We present a field-based signal extraction of weak lensing from noisy observations on the curved and masked sky. We test the analysis on a simulated Euclid-like survey, using a Euclid-like mask and noise level. To make optimal use of the information available in such a galaxy survey, we present a Bayesian method for inferring the angular power spectra of the weak lensing fields, together with an inference of the noise-cleaned tomographic weak lensing shear and convergence (projected mass) maps. The latter can be used for field-level inference with the aim of extracting cosmological parameter information including non-gaussianity of cosmic fields. We jointly infer all-sky E-mode and B-mode tomographic auto- and cross-power spectra from the masked sky, and potentially parity-violating EB-mode power spectra, up to a maximum multipole of ℓmax=2048. We use Hamiltonian Monte Carlo sampling, inferring simultaneously the power spectra and denoised maps with a total of ∼16.8 million free parameters. The main output and natural outcome is the set of samples of the posterior, which does not suffer from leakage of power from E to B unless reduced to point estimates. However, such point estimates of the power spectra, the mean and most likely maps, and their variances and covariances, can be computed if desired.