Stability of Image-Reconstruction Algorithms

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.

Stability of Image-Reconstruction Algorithms

Pol del Aguila Pla; Sebastian Neumayer; Michael Unser

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( 2 and 1 regularization) and present novel stability results for p -regularized linear inverse problems for p(1,) . Our results guarantee Lipschitz continuity for small p and Hölder continuity for larger p . They generalize well to the Lp (Ω)  function spaces.


Inverse problems are at the core of computational imaging. Medical imaging critically depends on the guarantees provided by established image-reconstruction methodologies to inform diagnostic and treatment decisions. New techniques based on artificial intelligence and deep neural networks offer major average performance improvements in most applications [1][2][3][4], at the cost of poor practical stability [5][6] and a lack in theoretical guarantees. In particular, seemingly small perturbations of the measurements can produce large errors in the resulting image. Insidiously, these errors may incorporate deceptive patterns that look realistic because they were learnt from the training database (hallucination) [7].

SPS on Twitter

  • DEADLINE EXTENDED: The 2023 IEEE International Workshop on Machine Learning for Signal Processing is now accepting…
  • ONE MONTH OUT! We are celebrating the inaugural SPS Day on 2 June, honoring the date the Society was established in…
  • The new SPS Scholarship Program welcomes applications from students interested in pursuing signal processing educat…
  • CALL FOR PAPERS: The IEEE Journal of Selected Topics in Signal Processing is now seeking submissions for a Special…
  • Test your knowledge of signal processing history with our April trivia! Our 75th anniversary celebration continues:…

IEEE SPS Educational Resources

IEEE SPS Resource Center

IEEE SPS YouTube Channel