arXiv subjects

Ulugbek S. Kamilov

Publications and source records attributed to Ulugbek S. Kamilov.

103 records · Page 6Linked to original sources

arXiv2017

Accelerated Image Reconstruction for Nonlinear Diffractive Imaging

The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship, there is an increased interest in considering nonlinear formulations that can account for multiple light scattering. In this paper, we propose an image reconstruction method, called CISOR, for nonlinear diffractive imaging, based on a nonconvex optimization formulation with total variation (TV) regularization. The nonconvex solver used in CISOR is our new variant of fast iterative shrinkage/thresholding algorithm (FISTA). We provide fast and memory-efficient implementation of the new FISTA variant and prove that it reliably converges for our nonconvex optimization problem. In addition, we systematically compare our method with other state-of-the-art methods on simulated as well as experimentally measured data in both 2D and 3D settings.

cs.CV↗

arXiv2017

Online Convolutional Dictionary Learning for Multimodal Imaging

Computational imaging methods that can exploit multiple modalities have the potential to enhance the capabilities of traditional sensing systems. In this paper, we propose a new method that reconstructs multimodal images from their linear measurements by exploiting redundancies across different modalities. Our method combines a convolutional group-sparse representation of images with total variation (TV) regularization for high-quality multimodal imaging. We develop an online algorithm that enables the unsupervised learning of convolutional dictionaries on large-scale datasets that are typical in such applications. We illustrate the benefit of our approach in the context of joint intensity-depth imaging.

cs.CV↗

arXiv2017

SEAGLE: Sparsity-Driven Image Reconstruction under Multiple Scattering

Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with Accelerated Gradient Descent on Lippmann-Schwinger Equation (SEAGLE)-for robust imaging under multiple scattering based on a combination of a new nonlinear forward model and a total variation (TV) regularizer. The proposed forward model can account for multiple scattering, which makes it advantageous in applications where linear models are inaccurate. Specifically, it corresponds to a series expansion of the scattered wave with an accelerated-gradient method. This expansion guarantees the convergence even for strongly scattering objects. One of our key insights is that it is possible to obtain an explicit formula for computing the gradient of our nonlinear forward model with respect to the unknown object, thus enabling fast image reconstruction with the state-of-the-art fast iterative shrinkage/thresholding algorithm (FISTA). The proposed method is validated on both simulated and experimentally measured data.

cs.CV↗

arXiv2016

Compressive Imaging with Iterative Forward Models

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon, which makes the method preferable in applications where linear measurement models are inaccurate. We construct the measurement model by expanding the scattered wave-field with an accelerated-gradient method, which is guaranteed to converge and is suitable for large-scale problems. We provide explicit formulas for computing the gradient of our measurement model with respect to the unknown image, which enables image formation with a sparsity- driven numerical optimization algorithm. We validate the method both analytically and with numerical simulations.

cs.CV↗

arXiv2016

A Recursive Born Approach to Nonlinear Inverse Scattering

The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.

cs.LG↗

arXiv2016

Depth Superresolution using Motion Adaptive Regularization

Spatial resolution of depth sensors is often significantly lower compared to that of conventional optical cameras. Recent work has explored the idea of improving the resolution of depth using higher resolution intensity as a side information. In this paper, we demonstrate that further incorporating temporal information in videos can significantly improve the results. In particular, we propose a novel approach that improves depth resolution, exploiting the space-time redundancy in the depth and intensity using motion-adaptive low-rank regularization. Experiments confirm that the proposed approach substantially improves the quality of the estimated high-resolution depth. Our approach can be a first component in systems using vision techniques that rely on high resolution depth information.

cs.CV↗

arXiv2016

Parallel proximal methods for total variation minimization

Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our method replaces the standard proximal step of TV by a simpler alternative that computes several independent proximals. We prove that the proposed parallel proximal method converges to the TV solution, while requiring no sub-iterations. The results in this paper could enhance the applicability of TV for solving very large scale imaging inverse problems.

