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Deconvolution is a mathematical operation used in signal processing to recover a signal (e.g. an image) that is degraded by a physical process than can be described with a convolution.
For example, in optical devices (microscopes or telescopes) deconvolution attempts to reconstruct an object from an image that is degraded by blurring and noise. In these cases the blurring is largely due to optical or atmospheric aberrations; the noise is usually photon noise or electronic noise manifesting in low intensity acquisitions. All images are subject to some sort of degrading process. Consider as a 2D example a moving camera that creates a vague picture (the measured image) of a scene (the object). Here the camera displacement is an a priori known degrading process. Restoration by deconvolution applies the inverse process on the degraded image in order to recover the true object. In microscopy the same technique is applied on 2D or even 3D images where the degrading process is the diffraction and aberration of the microscope lens.
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