Pakshal Narendra Bohra

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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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Pakshal Narendra Bohra

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

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

Dynamic Fourier ptychography with deep spatiotemporal priors

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

Learning Activation Functions in Deep (Spline) Neural Networks

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

Computation of "Best" Interpolants in the Lp Sense

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

Approximation of Lipschitz Functions Using Deep Spline Neural Networks

A Neural-Network-Based Convex Regularizer for Inverse Problems

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

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