Reconstruction

The reconstruction algorithm uses simulated annealing to drive a system to minimise a cost function. This cost function is the mismatch in the two-point correlation function between an ideal state and a present one. After initialising the system with a trial (random) binary image, we move towards an image with similar $C_{2}$ and $S_{2}$. This is done via a series of discrete pixel substitutions. After each substitution, we calculate how $C_{2}$ and $S_{2}$ have changed by subtracting those pixel's original contributions. We then add the new contribution to $C_{2}$ and $S_{2}$ from the substitution. By this we reduce the needed number of computations.

This is simple for $S_{2}$ as we simply compute all contributions from the pixels involved in the swap and find the difference. For $C_{2}$ we must first determine which collections of pixels are involved in the interaction, then compute their contributions to $C_{2}$ and $S_{2}$.

Adjusting the reconstruction algorithm

The temperature is currently set automatically, but this could instead be driven by a schedule more complex than geometric decay.

Surface optimisation is key to the success of the algorithm as it reduces the set of pixels permitted to mutate. Despite this, it biases the resultant reconstruction towards larger particles, and hinders the closing of bridges. Several convolutional stages could help to reduce this tendency and better settle the system.

It may be worth using more aggressive shuffles to begin with and fully recompute $C_{2}$ and $S_{2}$.

histrecon_u(dims, C2, S2, philen)

dims, C2, S2, philen = get_C2_S2(fname)
guess, S2n, C2n, S2_BN1, C2_BN1, SN1 = histrecon((200, 200)), C2, S2, 12000)

get_C2_S2(fname)