In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. Three methods for sparsifying DDWT coefficients, i.e., matching pursuit, basis pursuit, and noise shaping, are compared. We found that noise shaping achieves the best nonlinear approximation efficiency with the lowest computational complexity. The interscale, intersubband, and intrasubband dependency among the DDWT coefficients are analyzed. Three subband coding methods, i.e., SPIHT, EBCOT, and TCE, are evaluated for coding DDWT coefficients. Experimental results show that TCE has the best performance. In spite of the redundancy of the transform, our DDWT TCE scheme outperforms JPEG2000 up to 0.70 dB at low bit rates and is comparable to JPEG2000 at high bit rates. The DDWT TCE scheme also outperforms two other image coders that are based on directional filter banks. To further improve coding efficiency, we extend the DDWT to an...