[Paper Review] Proceedings of the third "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'16)

Abrol, V., Absil, O.+59 more|arXiv (Cornell University)|Sep 14, 2016

Data Management and Algorithms6 references3 citations

TL;DR

This proceedings volume from iTWIST'16 presents cutting-edge research on sparse modeling and its technological applications, featuring 24 peer-reviewed contributions on topics including compressive sensing, blind deconvolution, sparse machine learning, and inverse problems. The work advances theoretical foundations and practical implementations across domains such as medical imaging, astronomy, and signal processing, with key results in improved recovery accuracy, faster algorithms, and novel sparsity-promoting priors.

ABSTRACT

The third edition of the "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) took place in Aalborg, the 4th largest city in Denmark situated beautifully in the northern part of the country, from the 24th to 26th of August 2016. The workshop venue was at the Aalborg University campus. One implicit objective of this biennial workshop is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For this third edition, iTWIST'16 gathered about 50 international participants and features 8 invited talks, 12 oral presentations, and 12 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing (e.g., optics, computer vision, genomics, biomedical, digital communication, channel estimation, astronomy); Application of sparse models in non-convex/non-linear inverse problems (e.g., phase retrieval, blind deconvolution, self calibration); Approximate probabilistic inference for sparse problems; Sparse machine learning and inference; "Blind" inverse problems and dictionary learning; Optimization for sparse modelling; Information theory, geometry and randomness; Sparsity? What's next? (Discrete-valued signals; Union of low-dimensional spaces, Cosparsity, mixed/group norm, model-based, low-complexity models, ...); Matrix/manifold sensing/processing (graph, low-rank approximation, ...); Complexity/accuracy tradeoffs in numerical methods/optimization; Electronic/optical compressive sensors (hardware).

Motivation & Objective

• To explore and extend the theoretical and practical boundaries of sparse modeling in signal and image reconstruction.
• To address challenges in non-convex and blind inverse problems using sparsity-promoting optimization and probabilistic inference.
• To develop efficient algorithms for compressive sensing, low-rank approximation, and sparse recovery in high-dimensional data.
• To integrate sparsity with physical models in applications such as MRI, hyperspectral imaging, and PET reconstruction.
• To investigate new sparsity structures, including group sparsity, cosparsity, and hierarchical priors, for improved signal representation and recovery.

Proposed method

• Employing synthesis and analysis sparsity models for signal representation in inverse problems.
• Applying non-convex optimization techniques, such as non-convex relaxation and proximal algorithms, to enhance recovery performance.
• Introducing hierarchical Bayesian priors, including Student-t and generalized restricted Boltzmann machines, for robust sparsity enforcement.
• Developing fast algorithms for sparse linear prediction and low-rank matrix recovery using convex optimization and manifold learning.
• Utilizing Bézier functions and manifold interpolation for geometric modeling of sparse signals.
• Implementing active screening and threshold learning strategies in iterative solvers like FISTA to accelerate convergence.

Experimental results

Research questions

• RQ1 How can sparsity be effectively leveraged to improve recovery in blind deconvolution and phase retrieval problems?
• RQ2 What are the theoretical and practical limits of sparse recovery under non-convex and non-linear constraints?
• RQ3 How can hierarchical and group sparsity models enhance reconstruction accuracy in medical and astronomical imaging?
• RQ4 In what ways can probabilistic inference and Bayesian methods improve robustness in compressed sensing with noisy or corrupted data?
• RQ5 How can sparsity be combined with physical models to enable direct, physics-driven reconstruction in dynamic MRI and spectral CT?

Key findings

• A non-convex approach to blind calibration in linear random sensing models demonstrated improved robustness and accuracy over convex alternatives.
• Sparse support recovery using ℓ∞ data fidelity achieved better performance in high-noise regimes compared to standard ℓ2-based methods.
• The use of generalized restricted Boltzmann machines enabled effective compressed sensing recovery with improved generalization on synthetic and real data.
• A fast algorithm for high-order sparse linear prediction reduced computational complexity while maintaining accuracy in audio and speech processing applications.
• Incorporating anatomical priors into blind PET deconvolution significantly enhanced image resolution and reduced artifacts.
• A student-t based hierarchical prior enabled robust 2D and 3D computed tomography reconstruction with reduced Gibbs artifacts and improved edge preservation.