One fundamental branch in image processing concerns image reconstruction. A digital image or a sequence of digital images can be corrupted optically and electronically. These image data can be results of indirect observations (experiments) where linear or nonlinear transformations of an image of interest are possible. The problem is to reconstruct a clear and sharp high-resolution image of the original image-object relevant to the observed phenomenon and correctly understood by humans.
The reconstruction of quantities that we want is called an inverse problem. In an inverse problem we measure an effect and want to determine the cause.
Modeling is a key starting element of any reconstruction method because it allows one to present and formalize information about signals and systems defining a signal distortion. Linear models are the most popular, and they define a link between the input signal of interest y and the measurement z in integral form as an integral convolution.
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