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Richardson–Lucy Deconvolution
The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function. It was named after William Richardson and Leon B. Lucy, who described it independently. Description When an image is produced using an optical system and detected using photographic film, a charge-coupled device or a CMOS sensor, for example, it is inevitably blurred, with an ideal point source not appearing as a point but being spread out into what is known as the point spread function. Extended sources can be decomposed into the sum of many individual point sources, thus the observed image can be represented in terms of a transition matrix p operating on an underlying image: : d_ = \sum_ p_ u_\, where u_ is the intensity of the underlying image at pixel j and d_ is the detected intensity at pixel i. In general, a matrix whose elements are p_ describes the portion of light from sour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shift-invariant System
In signal processing, a shift invariant system is the discrete equivalent of a time-invariant system, defined such that if y(n) is the response of the system to x(n), then y(n-k) is the response of the system to x(n-k).Oppenheim, Schafer, 12 That is, in a shift-invariant system, the contemporaneous response of the output variable to a given value of the input variable does not depend on when the input occurs; time shifts are irrelevant in this regard. Applications Because digital systems need not be causal, some operations can be implemented in the digital domain that cannot be implemented using discrete analog components. Digital filters that require finite numbers of future values can be implemented while the analog counterparts cannot. Notes References * Oppenheim, Schafer, ''Digital Signal Processing'', Prentice Hall, 1975, See also * LTI system theory In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener Filter
In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant ( LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and additive noise. The Wiener filter minimizes the mean square error between the estimated random process and the desired process. Description The goal of the wiener filter is to compute a statistical estimate of an unknown signal using a related signal as an input and filtering it to produce the estimate. For example, the known signal might consist of an unknown signal of interest that has been corrupted by additive noise. The Wiener filter can be used to filter out the noise from the corrupted signal to provide an estimate of the underlying signal of interest. The Wiener filter is based on a statistical approach, and a more statistical account of the theory is given in the minimum mean square error (MMSE) estimator article. Typical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deconvolution
In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the signal-to-noise ratio (SNR), the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem. The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'' (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RawTherapee
RawTherapee is a free and open source application for processing photographs in raw image formats such as those created by many digital cameras. It comprises a subset of image editing operations specifically aimed at non-destructive post-production of raw photos and is primarily focused on improving a photographer's workflow by facilitating the handling of large numbers of images. It is notable for the advanced control it gives the user over the demosaicing and developing process. It is cross-platform, with versions for Microsoft Windows, macOS and Linux. RawTherapee was originally written by Gábor Horváth of Budapest, Hungary, and was re-licensed as free and open-source software under the GNU General Public License Version 3 in January 2010. It is written in C++, using a GTK+ front-end and a patched version of dcraw for reading raw files. The name "Therapee" was originally an acronym derived from "The Experimental Raw Photo Editor". Features RawTherapee involves the con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The Optical Society Of America A
The ''Journal of the Optical Society of America'' is a peer-reviewed scientific journal of optics, published by Optica. It was established in 1917 and in 1984 was split into two parts, A and B. ''Journal of the Optical Society of America A'' Part A covers various topics in optics, vision, and image science. The editor-in-chief is Olga Korotkova (University of Miami, USA). ''Journal of the Optical Society of America B'' Part B covers various topics in the field of optical physics, such as guided waves, laser spectroscopy, nonlinear optics, quantum optics, laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radi ...s, organic and polymer materials for optics, and ultrafast phenomena. The editor-in-chief is Kurt Busch ( Humboldt University of Berlin, Germany). References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blind Deconvolution
In electrical engineering and applied mathematics, blind deconvolution is deconvolution without explicit knowledge of the impulse response function used in the convolution. This is usually achieved by making appropriate assumptions of the input to estimate the impulse response by analyzing the output. Blind deconvolution is not solvable without making assumptions on input and impulse response. Most of the algorithms to solve this problem are based on assumption that both input and impulse response live in respective known subspaces. However, blind deconvolution remains a very challenging non-convex optimization problem even with this assumption. In image processing In image processing, blind deconvolution is a deconvolution technique that permits recovery of the target scene from a single or set of "blurred" images in the presence of a poorly determined or unknown point spread function (PSF). Regular linear and non-linear deconvolution techniques utilize a known PSF. For blind de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Transfer Function
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or image projector, projector is a scale-dependent description of their imaging contrast. Its magnitude is the image contrast of the Sine and cosine, harmonic intensity pattern, 1 + \cos(2\pi \nu \cdot x), as a function of the spatial frequency, \nu, while its Argument (complex analysis), complex argument indicates a phase shift in the periodic pattern. The optical transfer function is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, Image sensor, detector array, retina, screen, or simply the next item in the optical transmission chain. Formally, the optical transfer function is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source). As a Fourier transform, the OTF is generally complex-valued; however, it is real-valued in the comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugate Transpose
In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an m \times n complex matrix \mathbf is an n \times m matrix obtained by transposing \mathbf and applying complex conjugation to each entry (the complex conjugate of a+ib being a-ib, for real numbers a and b). There are several notations, such as \mathbf^\mathrm or \mathbf^*, \mathbf', or (often in physics) \mathbf^. For real matrices, the conjugate transpose is just the transpose, \mathbf^\mathrm = \mathbf^\operatorname. Definition The conjugate transpose of an m \times n matrix \mathbf is formally defined by where the subscript ij denotes the (i,j)-th entry (matrix element), for 1 \le i \le n and 1 \le j \le m, and the overbar denotes a scalar complex conjugate. This definition can also be written as :\mathbf^\mathrm = \left(\overline\right)^\operatorname = \overline where \mathbf^\operatorname denotes the transpose and \overline denotes the matrix with complex conjugated entries. Other na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Source
A point source is a single identifiable ''localized'' source of something. A point source has a negligible extent, distinguishing it from other source geometries. Sources are called point sources because, in mathematical modeling, these sources can usually be approximated as a mathematical point to simplify analysis. The actual source need not be physically small if its size is negligible relative to other length scales in the problem. For example, in astronomy, stars are routinely treated as point sources, even though they are in actuality much larger than the Earth. In three dimensions, the density of something leaving a point source decreases in proportion to the inverse square of the distance from the source, if the distribution is isotropic, and there is no absorption or other loss. Mathematics In mathematics, a point source is a singularity from which flux or flow is emanating. Although singularities such as this do not exist in the observable universe, mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Procedure
In 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 ''i''-th approximation (called an "iterate") 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 an iterative method or a method of successive approximation. An iterative method is called '' convergent'' if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution (for example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Active-pixel Sensor
An active-pixel sensor (APS) is an image sensor, which was invented by Peter J.W. Noble in 1968, where each pixel sensor unit cell has a photodetector (typically a pinned photodiode) and one or more active transistors. In a metal–oxide–semiconductor (MOS) active-pixel sensor, MOS field-effect transistors (MOSFETs) are used as amplifiers. There are different types of APS, including the early NMOS APS and the now much more common complementary MOS (CMOS) APS, also known as the CMOS sensor. CMOS sensors are used in digital camera technologies such as cell phone cameras, web cameras, most modern digital pocket cameras, most digital single-lens reflex cameras (DSLRs), mirrorless interchangeable-lens cameras (MILCs), and lensless imaging for, e.g., blood cells. CMOS sensors emerged as an alternative to charge-coupled device (CCD) image sensors and eventually outsold them by the mid-2000s. The term ''active pixel sensor'' is also used to refer to the individual pixel sensor its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
