Despite the inability of these grids to describe the data, Demeler and colleagues suggest that the combination of results from the application of a large number of different, but similarly coarse, grids (all with 10 9 10 or lower resolution; Demeler et al. 2009 ) can be used in some way to achieve an analysis equivalent to that of a high-resolution grid. In the simplest form, this argument would be incompatible with basic matrix algebra, because it neglects cross-correlation between points from different grids. Discarding the magnitude of species' populations in this concatenated distribution, and using only the pattern of b Fig. 6 Comparison of strategies to compute parsimonious distributions that display the information content of the IgG data shown in Fig. 1 . a Contour plot of the size-and-shape distribution obtained with the high-resolution grid of 10 9 100 (f r , s)-values, after application of Tikhonov regularization, as shown in Fig. 1d . b The sum of 50 sizeand-shape distributions calculated with the exact standard method using the same high-resolution grid, but each based on synthetic data sets generated from the best-fit distribution of Fig. 1 with added normally distributed noise at the same magnitude as exhibited by the experimental data. c Integration of the main 6 S peak of the size-andshape distribution as calculated in Fig. 1 allows to determine the weighted-average s-value and f r -value, which can be used in the Bayesian framework to calculate the size-and-shape distribution c d (s, f r ) (Brown et al. 2007 ) that is closest to that of a single species, within the limits imposed by the requirement to produce a fit of statistically indistinguishable quality to that shown in a. As can be discerned from the secondary peak at *6 S with low frictional ratio, a strictly monodisperse interpretation of the main peak is contradicted by the experimental data. (Note the different scales on the color bar) nonnegativity constraints from such an analysis, is in conflict with the established Lawson and Hanson algorithm NNLS. The effect of the empirical extension to multiple stages is uncertain, and may not converge. Although one could construe cases where it will certainly work (such as distributions consisting of a single species), the Demeler scheme for generating nonequidistant small grids in multiple stages appears fundamentally flawed for the general case. The strategy of sequentially applying different, equally coarse, grids is in contrast to established multigrid methods for integral equations, which provide successfully finer parameter discretization (Kress 1999) . The division of the full problem into separate subproblems to be solved in parallel, followed by merging their partial solutions, has been used successfully in some image restoration problems (Bevilacqua and Piccolomini 2000) where the image regions are known to be uncorrelated with each other due to a localized point-spread function. However, this condition is not fulfilled in the present case. In SV analysis, the cross-correlation of signals from different species can be very large. This is reflected by the fact that (1) is ill posed, and illustrated by the fact that the matrices in Fig. 4b and c are different. For a correct solution of the SV problem, the regular high-resolution grid should be considered fully and unbiased by any scheme of preselection of excluded parameter regions. The latter is quite feasible with standard algorithms and commonly available computational resources, and we note that the problem is fairly small compared with many image analysis problems of similar structure.