Matched filters are used in radar systems to identify echo signals embedded in noise. They allow us to extract range and Doppler information about the target from the reflected signal. In high frequency radars, matched filters make the system expensive and complex. For that reason, the radar research community is looking at techniques like compressive sensing or compressive sampling to eliminate the use of matched filters and high frequency analog-to-digital converters. In this work, compressive sensing is proposed as a method to increase the resolution and eliminate the use of matched filters in chaotic radars. Two basic scenarios are considered, one for stationary targets and one for non-stationary targets. For the stationary targets, the radar scene was a one dimensional vector, in which each element from the vector represents a target position. For the non-stationary targets, the radar scene was a two dimensional matrix, in which one direction of the matrix represents the target’s range, and the other direction represents the target’s velocity. Using optimization techniques, it was possible to recover both radar scenes from an under sampled echo signal. The reconstructed scenes were compared against a traditional matched filter system. In both cases, the matched filter was capable of recovering the radar scene. However, there was a considerable amount of artifacts introduced by the matched filter that made target identification a daunting task. On the other hand, using compressive sensing it was possible to recover both radar scenes perfectly, even when the echo signal was under sampled.