Efficient Least Absolute Deviation Adaptive Wavelet Filter Bank

Compact representation of signals and images is a key for many applications. Compactness is often achieved through linear transforms with good energy concentration property. We present an adaptive wavelet filter bank with fixed number of vanishing moments, plus additional local adaptation. Proposed adaptation method is conducted at each sample according to the least absolute deviation (LAD) criterion. Fixed vanishing moments provide for polynomial annihilation. Adaptation is aimed to achieve maximum sparseness for a wider class of signals, such as sine waves. LAD criterion results in more accurate adaptation on sudden changes of signal statistics. In this paper, an efficient LAD realization is proposed, in spite of nonexistence of the closed form solution. Combining least squares and LAD criterion, we have achieved unbiased adaptation, robust to noise. Due to its simplicity and acceptable computational speed, the proposed scheme is a good candidate for the real-world applications. In this paper, advantages of the proposed scheme are shown in signal denoising and reconstruction.