Proximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging


We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind ptychographic imaging. Compared to other schemes in the literature, our approach differs in two ways: (i) it is posed within a clear mathematical framework with practical verifiable assumptions, and (ii) under the given assumptions, it is provably convergent to critical points. A numerical comparison of our proposed algorithm with the current state of the art on simulated and experimental data validates our approach and points toward directions for further improvement.


  1. alternating minimization
  2. deconvolution
  3. Kurdyka--Łojasiewicz
  4. nonconvex-nonsmooth minimization
  5. ptychography

MSC codes

  1. Primary
  2. 90C26
  3. 49J52
  4. 65K10
  5. 68U10; Secondary
  6. 94A08
  7. 65K05
  8. 78M30

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Information & Authors


Published In

cover image SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Pages: 426 - 457
ISSN (online): 1936-4954


Submitted: 11 August 2014
Accepted: 20 November 2014
Published online: 24 February 2015


  1. alternating minimization
  2. deconvolution
  3. Kurdyka--Łojasiewicz
  4. nonconvex-nonsmooth minimization
  5. ptychography

MSC codes

  1. Primary
  2. 90C26
  3. 49J52
  4. 65K10
  5. 68U10; Secondary
  6. 94A08
  7. 65K05
  8. 78M30



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