Generalised Skilling–Bryan Minimisation for Micro-Rotation Imaging in Light Microscopy

The original Skilling–Bryan method, first introduced in the field of astronomy, minimises the statistical cost function assuming Gaussian noise and the entropy prior functional. In contrast to the conventional trust region methods, where the solution search in a high-dimensional space may be very expensive, the Skilling–Bryan scheme minimises the cost function in a subspace instead, yielding much more efficient computation. However, in low-photon-count processes, such as image formation in confocal microscopy, Poisson noise assumption is more suitable. In addition, it would be desirable to use the 2nd order, Skilling–Bryan optimisation framework in applications where general prior functionals with the positivity constraint is required. In this work, we hence generalise the Skilling–Bryan method to be used with the Poisson noise model as well as with various kinds of prior functions including the total variation prior. The proposed method is generic whereas here it is applied in the micro-rotation imaging, where we aim at 3D reconstruction of a rotating object from 2D projections taken by a light microscope. On the basis of our investigation, the extended Skilling– Bryan method is promising for computing estimates in high-dimensional problems efficiently.