Nonconvex Structured Phase Retrieval: A Focus on Provably Correct Approaches

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

Nonconvex Structured Phase Retrieval: A Focus on Provably Correct Approaches

By: 
Namrata Vaswani
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, subdiffraction imaging, and astronomy. In each of these domains, the physics of the acquisition system dictates that only the magnitude (intensity) of certain linear projections of the signal or image can be measured. Without any assumptions on the unknown signal, accurate recovery necessarily requires an overcomplete set of measurements. The only way to reduce the measurements/sample complexity is to place extra assumptions on the unknown signal/image. A simple and practically valid set of assumptions is obtained by exploiting the structure inherently present in many natural signals or sequences of signals.

Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, subdiffraction imaging, and astronomy. In each of these domains, the physics of the acquisition system dictates that only the magnitude (intensity) of certain linear projections of the signal or image can be measured. Without any assumptions on the unknown signal, accurate recovery necessarily requires an overcomplete set of measurements. The only way to reduce the measurements/sample complexity is to place extra assumptions on the unknown signal/image. A simple and practically valid set of assumptions is obtained by exploiting the structure inherently present in many natural signals or sequences of signals.

Two commonly used structural assumptions are: 1) the sparsity of a given signal/image or 2) a low-rank (LR) model on the matrix formed by a set, e.g., a time sequence, of signals/images. Both have been explored for solving the PR problem in a sample-efficient fashion. This article describes this work, with a focus on nonconvex approaches that come with sample complexity guarantees under simple assumptions. We also briefly describe other different types of structural assumptions that have been used in recent literature.

SPS on Twitter

  • Join us on Friday, 21 May at 1:00 PM EST when Dr. Amir Asif (York University) shares his journey and the importance… https://t.co/SLJGLI3K8u
  • There's still time to apply for PROGRESS! Visit https://t.co/0h4GgRY1Jr to connect with signal processing leaders a… https://t.co/dQNnkxpv8f
  • This Saturday, 8 May, join the SPS JSS Academy of Technical Education Noida Student Branch Chapter in collaboration… https://t.co/lFVmmVucvG
  • The SPACE Webinar Series continues this Tuesday, 4 May at 10:00 AM Eastern when Dr. Lei Tian presents "Modeling and… https://t.co/9emEVjOInK
  • The second annual IEEE SIGHT Day will take place on 28 April! This year’s theme is “Celebrating 10 years of IEEE SI… https://t.co/V18yEHtJJl

SPS Videos


Signal Processing in Home Assistants

 


Multimedia Forensics


Careers in Signal Processing             

 


Under the Radar