Getting aliasing when I denoise a signal with wavedec, wthresh and waverec

I use the this example: https://de.mathworks.com/help/wavelet/examples/wavelet-interval-dependent-denoising.html

to denoise a signal. My problem is that when I create the denoised signal with "waverec" I have aliasing in my signal.

I think this happens because of the downsampling during "wavedec". Can you guys offer a solution for my problem?

Is there maybe any possibility to use wavedec without downsampling?