My research is centered on the application of optimization algorithms to different signal processing and machine learning applications involving a large amount of data and/or complex models. I am generally interested in developing scalable optimization techniques, enjoying guaranteed performance and convergence properties. I am also involved in the statistical analysis of high-dimensional non-convex optimization techniques. I am currently pursuing these goals in the following projects:

- Robust Subspace Clustering:

Subspace Clustering (SC) is a novel tool for unsupervised learning, which aims at partitioning a set of data points based on their association to linear subspaces. The advantages of SC are proven in a number of clustering tasks in image processing and computer vision. Sparse Subspace Clustering (SSC) is a convex optimization framework for SC with guaranteed performance based on the geometric properties of the underlying subspaces. In this project, we develop and analyze a modified version of SSC, which treats corruption in the data set, but is based on a non-convex optimization problem. Our goal is to develop a specific non-convex optimization technique, based on the properties of SSC, which allows us to establish global convergence and guaranteed performance, in a statistical sense, despit non-convexity.

- Deep Learning:

Deep learning generally refers to machine learning techniques, based on compositional models comprising simple non-linear units (layers). The purpose of this project is to study a specific type of deep learning with asymptotically large number of layers and “incremental” units, resembling the behavior of a non-linear ordinary differential equation. Our goal is to draw conclusions about the convergence and performance of these models, on account of their simple analytic structure. At the same time, these networks are closely tied to the popular Artificial Neural Networks (ANN) and we hope to be able to employ them for studying ANNs.

Besides the above projects, I am collaborating with other members of the VISSTA group in the following projects:

- Analysis Dictionary Learning for Image Classification in collaboration with Wen Tang
- Deep Dictionary Learning in collaboration with Shahin Aghdam
- Multi-Modal sensor fusion using Robust Subspace Recovery in Collaboration with Sally Ghanem
- Community Detection and Biological Neural network modeling in collaboration with Yuming Huang

**Publications:**

**Journal Papers **

- Bian X., A. Panahi and H. Krim (2018). Bi-Sparsity Pursuit: A Paradigm for Robust Subspace Recovery. Elsevier Signal Processing, Vol. 152, Nov. (2018), Pages 148-159 [PDF]
- Panahi, A. and M. Viberg (2017). Performance Analysis of Sparsity-Based Parameter Estimation. Signal Processing, IEEE Transactions on. 65.24 (2017): 6478-6488.
- Panahi, A. and M. Viberg (2012). Fast candidate points selection in the LASSO path. Signal Processing Letters, IEEE 19(2), 79–82.
- Mecklenbrauker, C. F., P. Gerstoft, A. Panahi, and M. Viberg (2013). Sequential Bayesian sparse signal reconstruction using array data. Signal Processing, IEEE Transactions on 61(24), 6344–6354.
- Khanzadi, M. R., D. Kuylenstierna, A. Panahi, T. Eriksson, and H. Zirath (2014). Calculation of the performance of communication systems from measured oscillator phase noise. Circuits and Systems I: Regular Papers, IEEE Transactions on 61(5), 1553–1565.

