Publications de Pakshal Narendra Bohra

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

Michaël Unser, Dimitris Perdios, Stanislas Ducotterd, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both theoretically and empi ...

2024

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Pakshal Narendra Bohra

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

EPFL2024

Dynamic Fourier ptychography with deep spatiotemporal priors

Michaël Unser, Pakshal Narendra Bohra

Fourier ptychography (FP) involves the acquisition of several low-resolution intensity images of a sample under varying illumination angles. They are then combined into a high-resolution complex-valued image by solving a phase-retrieval problem. The object ...

IOP Publishing Ltd2023

A Neural-Network-Based Convex Regularizer for Inverse Problems

Michaël Unser, Stanislas Ducotterd, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in quality. Unfortunately, these new methods often lack reliability and explainability, and there is a growing interest to address these ...

2023

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems"

Michaël Unser, Stanislas Ducotterd, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems". The corresponding scripts can be accessed on GitHub (https://github.com/axgoujon/convex_ridge_regularizers). The data is organized as follows: - ct_data_sets.tar.gz: contains prepr ...

Zenodo2023

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

Michaël Unser, Pakshal Narendra Bohra, Pol del Aguila Pla

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

2023

Approximation of Lipschitz Functions Using Deep Spline Neural Networks

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

Although Lipschitz-constrained neural networks have many applications in machine learning, the design and training of expressive Lipschitz-constrained networks is very challenging. Since the popular rectified linear-unit networks have provable disadvantage ...

2023

Bayesian Inversion for Nonlinear Imaging Models Using Deep Generative Priors

Michaël Unser, Thanh-An Michel Pham, Pakshal Narendra Bohra, Jonathan Yuelin Dong

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the im ...

2022

Opportunities and Challenges for Generative Adversarial Reconstruction by Distribution Matching (CryoGAN)

Michaël Unser, Pakshal Narendra Bohra

2022

Learning Lipschitz-Controlled Activation Functions in Neural Networks for Plug-and-Play Image Reconstruction Methods

Michaël Unser, Dimitris Perdios, Sébastien Alexandre Emery, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon

Ill-posed linear inverse problems are frequently encountered in image reconstruction tasks. Image reconstruction methods that combine the Plug-and-Play (PnP) priors framework with convolutional neural network (CNN) based denoisers have shown impressive per ...

2021

Computation of "Best" Interpolants in the Lp Sense

Michaël Unser, Pakshal Narendra Bohra

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L p -norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts ...

2020

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

2020

Learning Activation Functions in Deep (Spline) Neural Networks

Michaël Unser, Harshit Gupta, Joaquim Gonçalves Garcia Barreto Campos, Shayan Aziznejad, Pakshal Narendra Bohra

We develop an efficient computational solution to train deep neural networks (DNN) with free-form activation functions. To make the problem well-posed, we augment the cost functional of the DNN by adding an appropriate shape regularization: the sum of the ...

2020