Iterative Method with Adaptive Thresholding (IMAT)
Compressed Sensing (CS) and Sparse Recovery
Iterative Method
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About the Algorithm The Iterative Method with Adaptive Thresholding (IMAT)

The Iterative Method with Adaptive Thresholding (IMAT) is a fast and efficient algorithm for sparse signal reconstruction. It was originally proposed for sparse signal reconstruction from random/missing samples. It was further modified to IMATI by adding interpolation to each iteration to achieve faster convergence. Another modification of IMAT, namely IMATCS was also proposed for compressed sensing recovery. IMAT proved to outperform Orthogonal Matching Pursuit (OMP) and Iterative Hard Thresholding (IHT) techniques in some applications regarding complexity and reconstruction quality. This algorithm gradually extracts the sparse signal components by iterative thresholding of the estimated signal promoting sparsity.


The following papers are published so far on IMAT and its applications in different domains:
  1. Farokh Marvasti et al., "Sparse signal processing using iterative method with adaptive thresholding (IMAT), " 19th International Conference on Telecommunications (ICT 2012), pp. 1-6, April 2012. [PDF]
  2. Farokh Marvasti et al., "A Unified Approach to Sparse Signal Processing, " EURASIP Journal on Advances in Signal Processing, 2012. [PDF]
  3. M. Azghani, F. Marvasti, "Iterative Methods for Random Sampling and Compressed Sensing Recovery, " 10th International Conference on Sampling Theory and Applications (SAMPTA 2013), July 2013. [PDF]
  4. A. Zandieh, A. Zareian, M. Azghani, and F. Marvasti, "Reconstruction of Sub-Nyquist Random Sampling for Sparse and Multi-Band Signals," Submitted to IEEE Transactions on Signal Processing, November 2014. [PDF]
  5. M. Boloursaz, N. Salarieh, E. Shahrabi Farahani, and F. Marvasti, "Sparse Signal Reconstruction for Asynchronous Level Crossing A/Ds using the Iterative Method with Adaptive Thresholding (IMAT)," Submitted to IEEE Transactions on Instrumentation and Measurement, July 2016.
  6. Masoumeh Azghani, Panagiotis Kosmas, and Farokh Marvasti, "Microwave Medical Imaging Based on Sparsity and an Iterative Method With Adaptive Thresholding," IEEE Transactions on Medical Imaging, vol. 34, no. 2, pp. 357-365. [PDF]
  7. H. Zamani, H. Zayyani, and F. Marvasti, "An Iterative Dictionary Learning-based algorithm For DOA Estimation," IEEE Communications Letters, July, 2016. [PDF]
  8. Ashkan Esmaeili, Ehsan Asadi, and Farokh Marvasti, "Iterative Null-space Projection Method of Adaptive Thresholding in Sparse Signal Recovery and Matrix Completion". [PDF]
  9. A. Taimori, F. Marvasti, "Measurement-Adaptive Sparse Image Sampling and Recovery," Submitted to IEEE Transactions on Computational Imaging, 2017. [PDF]


The following Codes illustrate IMAT performance in various applications:
  1. Basic IMAT Algorithm for sparse image reconstruction from missing samples, by M. Boloursaz.
  2. IMAT algorithm for random sampling recovery of sparse signals, by M. Azghani..
  3. IMATI Algorithm for random sampling recovery of sparse signals.
  4. IMATCS Algorithm for Compressed Sensing recovery of sparse signals.
  5. Performance comparison between IMAT, OMP, LASSO, and Iterative algorithms for voice reconstruction from Level Crossing (LC) samples.
  6. Application of IMAT for high resolution spectrum estimation in heart rate tracking from PPG signals. These codes ranked 8'th in the second ICASSP Signal Processing Cup!
  7. Application of IMATGI in Sparsity Promoting Interpolation of Signals Defined on Graphs.
  8. INPMAT algorithm.
  9. Measurement-Adaptive Sampling Cellular Automaton Recovery (MASCAR) Algorithm.


2000 - Present

Advanced Topics in Digital Signal Processing (DSP).

Course Materials

  • Uniform/Non-uniform Sampling Theory.
  • Signal Interpolation and Reconstruction.
  • Iterative Methods for Inverse Systems.
  • Study on DFT Codes and Non-linear Methods.
  • Applications of Iterative Methods in Analogue and Digital Modulation Schemes.


IMAT is developed by contributions from the following ACRI (Advanced Communications Research Institute) LAB members: Current Team Members:
ACRI Member


  • M. Boloursaz, PHD Candidate
  • A. Zareian, BSc Student
  • A. Zandieh, BSc Student

Former Contributors:

  • R. Eghbali
  • M. Soltanolkotabi
  • A. Kazerooni
  • A. Rashidinejad

Get in Touch

Our address:

Multimedia and Signal processing Lab. (MSL)
EE302, Electrical Engineering Department
Sharif University of Technology
Azadi Ave., Tehran, Iran.
Telephone: (+98)(21) 6616 4338
FAX: (+9821) 66036002