  Many numerical algorithms have been established to reconstruct pressure
fields from measured kinematic data with noise by Particle Image Velocimetry
(PIV), such as the Pressure Poisson solver and the Omni-Directional Integration
(ODI) method. This study adopts Gaussian Process Regression (GPR), a
probabilistic framework with an intrinsic de-noising mechanism to tackle
drawbacks of traditional Pressure Poisson solver and compares the performance
with ODI. To evaluate the accuracy of the algorithm, GPR and ODI are tested in
detail in a canonical setup of forced homogeneous isotropic turbulence from the
Johns Hopkins Turbulence Database. According to the result, GPR has the same
level of accuracy as ODI with optimized hyper-parameters for the isotropic
turbulence flow. However, GPR has the tendency to flatten impulsive signals.
Therefore, without further modifications, it is not suitable to detect flow
structures with impulsive true signals. The error propagation of the proposed
framework is also analyzed and discussed in both physical and spectral spaces.
