Linear and non-linear approximation with wavelets

Linear approximation is obtained by keeping M low frequency coefficients and then applying the inverse wavelet transform. Here we take M=n^2/4 by keeping n/2 x n/2 low frequency coefficients.

Linear approximation is obtained by keeping M=n^2/4 best coefficients, that are the M largest amplitude coefficients.

We can now compute the approximation error and display both the coefficients and the resulting images. The non-linear approximation is usually much better for images that contains edges because linear approximation blurs features (it is non-adaptive).