Schwab, Harald

Fast density estimation from histograms in shift invariant spaces

Sampl. Theory Signal Image Process Vol.3 No.2 (2004) p.157--173, MR2065187


Histograms are mostly used as data presentation. In many applications we are interested in a good approximation of the density function, which creates the histograms.
Standard techniques like the kernel density estimation are applied for approximating the density function. The problem of these techniques is that the data which define the histogram need to be known apriori.
To avoid this problem we present an algorithm, which reconstructs the density function only from the given histogram (i.e., the width and the height of the bins are used as input) and without knowledge about the specific measurements. This becomes possible because we use techniques for reconstruction from averages. Using the fast efficient algorithm presented by Grochenig and Schwab [7] it is shown in this paper, that this reconstruction scheme can be used for the case of averaging and provides go od results for the approximation of the density function from a given histogram.
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