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.
Cryptogenic organizing pneumoniaCryptogenic organizing pneumonia (COP), formerly known as bronchiolitis obliterans organizing pneumonia (BOOP), is an inflammation of the bronchioles (bronchiolitis) and surrounding tissue in the lungs. It is a form of idiopathic interstitial pneumonia. It is often a complication of an existing chronic inflammatory disease such as rheumatoid arthritis, dermatomyositis, or it can be a side effect of certain medications such as amiodarone. COP was first described by Gary Epler in 1985.
Idiopathic pulmonary fibrosisIdiopathic pulmonary fibrosis (IPF), or (formerly) fibrosing alveolitis, is a rare, progressive illness of the respiratory system, characterized by the thickening and stiffening of lung tissue, associated with the formation of scar tissue. It is a type of chronic scarring lung disease characterized by a progressive and irreversible decline in lung function. The tissue in the lungs becomes thick and stiff, which affects the tissue that surrounds the air sacs in the lungs.
Pulmonary fibrosisPulmonary fibrosis is a condition in which the lungs become scarred over time. Symptoms include shortness of breath, a dry cough, feeling tired, weight loss, and nail clubbing. Complications may include pulmonary hypertension, respiratory failure, pneumothorax, and lung cancer. Causes include environmental pollution, certain medications, connective tissue diseases, infections, and interstitial lung diseases. However, in most cases the cause is unknown, and termed idiopathic pulmonary fibrosis.
Yves MeyerYves F. Meyer (mɛjɛʁ; born 19 July 1939) is a French mathematician. He is among the progenitors of wavelet theory, having proposed the Meyer wavelet. Meyer was awarded the Abel Prize in 2017. Born in Paris in a Jewish family, Yves Meyer studied at the Lycée Carnot in Tunis; he won the French General Student Competition (Concours Général) in Mathematics, and was placed first in the entrance examination for the École Normale Supérieure in 1957. He obtained his Ph.D. in 1966, under the supervision of Jean-Pierre Kahane.
Riesz transformIn the mathematical theory of harmonic analysis, the Riesz transforms are a family of generalizations of the Hilbert transform to Euclidean spaces of dimension d > 1. They are a type of singular integral operator, meaning that they are given by a convolution of one function with another function having a singularity at the origin. Specifically, the Riesz transforms of a complex-valued function ƒ on Rd are defined by for j = 1,2,...,d. The constant cd is a dimensional normalization given by where ωd−1 is the volume of the unit (d − 1)-ball.
Lung cancerLung cancer, also known as lung carcinoma, is a malignant tumor that begins in the lung. Lung cancer is caused by genetic damage to the DNA of cells in the airways, often caused by cigarette smoking or inhaling damaging chemicals. Damaged airway cells gain the ability to multiply unchecked, causing the growth of a tumor. Without treatment, tumors spread throughout the lung, damaging lung function. Eventually lung tumors metastasize, spreading to other parts of the body.
PneumoniaPneumonia is an inflammatory condition of the lung primarily affecting the small air sacs known as alveoli. Symptoms typically include some combination of productive or dry cough, chest pain, fever, and difficulty breathing. The severity of the condition is variable. Pneumonia is usually caused by infection with viruses or bacteria, and less commonly by other microorganisms. Identifying the responsible pathogen can be difficult. Diagnosis is often based on symptoms and physical examination.
Corner detectionCorner detection is an approach used within computer vision systems to extract certain kinds of features and infer the contents of an image. Corner detection is frequently used in motion detection, , video tracking, image mosaicing, panorama stitching, 3D reconstruction and object recognition. Corner detection overlaps with the topic of interest point detection. A corner can be defined as the intersection of two edges. A corner can also be defined as a point for which there are two dominant and different edge directions in a local neighbourhood of the point.
Digital signal processingDigital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.
LungThe lungs are the primary organs of the respiratory system in humans and most other animals, including some snails and a small number of fish. In mammals and most other vertebrates, two lungs are located near the backbone on either side of the heart. Their function in the respiratory system is to extract oxygen from the air and transfer it into the bloodstream, and to release carbon dioxide from the bloodstream into the atmosphere, in a process of gas exchange.
