Ulugbek S. Kamilov

Research Scientist

Computational Sensing
Mitsubishi Electric Research Laboratories (MERL)

201 Broadway, 8th Floor
Cambridge, MA 02139, USA


Current research focus:

My research focuses on the development of new sensing systems for imaging and analyzing previously inaccessible information. Specifically, by leveraging the full power of numerical optimization, machine learning, and statistical inference, I aim to get the highest-quality images in the shortest amount of time. Research efforts are taking place at two complimentary levels: fundamental and mathematical aspects of imaging and application-oriented projects in collaboration with industry and research.

Broader areas of expertise:

Signal and image processing. Sparse regularization and compressive sensing. Traditional and convolutional sparse representations. Tomographic imaging. Multimodal imaging. Inverse problems. Statistical inference. Large-scale optimization algorithms. Belief propagation and message passing.

SEAGLE: Robust Computational Imaging under Multiple Scattering


Linear scattering models assume weakly scattering objects, making corresponding imaging methods inherently inaccurate for many applications. This places fundamental limits—in terms of resolution, penetration, and quality—on the imaging systems relying on such models. We developed a new computational imaging method called SEAGLE that combines a nonlinear scattering model and a total variation (TV) regularized inversion algorithm. The key benefit of SEAGLE is its efficiency and stability, even for objects with large permittivity contrasts. This makes SEAGLE suitable for robust imaging under multiple scattering.

  • H.-Y. Liu, U. S. Kamilov, D. Liu, H. Mansour, and P. T. Boufounos, "Compressive Imaging with Iterative Forward Models," Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process. (ICASSP 2017) (New Orleans, USA, March 5-9), in press. [pre-print]
    • IEEE ICASSP 2017 Student Paper Award finalist.

Multimodal Imaging and Fusion


Multimodal imaging is becoming increasingly important in a number of applications, providing new capabilities and new processing challenges. My team is investigating the benefit of combining multiple sensors for obtaining a high-quality multimodal view of an object. Our latest formulation incorporates temporal information and exploits the motion of objects in video sequences to significantly improve the quality of captured multimodal images.

  • U. S. Kamilov and P. T. Boufounos, "Motion-Adaptive Depth Superresolution," IEEE Trans. Image Process, vol. 26, no. 4, April 2017. [link]
  • J. Castorena, U. S. Kamilov, and P. T. Boufounos, "Autocalibration of Lidar and Optical Cameras via Edge Alignment," Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process. (ICASSP 2016) (Shanghai, China, March 20-25), pp. 2862—2866. [link] [pre-print]

Learning Proximal-Gradient Algorithms


Proximal-gradient methods are extremely popular due to their ability to seamlessly combine the knowledge of data formation with the prior information on the signal. A key feature of such approaches is that both data-fidelity term and the regularizer are manually designed in an attempt to capture the statistical distribution of natural signals. One of our recent research areas is to study how some core ideas from Deep Learning can be used for designing optimal imaging methods directly from data.

  • U. S. Kamilov and H. Mansour, "Learning optimal nonlinearities for iterative thresholding algorithms," IEEE Signal Process. Letters, vol. 23, no. 5, pp. 747-751, May 2016. [link] [pre-print]
  • U. S. Kamilov and H. Mansour, "Learning MMSE Optimal Thresholds for FISTA," Proc. 3rd International Traveling Workshop on Interactions between Sparse models and Technology (iTWIST 2016) (Aalborg, Denmark, August 24-26), p. 42. [link] [pre-print]

Learning Tomography


Optical Diffraction Tomography (ODT) is the one of the most popular technique for 3D imaging of biological samples. Learning Tomography (LT) is our novel extension of ODT that can numerically form images of 3D bilogical samples in the presence of multiple scattering. Our techique formulates the measurement model as an artificial multilayer neural network and relies on total variation (TV) regularization for forming high-quality images under few noisy measurements. We demonstrated the methods experimentally by imaging HeLa and hTERT-RPE1 cells.

