Extracting a shape function for a signal with intra-wave frequency modulation

In this paper, we consider signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu. A shape function could be any periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that s is a periodic function, we can identify certain low rank structure of the signal. This structure enables us to extract the shape function from the signal. To test the robustness of our method, we apply our method on several synthetic and real signals. The results are very encouraging

On the Uniqueness of Sparse Time-Frequency Representation of Multiscale Data

In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time frequency decomposition is unique up to an error that is determined by the scale separation property of the signal. We further show that the unique decomposition can be obtained approximately by the sparse time frequency decomposition using nonlinear matching pursuit

The angular spectrum of the scattering coefficient map reveals subsurface colorectal cancer

Abstract Colorectal cancer diagnosis currently relies on histological detection of endoluminal neoplasia in biopsy specimens. However, clinical visual endoscopy provides no quantitative subsurface cancer information. In this ex vivo study of nine fresh human colon specimens, we report the first use of quantified subsurface scattering coefficient maps acquired by swept-source optical coherence tomography to reveal subsurface abnormities. We generate subsurface scattering coefficient maps with a novel wavelet-based-curve-fitting method that provides significantly improved accuracy. The angular spectra of scattering coefficient maps of normal tissues exhibit a spatial feature distinct from those of abnormal tissues. An angular spectrum index to quantify the differences between the normal and abnormal tissues is derived, and its strength in revealing subsurface cancer in ex vivo samples is statistically analyzed. The study demonstrates that the angular spectrum of the scattering coefficient map can effectively reveal subsurface colorectal cancer and potentially provide a fast and more accurate diagnosis

Chip-scale WDM devices using photonic crystals

Issued as final reportAir Force Office of Scientific Researc