Wideband radar systems are highly resolved in range, which is a desirable feature for mitigating clutter. However, due to a smaller range resolution cell, moving targets are prone to migrate along the range during the coherent processing interval (CPI). This range walk, if ignored, can lead to huge performance degradation in detection. Even if compensated, conventional processing may lead to high sidelobes preventing from a proper detection in case of a multitarget scenario. Turning to a compressed sensing framework, we present a Bayesian algorithm that gives a sparse representation of migrating targets in case of a wideband waveform. Particularly, it is shown that the target signature is the sub-Nyquist version of a virtually well-sampled two-dimensional (2D)-cisoid. A sparse-promoting prior allows then this cisoid to be reconstructed and represented by a single peak without sidelobes. Performance of the proposed algorithm is finally assessed by numerical simulations on synthetic and semiexperimental data. Results obtained are very encouraging and show that a nonambiguous detection mode may be obtained with a single pulse repetition frequency (PRF).