MATLAB: Dropping Wavelet Coefficients After Wavelet Transform

Question

I have a 512 sample signal that I pass through a wavelet transform. I get a series of wavelet coefficients some of which are sparse (zeros). I want to drop some of these insignificant coefficients and pass it through another algorithm without changing the original signal too much (I understand that there is some loss of data). Essentially, I want to use a subset of these wavelet coefficients. Keep in mind I am not going back to the original signal. I want to use the wavelet representation for further processing but I want to drop some of the coefficients.

Answer 1

So why not reconstruct the approximation using the inverse wavelet transform?

That is the whole basis of wavelet denoising. Hard thresholding sets a number of coefficients to zero and then you reconstruct the signal via the inverse wavelet transform.