LogLikelihood Hessian methods return data with incorrect sign

[robbietuk]

Current implementation of the log-likelihood Hessian in STIR is

H_{jk} = \sum_i P_{ij}(y_i / ((P \lambda)_i + a_i)^2) P_{ik}

This is incorrect and should be negative this equation as the log-likelihood is a concave function.

H_{jk} = (-) \sum_i P_{ij}(y_i / ((P \lambda)_i + a_i)^2) P_{ik}

Two loglikelihood methods that compute the Hessian (vector product) are accumulate_sub_Hessian_times_input and add_multiplication_with_approximate_sub_Hessian_without_penalty

Two classes utilise these Hessian methods in STIR:

• SqrtHessianRowSum -> compute_Hessian_row_sum and compute_approximate_Hessian_row_sum, and
• OSSPS -> precompute_denominator_of_conditioner_without_penalty

These implementations of the Hessian methods expect the voxel values to be non-negative for other implementations. The suggestion is to correct the computation of the Hessian to include the minus sign and then flip signs of the voxel values output of the Hessian method.

Changes will impact backwards compatability regarding the Hessian methods outside of STIR.

[robbietuk]

Resolved by #902