Considering progress in wireless and network telecommunication, need for digital image compression is inevitable. There are many methods in image compression which some of them have acceptable results. Lossy image compression algorithms are applicable whenever the exact reconstruction of an image is not expected. These algorithms are usually based on transform methods. A traditional scheme to realize multi-resolution image representation (MIR) is to apply 1-D filters separately in horizontal and vertical directions, commonly referred to as “separable” transform. In contrast, “non-separable” transforms consist of 2-D filters and 2-D downsampling matrices which cannot be factorized into 1-D filter/downsampling pairs. The traditional wavelet transform (WT) is categorized as a separable transform, which is used in various applications such as compression, noise removal, image edge enhancement, and feature extraction. Contours are abundant in natural images and cannot be categorized as either horizontal or vertical edges. However, wavelet has poor diagonal orientation selectivity since frequencies with different orientations are gathered into one subband in each resolution. For example, in image coding for low bit rates, reconstructed images often have blurred regions. Combination of separable and non-separable filter banks have been applied to reduce these artefacts. Dividing image in to homogeneous and heterogeneous regions is a new method which is employed recently. In this method each layer of image is compressed by the best transform. The contourlet transform is used to extract curves in texture areas. This transform employs laplacian pyramid and directional filter banks to take out contours and curves which aren't detected completely through other transforms like wavelet. The only problem of the contourlet is its redundancy which is a bottleneck for low bit rate compression purposes. In this thesis we propose new compression methods to avoid this problem. We first introduce contourlet transform and show our simulation results. Then we suggest multilayered methods for compression in low bit rate. In these methods the first transform is wavelet which removes texture regions from first layer image. To compress second layer we used contourlet to extract curves and directional edges. We showed that images that are compressed and reconstructed by our method at low bit rates have good qualities both visually and in terms of the produced Rs. Key Words image compression, multilayer methods, wavelet, contourlet, structure tensor.