**Papers in conference proceedings **

- Ghanem S. A. Panahi and H. Krim (2018), Information Subspace-Based Fusion for Vehicle Classification. European Signal Processing Conference (EUSIPCO), 2018 [PDF]
- Huang Y., A. Panahi and H. Krim (2018), Fusion of Community Structures in Multiplex Networks by Label Constraints. European Signal Processing Conference (EUSIPCO), 2018 [PDF]
- Breloy A., M. N. Elkorso, A. Panahi and H. Krim (2018), Robust Subspace Clustering for Radar Detection. European Signal Processing Conference (EUSIPCO), 2018
- Tang W., A. Panahi, H. Krim and L. Dai (2018). Structured Analysis Dictionary Learning for Image Classification, International Conference on Acoustics, Speech and Signal Processing (ICASSP 2018) [PDF]
- Panahi, A., H. Krim and L. Dai (2018). Demystifying Deep Learning: a Geometric Approach to Iterative Projections. International Conference on Acoustic, Speech and Signal Processing (ICASSP), 2018. [PDF]
- Panahi, A., X. Bian, H. Krim and L. Dai (2018), Robust Subspace Clustering by Bi-sparsity Pursuit: Guarantees and Sequential Algorithm. Applications of Computer Vision (WACV), 2018 IEEE Conference on. [PDF]
- Panahi, A., D. Dubhashi, F. D. Johansson and C. Bhattacharyya (2017). Clustering by Sum of Norms: Stochastic Incremental Algorithm, Convergence and Cluster Recovery. In: International Conference on Machine Learning (ICML), PMLR 70:2769-2777
- Panahi, A. and B. Hassibi (2017). A Universal Analysis of Large-Scale Regularized Least Squares Solutions. Neural Information Processing Systems (NIPS), 2017 Conference on.
- Panahi, A., M. Strom, and M. Viberg (2015). Wideband Waveform Design for Robust Target Detection. In: Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on. IEEE.
- Panahi, A., M. Viberg, and B. Hassibi (2015). A numerical Implementation of Gridless Compressed Sensing. In: Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on. IEEE.
- Thrampoulidis, C., A. Panahi, and B. Hassibi (2015). Precise Error Analysis for the LASSO. In: Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on. IEEE.
- Thrampoulidis, C., A. Panahi, and B. Hassibi (2015). Asymptotically exact error analysis for the generalized equation-LASSO. Information Theory (ISIT), 2015 IEEE International Symposium on. IEEE, 2015.
- Movahed, A., A. Panahi, and M. C. Reed (2014). Recovering signals with variable sparsity levels from the noisy 1-bit compressive measurements. In: Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on. IEEE, pp.6454–6458.
- Panahi, A., M. Strom, and M. Viberg (2014). Basis pursuit over continuum applied to range Doppler estimation problem. In: Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014 IEEE 8th. IEEE, pp.381–384.
- Panahi, A. and M. Viberg (2014). Gridless compressive sensing. In: Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on. IEEE, pp.3385–3389.
- Strom, M., A. Panahi, M. Viberg, and K. Falk (2014). Wideband waveform design for clutter suppression. In: Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014 IEEE 8th. IEEE, pp.297–300.
- Panahi, A. and M. Viberg (2013). A novel method of DOA tracking by penalized least squares. In: Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013 IEEE 5
^{th}International Workshop on. IEEE, pp.61–64. - Khanzadi, M. R., A. Panahi, D. Kuylenstierna, and T. Eriksson (2012). A model-based analysis of phase jitter in RF oscillators. In: Frequency Control Symposium (FCS), 2012 IEEE International. IEEE, pp.1–4.
- Movahed, A., A. Panahi, and G. Durisi (2012). A robust RFPI-based 1-bit compressive sensing reconstruction algorithm. In: Information Theory Workshop (ITW), 2012 IEEE. IEEE, pp.567–571. Resume: Ashkan Panahi
- Panahi, A. and M. Viberg (2012). A robust ℓ1 penalized DOA estimator. In: Signals, Systems and Computers (ASILOMAR), 2012 Conference Record of the Forty Sixth Asilomar Conference on. IEEE, pp.2013–2017.
- Panahi, A. and M. Viberg (2011). Fast LASSO based DOA tracking. In: Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2011 4th IEEE International Workshop on. IEEE, pp.397–400.
- Panahi, A. and M. Viberg (2011). Maximum a posteriori based regularization parameter selection. In: Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on. IEEE, pp.2452–2455.
- Panahi, A. and M. Viberg (2011). On the resolution of the LASSO-based DOA estimation method. In: Smart Antennas (WSA), 2011 International ITG Workshop on. IEEE, pp.1–5.
- Rashidi, M., K. Haghighi, A. Panahi, and M. Viberg (2011). A NLLS based sub-nyquist rate spectrum sensing for wideband cognitive radio. In: New Frontiers in Dynamic Spectrum Access Networks (DySPAN), 2011 IEEE Symposium on. IEEE, pp.545–551.
- Khanzadi, M. R., K. Haghighi, A. Panahi, and T. Eriksson (2010). A novel cognitive modulation method considering the performance of primary user. In: Wireless Advanced (WiAD), 2010 6th Conference on. IEEE, pp.1–6.