Wavelet noise

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Wavelet noise is an alternative to Perlin noise which reduces the problems of aliasing and detail loss that are encountered when Perlin noise is summed into a fractal.

Perlin noise

Perlin noise is a type of gradient noise developed by Ken Perlin in 1983 as a result of his frustration with the "machine-like" look of computer graphics at the time. He formally described his findings in a SIGGRAPH paper in 1985 called An image Synthesizer. In 1997, Perlin was awarded an Academy Award for Technical Achievement for creating the algorithm:

To Ken Perlin for the development of Perlin Noise, a technique used to produce natural appearing textures on computer generated surfaces for motion picture visual effects.

The development of Perlin Noise has allowed computer graphics artists to better represent the complexity of natural phenomena in visual effects for the motion picture industry.

Aliasing Effect that causes signals to become indistinguishable when sampled; often producing detectable aberrations

In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable when sampled. It also refers to the distortion or artifact that results when the signal reconstructed from samples is different from the original continuous signal.

Fractal A self-similar pattern or set

In mathematics, a fractal is a subset of a Euclidean space for which the Hausdorff dimension strictly exceeds the topological dimension. Fractals tend to appear nearly the same at different levels, as is illustrated here in the successively small magnifications of the Mandelbrot set; Because of this, fractals are encountered ubiquitously in nature. Fractals exhibit similar patterns at increasingly small scales called self similarity, also known as expanding symmetry or unfolding symmetry; If this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self-similar.

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Wavelet function for integral Fourier-like transform

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one recorded by a seismograph or heart monitor. Generally, wavelets are intentionally crafted to have specific properties that make them useful for signal processing. Using a "reverse, shift, multiply and integrate" technique called convolution, wavelets can be combined with known portions of a damaged signal to extract information from the unknown portions.

Noise reduction is the process of removing noise from a signal.

Continuous wavelet transform

In mathematics, the continuous wavelet transform (CWT) is a formal tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously.

Discrete wavelet transform

In 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.

The Hermitian hat wavelet is a low-oscillation, complex-valued wavelet. The real and imaginary parts of this wavelet are defined to be the second and first derivatives of a Gaussian respectively:

Ken Perlin American computer scientist & university professor

Kenneth H. Perlin is a professor in the Department of Computer Science at New York University, founding director of the Media Research Lab at NYU, and the Director of the Games for Learning Institute. His research interests include graphics, animation, multimedia, and science education. He developed or was involved with the development of techniques such as Perlin noise, hypertexture, real-time interactive character animation, and computer-user interfaces such as zooming user interfaces, stylus-based input (Quikwriting), and most recently, cheap, accurate multi-touch input devices. He is also the Chief Technology Advisor of ActorMachine, LLC.

In computing, procedural generation is a method of creating data algorithmically as opposed to manually. In computer graphics, it is also called random generation and is commonly used to create textures and 3D models. In video games, it is used to automatically create large amounts of content in a game. Advantages of procedural generation include smaller file sizes, larger amounts of content, and randomness for less predictable gameplay.

The Stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT). Translation-invariance is achieved by removing the downsamplers and upsamplers in the DWT and upsampling the filter coefficients by a factor of in the th level of the algorithm. The SWT is an inherently redundant scheme as the output of each level of SWT contains the same number of samples as the input – so for a decomposition of N levels there is a redundancy of N in the wavelet coefficients. This algorithm is more famously known as "algorithme à trous" in French which refers to inserting zeros in the filters. It was introduced by Holschneider et al.

Wavelet modulation, also known as fractal modulation, is a modulation technique that makes use of wavelet transformations to represent the data being transmitted. One of the objectives of this type of modulation is to send data at multiple rates over a channel that is unknown. If the channel is not clear for one specific bit rate, meaning that the signal will not be received, the signal can be sent at a different bit rate where the signal to noise ratio is higher.

Simplex noise is a method for constructing an n-dimensional noise function comparable to Perlin noise but with fewer directional artifacts and, in higher dimensions, a lower computational overhead. Ken Perlin designed the algorithm in 2001 to address the limitations of his classic noise function, especially in higher dimensions.

Simulation noise is a function that creates a divergence-free field. This signal can be used in artistic simulations for the purposes of increasing the perception of extra detail.

Value noise

Value noise is a type of noise commonly used as a procedural texture primitive in computer graphics. It is conceptually different from, and often confused with gradient noise, examples of which are Perlin noise and Simplex noise. This method consists of the creation of a lattice of points which are assigned random values. The noise function then returns the interpolated number based on the values of the surrounding lattice points.

Gradient noise is a type of noise commonly used as a procedural texture primitive in computer graphics. It is conceptually different, and often confused with value noise. This method consists of a creation of a lattice of random gradients, dot products of which are then interpolated to obtain values in between the lattices. An artifact of some implementations of this noise is that the returned value at the lattice points is 0. Unlike the value noise, gradient noise has more energy in the high frequencies.

Speckle is a granular 'noise' that inherently exists in and degrades the quality of the active radar, synthetic aperture radar (SAR), medical ultrasound and optical coherence tomography images.

Worley noise

Worley noise is a noise function introduced by Steven Worley in 1996. In computer graphics it is used to create procedural textures, that is textures that are created automatically in arbitrary precision and don't have to be drawn by hand. Worley noise comes close to simulating textures of stone, water, or cell noise.

OpenSimplex noise is an n-dimensional gradient noise function that was developed in order to overcome the patent-related issues surrounding Simplex noise, while continuing to also avoid the visually-significant directional artifacts characteristic of Perlin noise.

Noise refers to many types of random or unwanted signals, most commonly acoustic noise, but also including the following: