Andrzej Krol profile picture
315-464-7029

Andrzej Krol, PhD

113B Upstate University Hospital
750 East Adams Street
Syracuse, NY 13210
Andrzej Krol's email address generated as an image

CURRENT APPOINTMENTS

Professor of Radiology
Professor of Pharmacology

SPECIALTIES

Medical Nuclear Physics

LANGUAGES

English
Polish

PATIENT TYPE

Adults and Children

WEB RESOURCES

RESEARCH PROGRAMS AND AFFILIATIONS

Biomedical Sciences Program
Center for Psychiatric Neuroimaging
Radiology

RESEARCH INTERESTS

Development of:

  • Extremely low-dose and high-resolution tomographic reconstruction methods in PET and SPECT
  • Advanced ultrafast PET detector
  • Advanced very high-sensitivity and high-spatial resolution brain PET scanner
  • Ultrafast laser-based betatron microfocal x-ray source for very high-resolution biomedical imaging
  • PET bioprobe for detection and treatment of hepatocellular carcinoma and other cancers
  • Advanced breast cancer detection methods in mammography

EDUCATION INTERESTS

  • Physics of Nuclear Medicine – preparation of Radiology residents for board exams
  • Physics of Nuclear Cardiology – preparation of Cardiology fellows for board exams

 

ASSOCIATIONS / MEMBERSHIPS

American Association of Physicists in Medicine
American College of Radiology (ACR)
American Roentgen Ray Society (ARRS)
New York Academy of Sciences
Society of Nuclear Medicine (SNM)

EDUCATION

Fellowship: SUNY Upstate Medical University, 1994, Medical Physics
Postdoctoral Fellow: SUNY Stony Brook, 1989
PhD: Warsaw University, Poland, 1980
MS: Warsaw University, Poland, 1974

RESEARCH ABSTRACT

Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.

PUBLICATIONS

Link to PubMed (Opens new window. Close the PubMed window to return to this page.)