Projecting from two perpendicular directions gives two independent sum ledgers that together constrain the hidden pixels. For the grid [1, 2; 3, 4] the row sums are 3 and 7, the column sums are 4 and 6, and the main diagonal sums to 5 exactly for the stated toy projection ledger; real scans need geometry calibration, detector response correction, noise handling, and uncertainty accounting.
The same tiny grid must satisfy both row and column projections. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.