The process of deconvolving wide-field or confocal microscopical image stacks comprises the convolution of the dataset with the inverse point-spread function (PSF) subject to a set of constraints or cost-functions to prevent the amplification of noise. For the implementation as a filter, it generally is difficult to predict and limit the filter size (support) of discrete inverse PSF, and the computational overhead of straightforward filtering is directly proportional to the size of the filter

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... .e. the number of elements within the filter). The discrete convolution process itself can be expressed as a simple element-wise scalar multiplication if the image has been transformed into frequency space by a FFT, this advantage justifies its popularity in the deconvolution operation. The "cost" of transformation to and from frequency space is lower than straight convolution if the filter of the inverse PSF requires more than some 10 to 50 elements. To be able to exploit this benefit, the convolution and the application of the constraints are implemented as two separate and consecutive steps despite being tightly linked. Due to this implementation, the choice of the constraints and cost functions becomes somewhat arbitrary set from the perspective of the involved physics and is mostly driven by the achievable computational efficiency. As a consequence, the steps of convolution and re-establishing constraints are iterated; if the series of produced images converges, the outcome will depend only on the PSF and the set of constraints, not on the implementation of the algorithm itself.