Lifting scheme is an efficient implementation method of the wavelet transform algorithm, and results in lossless data compression. It consists of three basic steps:Split, Predict, and Update.
Split: Split the signal into two disjoint subsets of samples. Divide the signal X[n] into even and odd components: Xe[n] and Xo[n], where Xe[n] = X[2n] and Xo[n] = X[2n + 1].
Predict: Generate the detail signals d[n] as the prediction error using a prediction operator P: d[n] = X_0[n] - P(X_e[n]).
Update: Generate the coarser (approximated) signals c[n] by applying an update operator U to d[n] and adding the result to Xe[n]: c[n] = X_e[n] + U(d[n]).
To implement one level of DWT using the lifting scheme, 9/7 and 5/3 filters have been used. Out of these two filters, 5/3 filter is more suitable for loss�less data compression. The following steps are nec�essary to get wavelet coefficients using this filter: • Split the input into coefficients at odd and even positions, • Perform a predict-step, that is the operation given below.
y[2n+1] = x[2n+1] - {x[2n] + x[2n+2]}/2
Perform update-step, that is the operation given below. y[2n] = x[2n] + {y[2n-1] + y[2n+1]}/4
These operations are realized in the below figures.
