Invertibility and Robustness of Phaseless Reconstruction
This addresses the phaseless reconstruction problem, which is incremental as it builds on existing theory by analyzing Lipschitz bounds and redundancy requirements.
The paper tackles the problem of reconstructing a vector from only the magnitudes of its coefficients under a redundant linear map, establishing theoretical performance bounds and showing that robust reconstruction requires more redundancy than a critical threshold.
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz bounds of the nonlinear analysis map and we establish theoretical performance bounds of any reconstruction algorithm. We show that robust and stable reconstruction requires additional redundancy than the critical threshold.