Jérôme Idier

Yuxin Zhang, Clément Huneau, Jérôme Idier et al.

Ultrasound image reconstruction can be approximately cast as a linear inverse problem that has traditionally been solved with penalized optimization using the $l_1$ or $l_2$ norm, or wavelet-based terms. However, such regularization functions often struggle to balance the sparsity and the smoothness. A promising alternative is using learned priors to make the prior knowledge closer to reality. In this paper, we rely on learned priors under the framework of Denoising Diffusion Restoration Models (DDRM), initially conceived for restoration tasks with natural images. We propose and test two adaptions of DDRM to ultrasound inverse problem models, DRUS and WDRUS. Our experiments on synthetic and PICMUS data show that from a single plane wave our method can achieve image quality comparable to or better than DAS and state-of-the-art methods. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/DRUS-v1.

Yuxin Zhang, Clément Huneau, Jérôme Idier et al.

Ultrasound imaging, despite its widespread use in medicine, often suffers from various sources of noise and artifacts that impact the signal-to-noise ratio and overall image quality. Enhancing ultrasound images requires a delicate balance between contrast, resolution, and speckle preservation. This paper introduces a novel approach that integrates adaptive beamforming with denoising diffusion-based variance imaging to address this challenge. By applying Eigenspace-Based Minimum Variance (EBMV) beamforming and employing a denoising diffusion model fine-tuned on ultrasound data, our method computes the variance across multiple diffusion-denoised samples to produce high-quality despeckled images. This approach leverages both the inherent multiplicative noise of ultrasound and the stochastic nature of diffusion models. Experimental results on a publicly available dataset demonstrate the effectiveness of our method in achieving superior image reconstructions from single plane-wave acquisitions. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/IUS2024_Diffusion.

J. Duan, Charles Soussen, David Brie et al.

The $\ell$-1 norm based optimization is widely used in signal processing, especially in recent compressed sensing theory. This paper studies the solution path of the $\ell$-1 norm penalized least-square problem, whose constrained form is known as Least Absolute Shrinkage and Selection Operator (LASSO). A solution path is the set of all the optimizers with respect to the evolution of the hyperparameter (Lagrange multiplier). The study of the solution path is of great significance in viewing and understanding the profile of the tradeoff between the approximation and regularization terms. If the solution path of a given problem is known, it can help us to find the optimal hyperparameter under a given criterion such as the Akaike Information Criterion. In this paper we present a sufficient condition on $\ell$-1 norm penalized least-square problem. Under this sufficient condition, the number of nonzero entries in the optimizer or solution vector increases monotonically when the hyperparameter decreases. We also generalize the result to the often used total variation case, where the $\ell$-1 norm is taken over the first order derivative of the solution vector. We prove that the proposed condition has intrinsic connections with the condition given by Donoho, et al \cite{Donoho08} and the positive cone condition by Efron {\it el al} \cite{Efron04}. However, the proposed condition does not need to assume the sparsity level of the signal as required by Donoho et al's condition, and is easier to verify than Efron, et al's positive cone condition when being used for practical applications.

Paul-André Barrière, Jérôme Idier, Yves Goussard et al.

This paper deals with improvements to the contrast source inversion method which is widely used in microwave tomography. First, the method is reviewed and weaknesses of both the criterion form and the optimization strategy are underlined. Then, two new algorithms are proposed. Both of them are based on the same criterion, similar but more robust than the one used in contrast source inversion. The first technique keeps the main characteristics of the contrast source inversion optimization scheme but is based on a better exploitation of the conjugate gradient algorithm. The second technique is based on a preconditioned conjugate gradient algorithm and performs simultaneous updates of sets of unknowns that are normally processed sequentially. Both techniques are shown to be more efficient than original contrast source inversion.

Yuxin Zhang, Clément Huneau, Jérôme Idier et al.

Despite its wide use in medicine, ultrasound imaging faces several challenges related to its poor signal-to-noise ratio and several sources of noise and artefacts. Enhancing ultrasound image quality involves balancing concurrent factors like contrast, resolution, and speckle preservation. In recent years, there has been progress both in model-based and learning-based approaches to improve ultrasound image reconstruction. Bringing the best from both worlds, we propose a hybrid approach leveraging advances in diffusion models. To this end, we adapt Denoising Diffusion Restoration Models (DDRM) to incorporate ultrasound physics through a linear direct model and an unsupervised fine-tuning of the prior diffusion model. We conduct comprehensive experiments on simulated, in-vitro, and in-vivo data, demonstrating the efficacy of our approach in achieving high-quality image reconstructions from a single plane wave input and in comparison to state-of-the-art methods. Finally, given the stochastic nature of the method, we analyse in depth the statistical properties of single and multiple-sample reconstructions, experimentally show the informativeness of their variance, and provide an empirical model relating this behaviour to speckle noise. The code and data are available at: (upon acceptance).

Yuxin Zhang, Clément Huneau, Jérôme Idier et al.

Despite today's prevalence of ultrasound imaging in medicine, ultrasound signal-to-noise ratio is still affected by several sources of noise and artefacts. Moreover, enhancing ultrasound image quality involves balancing concurrent factors like contrast, resolution, and speckle preservation. Recently, there has been progress in both model-based and learning-based approaches addressing the problem of ultrasound image reconstruction. Bringing the best from both worlds, we propose a hybrid reconstruction method combining an ultrasound linear direct model with a learning-based prior coming from a generative Denoising Diffusion model. More specifically, we rely on the unsupervised fine-tuning of a pre-trained Denoising Diffusion Restoration Model (DDRM). Given the nature of multiplicative noise inherent to ultrasound, this paper proposes an empirical model to characterize the stochasticity of diffusion reconstruction of ultrasound images, and shows the interest of its variance as an echogenicity map estimator. We conduct experiments on synthetic, in-vitro, and in-vivo data, demonstrating the efficacy of our variance imaging approach in achieving high-quality image reconstructions from single plane-wave acquisitions and in comparison to state-of-the-art methods. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/DRUSvar

Ramzi Ben Mhenni, Sébastien Bourguignon, Jérôme Idier

In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on solving a least-squares optimization problem, penalized by the L_1 norm of the remaining variables. Then, the component with maximum amplitude is selected. Simulation results on difficult sparse deconvolution problems involving a highly correlated dictionary reveal the efficiency of the method, which outperforms popular greedy algorithms and Basis Pursuit Denoising when the solution is sparse.

D. Ge, J. Idier, E. Le Carpentier

This paper proposes and compares two new sampling schemes for sparse deconvolution using a Bernoulli-Gaussian model. To tackle such a deconvolution problem in a blind and unsupervised context, the Markov Chain Monte Carlo (MCMC) framework is usually adopted, and the chosen sampling scheme is most often the Gibbs sampler. However, such a sampling scheme fails to explore the state space efficiently. Our first alternative, the $K$-tuple Gibbs sampler, is simply a grouped Gibbs sampler. The second one, called partially marginalized sampler, is obtained by integrating the Gaussian amplitudes out of the target distribution. While the mathematical validity of the first scheme is obvious as a particular instance of the Gibbs sampler, a more detailed analysis is provided to prove the validity of the second scheme. For both methods, optimized implementations are proposed in terms of computation and storage cost. Finally, simulation results validate both schemes as more efficient in terms of convergence time compared with the plain Gibbs sampler. Benchmark sequence simulations show that the partially marginalized sampler takes fewer iterations to converge than the $K$-tuple Gibbs sampler. However, its computation load per iteration grows almost quadratically with respect to the data length, while it only grows linearly for the $K$-tuple Gibbs sampler.