One of fundamental problems in sampling theory is to reconstruct (non-)periodic signals from their filtered signals in a stable way. In this paper, we obtain a universal upper bound to the rate of innovation for signals in a closed linear space, which can be stably reconstructed, via the optimal lower stability bound for filtering on that linear space.
BACKGROUND Periodogram analysis of time-series is widespread in biology. A new challenge for analyzing the microarray time series data is to identify genes that are periodically expressed. Such challenge occurs due to the fact that the observed time series usually exhibit non-idealities, such as noise, short length, and unevenly sampled time points. Most… (More)
There is considerable interest in using traditional Chinese medicine formulas (TCMF) to delay aging or treat age-related diseases. Due to cost and duration, the beneficial effects of TCMF on prolongation are mainly extrapolated from vitro studies or physiological indexes. Little is known about whether TCMF are beneficial in whole level, particularly with… (More)
Excitotoxicity has been implicated as the mechanism of neuronal damage resulting from acute insults such as stroke, epilepsy, and trauma, as well as during the progression of adult-onset neurodegenerative disorders such as Alzheimer's disease and amyotrophic lateral sclerosis (ALS). Excitotoxicity is defined as excessive exposure to the neurotransmitter… (More)
In this paper, we construct reproducing kernel in spline subspaces and use the reproducing kernel to obtain reconstructions formula from the weighted samples and incremental integral samples. We also improve A-P iterative algorithm, and use the algorithm to implement the reconstruction from weighted samples, and obtain explicit convergence rate of the… (More)
We consider convolution sampling and reconstruction of signals in certain reproducing kernel subspaces of L p , 1 ≤ p ≤ ∞. We show that signals in those subspaces could be stably reconstructed from their convolution samples taken on a relatively-separated set with small gap. Exponential convergence and error estimates are established for the iterative… (More)
The local reconstruction from samples is one of most desirable properties for many applications in signal processing. Local sampling is practically useful since we need only to consider a signal on a bounded interval and computer can only process only finite samples. However, the local sampling and reconstruction problem has not been given as much… (More)
We discuss the reproducing kernel structure in shift-invariant spaces and the weighted shift-invariant spaces, and obtain the reconstruction formula in time-warped weighted shift-invariant spaces, then apply them to a spline subspace. In the spline subspace, we give a reconstruction formula in a time-warped spline subspace. 1. Introduction. The problem of… (More)