Applications of Harmonic Analysis in Data Compression and Image Processing

Since emerging Fourier series for representing periodic functions(signals) in 1807, there were various new representation systems in literature such as short-time Fourier transform, wavelet transform, curvelet transform and shearlet transform. Nowdays power of representation systems are evaluated by ”sparsity” which is crucial in data compression. In this paper we compare the sparsity of Fourier, wavelet, curvelet and shearlet representations. Moreover, we show how shearlet transform to overcome the shortcoming of wavelet and curvelet transforms in dealing with issues arising in image processing.