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We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...

We propose a novel statistical formulation of the image-reconstruction problem from noisy linear measurements. We derive an extended family of MAP estimators based on the theory of continuous-domain sparse stochastic processes. We highlight the crucial rol ...

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 fro ...

We introduce a new wavelet-based method for the implementation of Total-Variation-type denoising. The data term is least-squares, while the regularization term is gradient-based. The particularity of our method is to exploit a link between the discrete gra ...

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 cont ...

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

We introduce a novel variational framework for the regularized reconstruction of time-resolved volumetric flow fields. Our objective functional takes the physical characteristics of the underlying flow into account in both the spatial and the temporal doma ...

In this paper, we reconstruct signals from underdetermined linear measurements where the componentwise gains of the measurement system are unknown a priori. The reconstruction is performed through an adaptation of the message-passing algorithm called adapt ...

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our ...

We introduce a new approach for the implementation of minimum mean-square error (MMSE) denoising for signals with decoupled derivatives. Our method casts the problem as a penalized least-squares regression in the redundant wavelet domain. It exploits the l ...

We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gra ...

We develop a variational algorithm for reconstructing phase objects from a series of bright field micrographs. Our mathematical model is based on the transport-of-intensity equation (TIE), which links the phase of a complex field to the axial derivative of ...

The steerable wavelet transform is a redundant image representation with the remarkable property that its basis functions can be adaptively rotated to a desired orientation. This makes the transform well-suited to the design of wavelet-based algorithms app ...

It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of ...

Cycle spinning is a widely used approach for improving the performance of wavelet-based methods that solve linear inverse problems. Extensive numerical experiments have shown that it significantly improves the quality of the recovered signal without increa ...

Emrah Bostan

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Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Reconstruction Of Biomedical Images And Sparse Stochastic Modeling

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Wavelet Shrinkage With Consistent Cycle Spinning Generalizes Total Variation Denoising

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Divergence-Free Wavelet Frames

Spatio-Temporal Regularization Of Flow-Fields

Autocalibrated Signal Reconstruction From Linear Measurements Using Adaptive Gamp

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

Generalized Total Variation Denoising Via Augmented Lagrangian Cycle Spinning With Haar Wavelets

Digital Phase Reconstruction via Iterative Solutions of Transport-of-Intensity Equation

Benefits of consistency in image denoising with steerable wavelets

Wavelet Statistics of Sparse and Self-Similar Images

Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems