We present an algorithm for the detection of candidate astronomical pulses. It is implemented in several steps. First, a spectrogram of a dispersed astronomical pulse is linearized in observing frequency followed by application of the Radon transform. The result of the transformation is displayed as a two-dimensional function. Next, the function is smoothed using a spatial low-pass filter. Finally, the maximum of the function above 90-deg angle is compared to the maximum of the standard deviation of the noise below 90-deg angle and a decision in favor of an astronomical pulse present or absent is made. Once pulse is detected, its dispersion measure (DM) is estimated by means of a basic equation relating the slope of the linearized dispersed pulse and the DM value. Performance of the algorithm is analyzed by applying it to a set of simulated fast radio bursts, experimental data of Masui pulse, and of seven rotating radio transients. The detection algorithm demonstrates results comparable to those by the conventional pulse detection algorithm.