Deblurring
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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 ...
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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 (physics), 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 * Linear prediction coder Signal processing {{signal-processing-stub ...
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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, ...
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Super-resolution
Super-resolution imaging (SR) is a class of techniques that enhance (increase) the resolution of an imaging system. In optical SR the diffraction limit of systems is transcended, while in geometrical SR the resolution of digital imaging sensors is enhanced. In some radar and sonar imaging applications (e.g. magnetic resonance imaging (MRI), high-resolution computed tomography), subspace decomposition-based methods (e.g. MUSIC) and compressed sensing-based algorithms (e.g., SAMV) are employed to achieve SR over standard periodogram algorithm. Super-resolution imaging techniques are used in general image processing and in super-resolution microscopy. Basic concepts Because some of the ideas surrounding super-resolution raise fundamental issues, there is need at the outset to examine the relevant physical and information-theoretical principles: * Diffraction limit: The detail of a physical object that an optical instrument can reproduce in an image has limits that are mandated b ...
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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 pr ...
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