Convolution and deconvolution based estimates of galaxy scaling relations from photometric redshift surveys

In addition to the maximum likelihood approach, there are two other methods which are commonly used to reconstruct the true redshift distribution from photometric redshift datasets: one uses a deconvolution method, and the other a convolution. We show how these two techniques are related, and how this relationship can be extended to include the study of galaxy scaling relations in photometric datasets. We then show what additional information photometric redshift algorithms must output so that they too can be used to study galaxy scaling relations, rather than just redshift distributions. We also argue that the convolution based approach may permit a more efficient selection of the objects for which calibration spectra are required.