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.
LiverThe liver is a major metabolic organ only found in vertebrate animals, which performs many essential biological functions such as detoxification of the organism, and the synthesis of proteins and biochemicals necessary for digestion and growth. In humans, it is located in the right upper quadrant of the abdomen, below the diaphragm and mostly shielded by the lower right rib cage. Its other metabolic roles include carbohydrate metabolism, the production of hormones, conversion and storage of nutrients such as glucose and glycogen, and the decomposition of red blood cells.
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.
Medical ultrasoundMedical ultrasound includes diagnostic techniques (mainly imaging techniques) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, muscles, joints, blood vessels, and internal organs, to measure some characteristics (e.g. distances and velocities) or to generate an informative audible sound. The usage of ultrasound to produce visual images for medicine is called medical ultrasonography or simply sonography, or echography.
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.
Liver cancerLiver cancer (also known as hepatic cancer, primary hepatic cancer, or primary hepatic malignancy) is cancer that starts in the liver. Liver cancer can be primary (starts in liver) or secondary (meaning cancer which has spread from elsewhere to the liver, known as liver metastasis). Liver metastasis is more common than that which starts in the liver. Liver cancer is increasing globally. Primary liver cancer is globally the sixth-most frequent cancer and the fourth-leading cause of death from cancer.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
UltrasoundUltrasound is sound with frequencies greater than 20 kilohertz. This frequency is the approximate upper audible limit of human hearing in healthy young adults. The physical principles of acoustic waves apply to any frequency range, including ultrasound. Ultrasonic devices operate with frequencies from 20 kHz up to several gigahertz. Ultrasound is used in many different fields. Ultrasonic devices are used to detect objects and measure distances. Ultrasound imaging or sonography is often used in medicine.
Blood vesselBlood vessels are the components of the circulatory system that transport blood throughout the human body. These vessels transport blood cells, nutrients, and oxygen to the tissues of the body. They also take waste and carbon dioxide away from the tissues. Blood vessels are needed to sustain life, because all of the body's tissues rely on their functionality.
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.
Liver transplantationLiver transplantation or hepatic transplantation is the replacement of a diseased liver with the healthy liver from another person (allograft). Liver transplantation is a treatment option for end-stage liver disease and acute liver failure, although availability of donor organs is a major limitation. The most common technique is orthotopic transplantation, in which the native liver is removed and replaced by the donor organ in the same anatomic position as the original liver.
Lobules of liverIn histology (microscopic anatomy), the lobules of liver, or hepatic lobules, are small divisions of the liver defined at the microscopic scale. The hepatic lobule is a building block of the liver tissue, consisting of a portal triad, hepatocytes arranged in linear cords between a capillary network, and a central vein. Lobules are different from the lobes of liver: they are the smaller divisions of the lobes. The two-dimensional microarchitecture of the liver can be viewed from different perspectives: The term "hepatic lobule", without qualification, typically refers to the classical lobule.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Focused ultrasoundHigh-intensity focused ultrasound (HIFU) is a non-invasive therapeutic technique that uses non-ionizing ultrasonic waves to heat or ablate tissue. HIFU can be used to increase the flow of blood or lymph or to destroy tissue, such as tumors, via thermal and mechanical mechanisms. Given the prevalence and relatively low cost of ultrasound generation mechanisms, The premise of HIFU is that it is expect a non-invasive and low-cost therapy that can at minimum outperform of care.
Medical imagingMedical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to reveal internal structures hidden by the skin and bones, as well as to diagnose and treat disease. Medical imaging also establishes a database of normal anatomy and physiology to make it possible to identify abnormalities.
Gabor waveletGabor wavelets are wavelets invented by Dennis Gabor using complex functions constructed to serve as a basis for Fourier transforms in information theory applications. They are very similar to Morlet wavelets. They are also closely related to Gabor filters. The important property of the wavelet is that it minimizes the product of its standard deviations in the time and frequency domain. Put another way, the uncertainty in information carried by this wavelet is minimized.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
CirrhosisCirrhosis, also known as liver cirrhosis or hepatic cirrhosis, and end-stage liver disease, is the impaired liver function caused by the formation of scar tissue known as fibrosis due to damage caused by liver disease. Damage to the liver leads to repair of liver tissue and subsequent formation of scar tissue. Over time, scar tissue can replace normal functioning tissue, leading to the impaired liver function of cirrhosis. The disease typically develops slowly over months or years.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Obstetric ultrasonographyObstetric ultrasonography, or prenatal ultrasound, is the use of medical ultrasonography in pregnancy, in which sound waves are used to create real-time visual images of the developing embryo or fetus in the uterus (womb). The procedure is a standard part of prenatal care in many countries, as it can provide a variety of information about the health of the mother, the timing and progress of the pregnancy, and the health and development of the embryo or fetus.
