Backup

To get rid of empty space, we will process it via gzip

$ sudo dd if=/dev/mmcblk0 conv=sync,noerror bs=64K | gzip -c > backup.img.gz

Restore

$ gunzip backup.img.gz
$ sudo dd if=backup.img of=/dev/mmcblk0 bs=4M && sync

Mount image

If you need just to explore the content of your backup or get only one file from it, you can mount it to a folder. First of all, you need to get an offset where your filesystem actually begins

$ fdisk -l backup.img                                                                        ~
Disk backup.img: 14.42 GiB, 15485370368 bytes, 30244864 sectors
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: dos
Disk identifier: 0x93c181e7

Device                          Boot Start      End  Sectors  Size Id Type
backup.img1       8192 30244863 30236672 14.4G 83 Linux

As you can see in the example above we have one partition that starts on 8192 sector and each sector is 512 bytes. Now, all we have to do is multiply 8192 * 512 = 4194304 and use it as an offset when mounting as a loop device

$ sudo mount -o offset=4194304 backup.img /mnt/backup