Errors restoring or creating a disk image from a volume using DiskUtility

I'm using Macbook Air running macOS Big Sur, and I was having troubles performing disk restore using DiskUtility.

ERROR 1: I was unable to restore a volume to a new blank disk image I created. 

There could be a couple reasons such as the size of the blank disk image is smaller than the size of the source volume or there was no partition in the disk image (must be manually created at least 1 partition). But, even if I did follow all these requirements, the restore still failed.

ERROR 2: When trying to create a new disk image from a device or folder, I got the error message like "...operation not permitted". 

The function to create a new image from a device/folder is useful because the size of the new disk image will automatically be set to the size of the source device/folder, and the contents of the device/folder are restored (cloned) to the new disk image. 

SOLUTION

The errors occured because DiskUtility did not have enough privileges to perform those operations. After assigning a Full Disk Access permission to DiskUtility, I could restore a volume to a disk image (and vice versa) without any problems.

How to assign Full Disk Access permission to DiskUtility?

Open System Preferences > Security & Privacy > Privacy then select Full Disk Access from the listbox on the left and click on the Plus sign to add DiskUtility to the right listbox and make sure it's checked.