Handbook of Convex Optimization Methods in Imaging Science by Vishal Monga

Author:Vishal Monga
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.14)

where t k [m, n], s p [m, n], and g λ p , d k [m, n] are uniformly sampled versions of their continuous forms, e.g. t k [m, n] = t k (mΔ, nΔ) for some Δ smaller than the Nyquist sampling interval. We assume that t k [m, n], i.e. uniformly sampled version of the kth observation, is approximately the same as the detector measurements with a pixel size of Δ (i.e., the averaged intensity over a pixel). We also assume that the size of the input objects are limited to the detector range as determined by N × N pixels, i.e., .

As expected, each measurement consists of superimposed images of different wavelengths, with each individual image being either in focus or out of focus. The goal in the inverse problem is to recover the unknown intensities of different spectral components from these superimposed measurements. In the inverse problem framework, the following matrix-vector form obtained from the above image-formation model will be used [34]:

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