Convolution with large image dimensions (multiple ciphertext)

[spyder73]

Question

Is it possible to split an image into - so to say - a bunch of sub-regions, apply im2col, and then handle the network further with more than one ciphertexts?

Further Information

So let's say i wanna apply a convolutional layer on a 48x48 image - as done in Tutorial 4. Now for 48 x 48, that seems to work just fine with the following he parameters:

"he_config": {
    "poly_modulus_degree": 32768,
    "bits_scale": 40,
    "coeff_mod_bit_sizes": [60, 40, 40, 40, 40, 40, 40, 60]
}

Yet if i try to have an image that is 64 x 64, i get error warnings because the ciphertext becomes too large and this disables functionalities like im2col_encoding & conv2d_im2col. The issue is that 32768 is the largest polymodulus degree and thus i feel like 48 x 48 a limit is reached here.

Potentially i would like to have even larger image dimensions. Is there a way to create such a split-up as i am imagining it?

So, divide the image into X pieces, apply im2col_encoding on each piece, and finally concatenate all the resulting (encoded) arrays, where each piece has their own ciphertext, into a large array that represents the full convolution? One would have to apply a specific logic, so that each bit of the array is linked to the right ciphertext.

Am i missing something?