ABSTRACT
Henrik Ohlsson Department of Electrical Engineering and Computer Sciences, University of California, Berkeley
Allen Y. Yang Department of Electrical Engineering and Computer Sciences, University of California, Berkeley
Roy Dong Department of Electrical Engineering and Computer Sciences, University of California, Berkeley
Michel Verhaegen Delft Center for Systems and Control, Delft University
S. Shankar Sastry Department of Electrical Engineering and Computer Sciences, University of California, Berkeley
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 9.1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 9.1.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
9.2 Quadratic Basis Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.2.1 Convex Relaxation via Lifting . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.2.2 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
9.3 Numerical Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 9.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
9.4.1 Nonlinear Compressive Sensing in Real Domain . . . . . . . . 206 9.4.2 The Shepp-Logan Phantom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 9.4.3 Subwavelength Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
9.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Vector
9.1 Introduction Consider the problem of finding the sparsest signal x satisfying a system
of linear equations:
‖x‖0 subj. to yi = bTi x, yi ∈ <, bi ∈ <n, i = 1, . . . , N.
