Are Wavelet Coefficients simply the pixel values of decomposed image in 2D Discrete Wavelet Transform

I've been working with Discrete Wavelet Transform, I'm new to this theory. I want to access and modify the wavelet coefficients of the decomposed image, Are those wavelet coefficients simply the pixel values of the decomposed image in 2D DWT?

This is for example the result of DWT Decomposition:

So, when I want to access and modify the Wavelet Coefficients, can I just iterate through the pixel values of above image? Thank you for your help.

No. The image is merely illustrative.

The image you are looking on does not exactly correspond to original coefficients. The original wavelet coefficients are real numbers. Unlike them, you are looking on their absolute values quantized into a range from 0 to 255.

It is not true that the coefficients were calculated as pairwise sums and differences of the input samples. The coefficients were calculated using two complementary filters. See the description here. However, it is essential that these coefficients were adjusted and it is no longer possible to synthesize the original image. If you need to synthesize the image, you cannot access the pixels of the referenced image.