Orthogonal frequency-division multiplexing (OFDM) is a multi-carrier modulation scheme that has been employed in many communication standards. The performance of OFDM is severely degraded by the presence of impulsive noise caused due to different nonlinear devices and power amplifiers. In this paper, we propose a novel automated framework to detect and remove impulse noise in OFDM system. The proposed method is based on sparse decomposition and l1-norm optimization algorithm of the received signal over an over-complete matrix composed of both sine and cosine waveforms and time-shifted impulse waveforms. By proper construction of the over-complete matrix, the impulse removal and symbol decoding have been performed simultaneously. Thus, it can reduce the computational complexity. Our method does not require any assumption about the location and magnitude of the impulse and does not demand pilot symbols or null subcarriers unlike other existing methods. Thus, the proposed method is blind in nature. The method is evaluated using different levels of impulse noise and signal-to-noise ratios varying from 0 to 20 dB. Preliminary evaluation results demonstrate the effectiveness of the sparse representation with the proposed dictionaries in effectively removing the impulse noise and improving the bit error rate under different noise levels. © 2017, Springer Science+Business Media New York.