On Image Compression using Digital Curvelet Transform

This paper describes a novel approach to digital image compression using a new mathematical transform: the curvelet transform. The transform has shown promising results over wavelet transform for 2D signals. Wavelets, though well suited to point singularities have limitations with orientation selectivity, and therefore, do not represent two-dimensional singularities (e.g. smooth curves) effectively. This paper employs the curvelet transform for image compression, exhibiting good approximation properties for smooth 2D functions. Curvelet improves wavelet by incorporating a directional component. The curvelet transform finds a direct discrete-space construction and is therefore computationally efficient. In this paper, we divided 2D spectrum into fine slices using iterated tree structured filter bank. Different amount of quantized curvelet coefficients were then selected for lossy compression and entropy encoding. A comparison with wavelet based compression was made for standard images like Lena, Barbara, etc. Curvelet transform has resulted in high quality image compression for natural images. Our implementation offers exact reconstruction, prone to perturbations, ease of implementation and low computational complexity. The algorithm works fairly well for grayscale and colored images