  • U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, "Learning Approach to Optical Tomography," Optica, vol. 2, no. 6, pp. 517-522, June 2015. [link]
  • U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, "Optical tomographic image reconstruction based on beam propagation and sparse regularization," IEEE Tans. Comput. Imag., vol. 2, no. 1, pp. 59-70, March 2016. [link]
  • U. S. Kamilov, D. Liu, H. Mansour, and P. T. Boufounos, "A Recursive Born Approach to Nonlinear Inverse Scattering," IEEE Signal Process. Letters, vol. 23, no. 8, pp. 1052-1056, August 2016. [pre-print]

Statistical Inference via Message Passing

factor graph

Our work is motivated by the recent trend whereby classical linear methods are being replaced by nonlinear alternatives that rely on the sparsity of naturally occurring signals. We adopt a statistical perspective and model the signal as a realization of a stochastic process that exhibits sparsity as its central property. Our general strategy for solving inverse problems then lies in the development of novel iterative solutions for performing the statistical estimation. Specifically, we explore methods based on belief propagation method and its approximation in the form of approximate message passing.

  • S. Rangan, A. K. Fletcher, P. Schniter, and U. S. Kamilov, "Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization," IEEE Trans. Inf. Theory., vol. 63, no. 1, pp. 676-697, January 2017. [link] [pre-print]
  • U. S. Kamilov, S. Rangan, A. K. Fletcher, and M. Unser, "Approximate Message Passing with Consistent Parameter Estimation and Applications to Sparse Learning," IEEE Trans. Inf. Theory., vol. 60, no. 5, pp. 2969-2985, May 2014. [link] [NIPS 2012] [pre-print] [code]
  • U. S. Kamilov, P. Pad, A. Amini, and M. Unser, "MMSE Estimation of Sparse Lévy Processes," IEEE Trans. Signal Process., vol. 61, no. 1, pp. 137-147, January 2013. [link] [pre-print] [code]

Message-Passing De-Quantization (MPDQ)

consistency set

Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal—sometimes greatly so. We have developed message-passing de-quantization (MPDQ) algorithms for minimum mean-squared error estimation of a random vector from quantized linear measurements, notably allowing the linear expansion to be overcomplete or undercomplete and the scalar quantization to be regular or non-regular. The algorithm is based on generalized approximate message passing (GAMP), a Gaussian approximation of loopy belief propagation for estimation with linear transforms and nonlinear componentwise-separable output channels. For MPDQ, scalar quantization of measurements is incorporated into the output channel formalism, leading to the first tractable and effective method for high-dimensional estimation problems involving non-regular scalar quantization. The algorithm is computationally simple and can incorporate arbitrary separable priors on the input vector including sparsity-inducing priors that arise in the context of compressed sensing.

  • U. S. Kamilov, V. K. Goyal, and S. Rangan, "Message-Passing De-Quantization with Applications to Compressed Sensing," IEEE Trans. Signal Process., vol. 60, no. 12, pp. 6270-6281, December 2012. [link] [pre-print] [code]
  • U. S. Kamilov, A. Bourquard, A. Amini, and M. Unser, "One-Bit Measurements with Adaptive Thresholds," IEEE Signal Process. Letters, vol. 19, no. 10, pp. 607-610, October 2012. [link] [pre-print] [code]

Cycle Spinning for Compressive Imaging


We provide a theoretical justification for the popular wavelet-domain estimation technique called cycle spinning in the context of general linear inverse problems. Cycle spinning has been extensively used for improving the visual quality of images reconstructed with wavelet-domain methods. We also refine traditional cycle spinning by introducing the concept of consistent cycle spinning that can be used to perform wavelet-domain statistical estimation. In particular, we empirically show that consistent cycle spinning achieves the minimum mean-squared error (MMSE) solution for denoising stochastic signals with sparse derivatives.

  • U. S. Kamilov, E. Bostan, and M. Unser, "Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems," IEEE Signal Process. Letters., vol. 21, no. 11, pp. 1326-1330, November 2014. [link] [pre-print]
  • A. Kazerouni, U. S. Kamilov, E. Bostan, and M. Unser, "Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning," IEEE Signal Process. Letters, vol. 20, no. 3, March 2013. [link] [pre-print] [code]
  • U. S. Kamilov, E. Bostan, and M. Unser, "Wavelet Shrinkage with Consistent Cycle Spinning Generalizes Total Variation Denoising," IEEE Signal Process. Letters, vol. 19, no. 4, pp. 187-190, April 2012. [link] [pre-print] [code]