Can the same CNN architecture be used for different data sets? I have a CNN architecture that works well on 32x32x3 images. Can I use that same architecture for a data set made up of 28x28x1 images? (Both data sets have 10 classes). If this is possible, what changes would I need to make to the architecture I have?
One way is to redesign your CNN architecture to fit your new data input. However, if you want to use the current model you have, you should: 

(1) Retraining: Re-train the model with new data set images

(2) Reshape new images: You should add a pre-processing layer to convert 28x28x1 images to 32x32x3 images. This could be done by replicating a single channel in other two channels and adding boundaries to your images. This deformation process should be the same on all new input images.