In optoacoustic tomography (OAT), also known as photoacoustic tomography, a variety of analytic reconstruction algorithms, such as filtered backprojection (FBP) algorithms, have been developed. Analytic algorithms are typically computationally more efficient than iterative image reconstruction algorithms but possess disadvantages that include the inabilty to accurately compensate for the response of the measurement system and stochastic noise. While these shortcomings can be circumvented by use of iterative image reconstruction methods, threedimensional (3D) iterative reconstruction is computationally burdensome. In this work, we present a novel datarestoration method that seeks to recover an accurate estimate of the pressure data with reduced noise levels from knowledge of the experimentally acquired transducer output data. From knowledge of the "restored" pressure data, a computationally efficient analytic algorithm can be applied for image reconstruction. Accordingly, this approach combines the advantages of an iterative reconstruction algorithm with the computational efficiency of an analytic algorithm. Curvelet-based data-space restoration is demonstrated by use of computer-simulation studies.