DWT architecture using filter bank
I understand they  implement the convolution by Lo and Hi db2 filters given after the sentence:


  Rather, we propose to use db2 filters. The filter coefficients for the
  db2 filter are represented as


I have not seen in the paper a claim that Lo_D and Hi_D in Figures 5b and 5c should be half-size. They are low-pass and high-pass branches. However, they should be followed by a downsampling to implement a  one level-DWT, or at least something similar.

There are different ways for  implementing a one level of a standard critically sampled DWT: direct, lattice, lifting, polyphase, Fourier. They should end up all with the  same number of samples as the original signal (away from the borders).