Lossless and lossy image compression using biorthogonal wavelet transforms with multiplierless operations

We present lossless and lossy image compression algorithms, based on biorthogonal wavelets, which provide high computational speed and excellent compression performance. A specific pair of spline biorthogonal wavelets are chosen, having dyadic rational filter coefficients; convolutions with these filters can be performed by using only arithmetic bit-shifting and integer addition operations. For lossless compression, we have investigated a new reversible embedded wavelet transform. For lossy compression, we have constructed two-dimensional reconstruction filter masks for carrying out bit-shifting to minimize data access operations when performing the inverse wavelet transform.