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Image Deblurring
Deblurring is the process of removing blurring artifacts from images. Deblurring recovers a sharp image ''S'' from a blurred image ''B'', where ''S'' is convolved with ''K'' (the blur kernel) to generate ''B''. Mathematically, this can be represented as B=S*K (where * represents convolution). While this process is sometimes known as ''unblurring'', ''deblurring'' is the correct technical word. The blur K is typically modeled as point spread function and is convolved with a hypothetical sharp image ''S'' to get ''B'', where both the ''S'' (which is to be recovered) and the point spread function ''K'' are unknown. This is an example of an inverse problem. In almost all cases, there is insufficient information in the blurred image to uniquely determine a plausible original image, making it an ill-posed problem. In addition the blurred image contains additional noise which complicates the task of determining the original image. This is generally solved by the use of a regularizatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Restoration (motion Blur, Wiener Filtering)
Image restoration is the operation of taking a corrupt/noisy image and estimating the clean, original image. Corruption may come in many forms such as motion blur, noise and camera mis-focus. Image restoration is performed by reversing the process that blurred the image and such is performed by imaging a point source and use the point source image, which is called the Point Spread Function (PSF) to restore the image information lost to the blurring process. Image restoration is different from image enhancement in that the latter is designed to emphasize features of the image that make the image more pleasing to the observer, but not necessarily to produce realistic data from a scientific point of view. Image enhancement techniques (like contrast stretching or de-blurring by a nearest neighbor procedure) provided by imaging packages use no ''a priori'' model of the process that created the image. With image enhancement noise can effectively be removed by sacrificing some resolution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel (image Processing)
In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between the kernel and an image. Details The general expression of a convolution is g(x,y)= \omega *f(x,y)=\sum_^a, where g(x,y) is the filtered image, f(x,y) is the original image, \omega is the filter kernel. Every element of the filter kernel is considered by -a \leq dx \leq a and -b \leq dy \leq b. Depending on the element values, a kernel can cause a wide range of effects. . The above are just a few examples of effects achievable by convolving kernels and images. Origin The origin is the position of the kernel which is above (conceptually) the current output pixel. This could be outside of the actual kernel, though usually it corresponds to one of the kernel elements. For a symmetric kernel, the origin is usually the center element. Convolution Convolution is the pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-correlation of and , or and . For complex-valued fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolved
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-correlation of and , or and . For complex-valued functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects. Inverse problems are some of the most important mathematical problems in science and mathematics because they tell us about parameters that we cannot directly observe. They have wide application in system identification, optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, nondestructive testing, slope stability analysis and many other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ill-posed Problem
The mathematical term well-posed problem stems from a definition given by 20th-century French mathematician Jacques Hadamard. He believed that mathematical models of physical phenomena should have the properties that: # a solution exists, # the solution is unique, # the solution's behaviour changes continuously with the initial conditions. Examples of archetypal well-posed problems include the Dirichlet problem for Laplace's equation, and the heat equation with specified initial conditions. These might be regarded as 'natural' problems in that there are physical processes modelled by these problems. Problems that are not well-posed in the sense of Hadamard are termed ill-posed. Inverse problems are often ill-posed. For example, the inverse heat equation, deducing a previous distribution of temperature from final data, is not well-posed in that the solution is highly sensitive to changes in the final data. Continuum models must often be discretized in order to obtain a numerica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regularization (physics)
In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that "new physics" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use. It is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for self-interaction feedback. Regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations. However, it is now well understood ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Echo Removal
Echo removal is the process of removing echo and reverberation artifacts from audio signals. The reverberation is typically modeled as the convolution of a (sometimes time-varying) impulse response with a hypothetical clean input signal, where both the clean input signal (which is to be recovered) and the impulse response are unknown. This is an example of an inverse problem. In almost all cases, there is insufficient information in the input signal to uniquely determine a plausible original image, making it an ill-posed problem. This is generally solved by the use of a regularization term to attempt to eliminate implausible solutions. This problem is analogous to deblurring in the image processing domain. See also * Echo suppression and cancellation * Digital room correction * Noise reduction Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deconvolution
In mathematics, deconvolution is the operation inverse to 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 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 the fields of ... [...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 blin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulation Transfer Function
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are captured or transmitted. It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector array, retina, screen, or simply the next item in the optical transmission chain. A variant, the modulation transfer function (MTF), neglects phase effects, but is equivalent to the OTF in many situations. Either transfer function specifies the response to a periodic sine-wave pattern passing through the lens system, as a function of its spatial frequency or period, and its orientation. Formally, the OTF 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 complex-valued; but it will be real-valued in the common case of a PSF that is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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