cs.IT↗

arXiv2015

Learning optimal nonlinearities for iterative thresholding algorithms

Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simple deep neural network (DNN) and developing a corresponding error backpropagation algorithm that allows to fine-tune the thresholding functions. Simulations on sparse statistical signals illustrate potential gains in estimation quality due to the proposed data adaptive ISTA.

cs.LG↗

arXiv2015

Isotropic inverse-problem approach for two-dimensional phase unwrapping

In this paper, we propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data-fidelity term that favors sparsity in the error between the true and wrapped phase differences, as well as a regularizer based on higher-order total-variation. One desirable feature of our method is its rotation invariance, which allows it to unwrap a much larger class of images compared to the state of the art. We demonstrate the effectiveness of our method through several experiments on simulated and real data obtained through the tomographic phase microscope. The proposed method can enhance the applicability and outreach of techniques that rely on quantitative phase evaluation.

physics.optics↗

arXiv2015

A Learning Approach to Optical Tomography

We describe a method for imaging 3D objects in a tomographic configuration implemented by training an artificial neural network to reproduce the complex amplitude of the experimentally measured scattered light. The network is designed such that the voxel values of the refractive index of the 3D object are the variables that are adapted during the training process. We demonstrate the method experimentally by forming images of the 3D refractive index distribution of cells.

physics.optics↗

arXiv2012

Approximate Message Passing with Consistent Parameter Estimation and Applications to Sparse Learning

We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise (possibly nonlinear) measurement channel. A novel method, called adaptive generalized approximate message passing (Adaptive GAMP), that enables joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector $\xbf$ is presented. The proposed algorithm is a generalization of a recently-developed EM-GAMP that uses expectation-maximization (EM) iterations where the posteriors in the E-steps are computed via approximate message passing. The methodology can be applied to a large class of learning problems including the learning of sparse priors in compressed sensing or identification of linear-nonlinear cascade models in dynamical systems and neural spiking processes. We prove that for large i.i.d. Gaussian transform matrices the asymptotic componentwise behavior of the adaptive GAMP algorithm is predicted by a simple set of scalar state evolution equations. In addition, we show that when a certain maximum-likelihood estimation can be performed in each step, the adaptive GAMP method can yield asymptotically consistent parameter estimates, which implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values. Remarkably, this result applies to essentially arbitrary parametrizations of the unknown distributions, including ones that are nonlinear and non-Gaussian. The adaptive GAMP methodology thus provides a systematic, general and computationally efficient method applicable to a large range of complex linear-nonlinear models with provable guarantees.

cs.IT↗

arXiv2012

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies continuous-domain signals as solutions of linear stochastic differential equations. Accordingly, we show that the class of admissible priors for the discretized version of the signal is confined to the family of infinitely divisible distributions. Our estimators not only cover the well-studied methods of Tikhonov and $\ell_1$-type regularizations as particular cases, but also open the door to a broader class of sparsity-promoting regularization schemes that are typically nonconvex. We provide an algorithm that handles the corresponding nonconvex problems and illustrate the use of our formalism by applying it to deconvolution, MRI, and X-ray tomographic reconstruction problems. Finally, we compare the performance of estimators associated with models of increasing sparsity.

cs.IT↗

arXiv2012

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools from the theory of splines, we derive the joint a priori distribution of the samples and show how this probability density function can be factorized. The factorization enables us to tractably implement the maximum a posteriori and minimum mean-square error (MMSE) criteria as two statistical approaches for estimating the unknowns. We compare the derived statistical methods with well-known techniques for the recovery of sparse signals, such as the $\ell_1$ norm and Log ($\ell_1$-$\ell_0$ relaxation) regularization methods. The simulation results show that, under certain conditions, the performance of the regularization techniques can be very close to that of the MMSE estimator.

cs.LG↗