Fig. 3

By turning the image patches into vectors, the sensing scheme can be written as a matrix Φ that omits pixels when applied to a patch. The vector \(\boldsymbol {e}_{i} \in \mathbb {R}^{P}\) has a one in the ith position and zeros in all other positions, so Φ has a subset of identity matrix columns. The illustration shows that the first pixel is eliminated while the second is kept. The zero columns are used here to motivate the idea, but in the actual sensing matrix, the zero columns are not present, so the compressed patch vector (\(\boldsymbol {y}\in \mathbb {R}^{Q}\)) is shorter than the signal patch vector (\(\boldsymbol {x}\in \mathbb {R}^{P},\, Q\ll P\))