Optimal discrimination and classification of THz spectra in the wavelet domain

Abstract

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems.

2-D Wavelet Segmentation in 3-D T-Ray Tomography

“…With the incremental wavelet scale, the noise is reduced and the target intensity (energy) is increased in an image. After computing undecimated 2-D DWTs [6], [7] of fused T-ray CT images, an increased energy with an increase in wavelet scale is used as a cue to extract the target regions. The wavelet scale correlation based segmentation algorithm is summarized as follows.…”

Distinguishing between materials in terahertz imaging using wide-band cross ambiguity functions

“…Rather than using an arbitrary mother function, it is proposed to use the reference pulse itself as a kind of mother function by using a cross ambiguity function [17]. It has been shown that classification is more robust to noise when the results of traditional analysis are transformed into a wavelet domain [16], and we demonstrate that transforming to the wavelet domain directly from the time domain preserves the differences in optical constants between nylon and resin.…”

“…Wavelets are a useful tool in terahertz pulsed imaging, in areas such as wavelet denoising [14,15], and terahertz waveform analysis [4,16]. Wavelet methods in data analysis involve transforming the reference and sample waveforms into the wavelet domain, through use of a mother function, and then correlating the results to obtain the translation and scale which give the best match.…”

Complex extreme learning machine applications in terahertz pulsed signals feature sets

“…We have further demonstrated that such analysis may be directly performed in the time, frequency or even the wavelet domains [10][11][12][13]. The current study is concerned with the classification of T-ray measurements on the basis of extracted features from their spectral signatures only.…”