WaveletA wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.
Wavelet transformIn mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.
Haar waveletIn mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis. The Haar sequence is now recognised as the first known wavelet basis and is extensively used as a teaching example. The Haar sequence was proposed in 1909 by Alfréd Haar.
Discrete wavelet transformIn numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.
Interstitial lung diseaseInterstitial lung disease (ILD), or diffuse parenchymal lung disease (DPLD), is a group of respiratory diseases affecting the interstitium (the tissue and space around the alveoli (air sacs) of the lungs. It concerns alveolar epithelium, pulmonary capillary endothelium, basement membrane, and perivascular and perilymphatic tissues. It may occur when an injury to the lungs triggers an abnormal healing response.
Usual interstitial pneumoniaUsual interstitial pneumonia (UIP) is a form of lung disease characterized by progressive scarring of both lungs. The scarring (fibrosis) involves the pulmonary interstitium (the supporting framework of the lung). UIP is thus classified as a form of interstitial lung disease. The term "usual" refers to the fact that UIP is the most common form of interstitial fibrosis. "Pneumonia" indicates "lung abnormality", which includes fibrosis and inflammation.
Idiopathic interstitial pneumoniaIdiopathic interstitial pneumonia (IIP), or noninfectious pneumonia are a class of diffuse lung diseases. These diseases typically affect the pulmonary interstitium, although some also have a component affecting the airways (for instance, cryptogenic organizing pneumonitis). There are seven recognized distinct subtypes of IIP. Classification can be complex, and the combined efforts of clinicians, radiologists, and pathologists can help in the generation of a more specific diagnosis.
Morlet waveletIn mathematics, the Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely related to human perception, both hearing and vision. Wavelet#History In 1946, physicist Dennis Gabor, applying ideas from quantum physics, introduced the use of Gaussian-windowed sinusoids for time-frequency decomposition, which he referred to as atoms, and which provide the best trade-off between spatial and frequency resolution.
Continuous wavelet transformIn mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously. The continuous wavelet transform of a function at a scale (a>0) and translational value is expressed by the following integral where is a continuous function in both the time domain and the frequency domain called the mother wavelet and the overline represents operation of complex conjugate.
Hypersensitivity pneumonitisHypersensitivity pneumonitis (HP) or extrinsic allergic alveolitis (EAA) is a syndrome caused by the repetitive inhalation of antigens from the environment in susceptible or sensitized people. Common antigens include molds, bacteria, bird droppings, bird feathers, agricultural dusts, bioaerosols and chemicals from paints or plastics. People affected by this type of lung inflammation (pneumonitis) are commonly exposed to the antigens by their occupations, hobbies, the environment and animals.
