RECORD
An algorithm for variable density sampling with block-constrained acquisition
Information Theory · Submitted 16 Oct 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Finally, we show that we can obtain better MRI reconstruction results using our sampling schemes than standard strategies such as equiangularly distributed radial lines.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the compressed sensing (CS) literature. Unfortunately, the sampling schemes suggested by current CS theories may not be relevant since they do not take the acquisition constraints into account (for example, continuity of the acquisition trajectory in Magnetic Resonance Imaging - MRI). In this paper, we propose a numerical method to perform variable density sampling with block constraints. Our main contribution is to propose a new way to draw the blocks in order to mimic CS strategies based on isolated measurements. The basic idea is to minimize a tailored dissimilarity measure between a probability distribution defined on the set of isolated measurements and a probability distribution defined on a set of blocks of measurements. This problem turns out to be convex and solvable in high dimension. Our second contribution is to define an efficient minimization algorithm based on Nesterov's accelerated gradient descent in metric spaces. We study carefully the choice of the metrics and of the prox function. We show that the optimal choice may depend on the type of blocks under consideration. Finally, we show that we can obtain better MRI reconstruction results using our sampling schemes than standard strategies such as equiangularly distributed radial lines.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Reducing acquisition time is of fundamental importance in various imaging modalities. | background 1.00 | 0.04 | 0.01 | asserted 1.00 |
| s1 | The concept of variable density sampling provides a nice framework to achieve this. | background 1.00 | 0.05 | 0.02 | asserted 0.90 |
| s2 | It was justified recently from a theoretical point of view in the compressed sensing (CS) literature. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s3 | Unfortunately, the sampling schemes suggested by current CS theories may not be relevant since they do not take the acquisition constraints into account (for example, continuity of the acquisition trajectory in Magnetic Resonance Imaging - MRI). | gap 0.98 | 0.07 | 0.02 | hedged possibility 0.95 |
| s4 | In this paper, we propose a numerical method to perform variable density sampling with block constraints. | contribution 0.99 | 0.92 | 0.07 | asserted 1.00 |
| s5 | Our main contribution is to propose a new way to draw the blocks in order to mimic CS strategies based on isolated measurements. | contribution 1.00 | 0.92 | 0.34 | asserted 1.00 |
| s6 | The basic idea is to minimize a tailored dissimilarity measure between a probability distribution defined on the set of isolated measurements and a probability distribution defined on a set of blocks of measurements. | method 0.95 | 0.68 | 0.06 | asserted 1.00 |
| s7 | This problem turns out to be convex and solvable in high dimension. | result 0.69 | 0.82 | 0.06 | asserted 1.00 |
| s8 | Our second contribution is to define an efficient minimization algorithm based on Nesterov's accelerated gradient descent in metric spaces. | contribution 0.97 | 0.95 | 0.06 | asserted 1.00 |
| s9 | We study carefully the choice of the metrics and of the prox function. | contribution 0.64 | 0.93 | 0.03 | asserted 0.88 |
| s10 | We show that the optimal choice may depend on the type of blocks under consideration. | result 0.76 | 0.92 | 0.05 | hedged possibility 0.74 |
| s11 | Finally, we show that we can obtain better MRI reconstruction results using our sampling schemes than standard strategies such as equiangularly distributed radial lines. | result 1.00 | 0.96 | 0.66 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the compressed sensing (CS) literature. Unfortunately, the sampling schemes suggested by current CS theories may not be relevant since they do not take the acquisition constraints into account (for example, continuity of the acquisition trajectory in Magnetic Resonance Imaging - MRI). In this paper, we propose a numerical method to perform variable density sampling with block constraints. Our main contribution is to propose a new way to draw the blocks in order to mimic CS strategies based on isolated measurements. The basic idea is to minimize a tailored dissimilarity measure between a probability distribution defined on the set of isolated measurements and a probability distribution defined on a set of blocks of measurements. This problem turns out to be convex and solvable in high dimension. Our second contribution is to define an efficient minimization algorithm based on Nesterov's accelerated gradient descent in metric spaces. We study carefully the choice of the metrics and of the prox function. We show that the optimal choice may depend on the type of blocks under consideration. Finally, we show that we can obtain better MRI reconstruction results using our sampling schemes than standard strategies such as equiangularly distributed radial lines.
Human review
How the literature uses it
2 arXiv papers cite this in 8 sentences
Papers citing it · 5 sentences without a confident label
Builds on it 1 paper
-
In this paper, we extend the setting of block-structured sensing introduced in [ref] and also considered in [ref] to the case where the blocks are not identically distributed and in which some of them can be deterministically chosen.
On oracle-type local recovery guarantees in compressed sensing · Contributions · 1.00
Compares with it 1 paper
-
In comparison, Proposition 4.6 in [ref] (with no structured sparsity) requires [equation] measurements, to get the same guarantees.
Compressed sensing with structured sparsity and structured acquisition · Breaking the limits with adapted structured sparsity · 1.00
Cites it as background 1 paper
-
In [ref] , the authors provided theoretical CS results when using block-constrained acquisitions.
Compressed sensing with structured sparsity and structured acquisition · The limits of structured acquisition · 0.89
What it cites · 10 sentences without a confident label
Cites as background 2 papers
-
The problem of choosing a distribution $$ leading to good image reconstruction is not addressed in this paper, since there already exist various theoretical results and heuristic strategies in the CS literature on this topic [ref] .
Stable and robust sampling strategies for compressive imaging · Problem setting · 0.99
-
The problem of choosing a distribution $$ leading to good image reconstruction is not addressed in this paper, since there already exist various theoretical results and heuristic strategies in the CS literature on this topic [ref] .
Breaking the coherence barrier: A new theory for compressed sensing · Problem setting · 0.99
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.