The design of a robust observer under denial-ofservice attacks is addressed for linear time invariant systems in the bounded-error framework. The cyber-attacks occur between the output of the sensors localized on the physical plant and the cyber part embedding the observer. The data required by the observer are thus available at sporadic measurement time instants. In this setting, an interval impulsive observer is synthesized. The stability analysis of the dynamics of the state estimation error is done leveraging finite-gain L1 stability theory for hybrid systems. The observer L1 gain is computed by combining interval analysis and the resolution of algebraic inequalities that greatly reduces the synthesis complexity when compared to the state-of-the-art approaches that usually rely on solving many bilinear matrix inequalities. A numerical example illustrates the approach and the performance of the designed robust observer.