The authors propose a pseudolocal tomography concept. Let \(d > 0\) be fixed, they consider the following pseudolocal tomography formula \[ f_d (x) = {1 \over 4 \pi^2} \int_{S^1} \int^{x. \theta + d}_{x. \theta - d} {\widehat f_d(\theta, p) \over x. \theta - p} dp d \theta,\;x \in \mathbb{R}^2 \] where \(S^1\) is the unit sphere in \(\mathbb{R}^2\), \(d \theta\) is the measure on \(S^1 \), and \(\widehat f(\theta, p)\) the Radon transform of \(f, \theta \in S^1\), \(p \in \mathbb{R}\). The function \(f_d\) has locality properties and preserves locations and sizes of discontinuities of the original density function and of its derivatives. In particular, one can recover locations and values of jumps of the original function \(f\) from these of \(f_d\). The resulting images of jumps are sharper than those in standard global tomography. Numerical aspects of pseudolocal tomography are discussed. Results of model experiments show the effectiveness of the methods proposed.