I would start by using WriteableBitmap instead, to get a WriteableBitmap from a BitmapImage you can do the following:
WriteableBitmap wb = new WriteableBitmap(bitmapImage);
Then I would recommend using the WriteableBitmapExtension library. It has support for resizing the image:
wb.Resize(newWidth, newHeight, WriteableBitmapExtensions.Interpolation.Bilinear);
To do the gaussian blur with WritableBitmapExtensions do the following (for some reason concolution doesn't edit the writableBitmap, so you have to assign it again to the same writableBitmap to see the result):
wb = wb.Convolute(WriteableBitmapExtensions.KernelGaussianBlur5x5);
or
wb = wb.Convolute(WriteableBitmapExtensions.KernelGaussianBlur3x3);
(Just different weights for the neighbouring pixels).
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