In this paper, an adaptive separable 2D wavelet transform is proposed. Wavelet transforms are widely used in signal and image processing due to its energy compaction property. Sparser representation corresponds to better performance in compression, denoising, compressive sensing, sparse component analysis and many other applications. The proposed scheme results in more compact representation then fixed wavelet. Instead of the commonly used least squares criterion, least absolute deviation (LAD) is introduced. It results in more accurate adaptation resistant to outliers. The advantages of the proposed method have been shown on synthetic and real-world images.