Image Pyramid Without Decimation I have an image processing algorithm which uses Gaussian and Laplacian Pyramid Decomposition.
At each level of the pyramid the algorithm decimates the previous level by a factor of 2.
The LPF the algorithm uses is Gaussian.

I was wondering whether I could get the same results without the decimation step (By altering the LPF).

As far as I know, the decimation step is equivalent of cutting by half the bandwidth of the LPF.

What I tried, with no success, is to double the STD of the LPF at each step and skip the decimation.

Is there another / better way to do it?
Thanks.
You can generate a scale volume from an image by convolving it with Gaussians of increasing $\sigma$. Or, equivalently, by convlolving it repeatedly with the same Gaussian.  It just won't be a pyramid. :)

One reason to generate a pyramid by downsampling is to reduce the amount of computation, because once you apply a low-pass filter the full resolution becomes redundant.  

Also, are you computing the Laplacian pyramid by using the difference of Gaussians?  In that case, you need to downsample each subsequent scale level, and then upsample it before you take the difference with the previous level.