Fast compressed image sensing based on sampling matrix design

We study a fast compressive image sensing (CIS) paradigm, with computational complexity O(m²), as an alternative to compressive sensing, where m denotes the length of a measurement vector y = φx that is sampled from the signal x of length n via the sampling matrix φ with dimensionality m × n. In order to balance between reconstruction quality and speed, a new sampling matrix φ is designed. The characteristics of our method are: (i) recovery speed is extremely fast due to a closed-form solution being derived; (ii) certain reconstruction accuracy is preserved because significant components of x can be reconstructed with higher priority via an elaborately designed φ. Comparisons with state-of-the-art compressive sensing methodologies are provided to demonstrate the feasibility of our method in terms of reconstruction quality and computational complexity.