A prime target of seismic data processing is to improve the signal-to-noise ratio of the seismic data. New signal processing tools such as Wavelet transform, Radon transform, Fan-beam transform, Ridgelet transform and Curvelet transform have proven their results in image processing. A comparative study has been performed with these techniques to test their ability to increase the signal-to-noise ratio of seismic data by removing random noises. We then described the comprehensive mathematical formulation of these algorithms and tested them on both synthetic seismic data, which was created with a known signal-to-noise ratio with desired geologic features, and real seismic data, which contained curved features with random noise. Wavelet transform, which extends the robustness of frequency-dependent filtering by adding time dimension and multi-scale wavelet translation, improves the signal-to noise-ratio through the threshold coefficient filtering of random noise. The Radon transform and Fan-beam transform provide the opportunity of angle-dependent filtering, but produce adverse effects on curved features of seismic data and decrease seismic resolution. Ridgelet and Curvelet transform are more robust than Radon and Fan-beam transform. But Ridgelet transform, which uses Radon transform in its coefficient calculation, also produces adverse effects on curved features and threshold filtering leads to a decrease in the signal-to-noise ratio. The results have shown that the Curvelet transform is robust enough to handle random noise and also preserve the inclined and curved features of seismic data. However, its coefficient calculation requires large computation time and memory space. © 2013 The Author(s).