Here are some snaps of Tribhuvan International Airport weather analysis using wavelet. Multi Resolutional analysis is used. The snaps are respectively Air temperature, Rain fall, Relative humidity and Wind speed.
Principal Component Analysis (PCA)
Simply, PCA is the statistical procedures where new basis of vector space will be found to treat variation of data better. Each point (x,y) in the vector space (let say X-Y) which correspond to each observation will be transformed into another vector space (let say U-V) where point (u,v) are handled easily than in [X-Y] vector space.
In image processing, the principal direction will be identified in such a way that data variation is minimum. Statistically, mean of the given data set will be origin for the new vector space and straight line for which difference of sample data will be minimum is principal direction. Transformed data to new vector space is said to be de-correlated and the new data set is compact representation of the original sampled data.
In hyperspectral imaging, PCA is used for data dimension reduction resulting low bandwidth for data transfer and low memory space for storage. If the data variation is other than some natural process or caused by random experiment error, PCA is better way for data reduction. Thus PCA is another statistical procedures which can be used in image compression.
Hyperspectral Imaging Basics
Recent
integration of imaging and spectroscopy with contiguous spectral analysis,
hyperspectral imaging is introduced. This is the technology as analytical tool
for non-destructive analysis. With the
hyperspectral imaging, even the composite distribution could be analysed.
The spectral range is 400 to 2500 nm within which images are captured with contiguous and narrow spectral band. It includes more than 200 spectral bands including some bands in infrared and ultraviolet with visible spectrum. This extra contiguous spectral information is used to classify object with higher accuracy.
The basic idea behind the spectral imaging is variation of amount of radiation reflected, absorbed and emitted is function of wavelength that is frequency for a given material.
This imaging has huge applications in food quality and safety measure. This spectral imaging could be used for the detection of bruise on citrus like fruits and on apple. This technology has usage on meat quality maintenance.
Hyperspectral Imaging
Newly emerging alternative to multi spectral imaging is hyperspectral imaging. In this technique, physical and biophysical characteristics are identified with the contiguous narrow spectral band where as in conventional multi spectral imaging likelihood is the features to discriminate the object not to identified the object.
Wavelet transformation and analysis can be used for the spectral analysis as the wavelet has the tools to decompose the signal into average and details with multiresolutional analysis.
Wavelet transformation and analysis can be used for the spectral analysis as the wavelet has the tools to decompose the signal into average and details with multiresolutional analysis.
Wavelet for Climate Data Analysis
Though there are a lots of factors affecting climate time series, non-linear interaction between different scales or interference of frequency component from its sidebands is associated with amplitude modulation which can be seen with frequency components in Fourier Spectrum without time information.
If some fundamental physical properties of the climate system undergoes secular changes which is followed by frequency modulation. Some of physical properties are increase in moisture content due to global warming. If the there is not finite time of occurrence then Fourier Spectrum is not sufficient to get dominant frequencies.
Another properties associated, abrupt change in frequency of climate time series is due to occurrence of catastrophic event with long term impact, which can be analysed with spikes or peaks with corresponding frequencies in Fourier Spectrum but contains no time information at which such abrupt changes occurred.
Similarly, another short term effect associated with sudden finite amplitude perturbation. This is specially due to volcanic eruption which causes global temperature variations, which can be detected in Fourier Spectrum with large number of component without time information.
For this all Wavelet Transform could be better solution which can give time information as well as frequency information though both time and frequency information could not be determined at the same time according to Heigenburg Principal, small frequency band can be localized at the small time interval.
If some fundamental physical properties of the climate system undergoes secular changes which is followed by frequency modulation. Some of physical properties are increase in moisture content due to global warming. If the there is not finite time of occurrence then Fourier Spectrum is not sufficient to get dominant frequencies.
Another properties associated, abrupt change in frequency of climate time series is due to occurrence of catastrophic event with long term impact, which can be analysed with spikes or peaks with corresponding frequencies in Fourier Spectrum but contains no time information at which such abrupt changes occurred.
Similarly, another short term effect associated with sudden finite amplitude perturbation. This is specially due to volcanic eruption which causes global temperature variations, which can be detected in Fourier Spectrum with large number of component without time information.
For this all Wavelet Transform could be better solution which can give time information as well as frequency information though both time and frequency information could not be determined at the same time according to Heigenburg Principal, small frequency band can be localized at the small time interval.
Multi Resolutional Analysis
When a signal is analysed using Wavelet Transform as analytical tool, wavelet function and scaling functions are used as high pass filter and complementary low pass filter respectively. If we go through multi resolutional analysis in depth, we can note that at first decomposition, original signal is decomposed into low band signal and high band signal. As the high band signal is not further decomposed rather low band signal is further decomposed, we will have high scale value at high frequency band resulting poor frequency resolution.
As the low band signal is further decomposed, with smaller scaling value resulting better frequency resolution. Smaller the scaling value better the frequency resolution is. As further decomposition is done at higher level, the signal will be down sampled resulting poorer time resolution at lower frequency band.
Thus it can be stated; wavelet transform has poor frequency resolution at higher frequency and better time resolution where as it has better frequency resolution at low frequency band and poorer time resolution.
As the low band signal is further decomposed, with smaller scaling value resulting better frequency resolution. Smaller the scaling value better the frequency resolution is. As further decomposition is done at higher level, the signal will be down sampled resulting poorer time resolution at lower frequency band.
Thus it can be stated; wavelet transform has poor frequency resolution at higher frequency and better time resolution where as it has better frequency resolution at low frequency band and poorer time resolution.
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