Images are decomposed by a cascade of four-filter banks. Here is the figure when separable wavelets are used:
The down arrow means that the image is subsampled by keeping only the pixels whose both coordinates are even. The signal processing is performed on the low resolution image aj+1 and the three detail images d1j+1, d2j+1 and d3j+1. The processed signal is recovered by another cascade of filter banks:
The up arrow means that the size of the image is doubled by inserting black rows and columns of pixels between every row and columns of the source image.
Here the wavelets are orthogonal, that is, the filters used at the top are the mirrors of the filters at the bottom. In practice this means that if a filter uses the value of a pixel at location (x+a,y+b) with a coefficient c, the mirror filter uses the value of the pixel at location (x-a,y-b) with the same coefficient c.
Now let us proceed with the first exercise.