency band edge was determined from suitable, frequently sampled blood glucose recordings using two methods: frequency domain estimation and signal reconstruction. The respective maximum acceptable sampling intervals, or Nyquist sampling periods (NSP), required to accurately represent blood glucose dynamics were calculated. Preliminary results based on the limited data available in the literature indicate that although blood glucose NSP values are higher in most diabetic subjects, values in some diabetic subjects are indistinguishable from those of normal subjects. High fidelity monitoring sufficient to follow the intrinsic blood glucose dynamics of all diabetic subjects requires a NSP of approximately 10 min, corresponding to a continuous frequency band edge of approximately 1 x 10(-3) Hz. This analysis provides key information for the design of clinical studies that include blood glucose dynamics and for the design of new glucose monitoring systems.

Blood Glucose↗

PubMed2003

Dictionary learning algorithms for sparse representation.

Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave/Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial "25 words or less"), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations. Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an overcomplete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error).

Algorithms↗