# Sparse MRI: The application of compressed sensing for rapid MR imaging.

##### Citations

4,869 citations

### Cites background from "Sparse MRI: The application of comp..."

...The implications of these facts are quite far-reaching, with potential applications in data compression [24, 28], digital photography [29], medical imaging [23, 30], error correction [31, 32], analog-todigital conversion [33], sensor networks [34, 35], and so on....

[...]

4,255 citations

### Cites background or methods from "Sparse MRI: The application of comp..."

...The goal of sparse MRI is to solve min u J(u) such that ‖Fu− f‖2 = 0....

[...]

...The general form for the Sparse MRI reconstruction problem is presented and discussed in [16], [14] and [23]....

[...]

...Note that, while ideal for compressed sensing, this type of sampling is not practical for most MRI applications....

[...]

...The particular application of compressed sensing which we will focus on is MR image reconstruction, or “Sparse MRI” [16, 14]....

[...]

...This is because most pulse sequences acquire k -space data in some sort of geometric pattern, such as a spiral [18, 24, 16]....

[...]

3,488 citations

2,412 citations

### Cites background from "Sparse MRI: The application of comp..."

...For more information on compressed sensing MRI refer to [73] and the references therein....

[...]

...Such algorithms have potential applications in fields ranging from medical imaging to astronomy [73, 15]....

[...]

2,372 citations

### Cites methods from "Sparse MRI: The application of comp..."

...Figure 5 presents compressed sensing of dynamic MRI—real-time acquisition of heart motion—by Michael Lustig and coworkers at the Stanford MRI lab [112, 111]....

[...]

##### References

[...]

18,609 citations

15,225 citations

14,587 citations

9,950 citations

### "Sparse MRI: The application of comp..." refers methods in this paper

...Proposed methods include: interior point methods (28, 30), projections onto convex sets (26), homotopy (Donoho et....

[...]

...Minimizing ||Ψm||1 promotes sparsity (28)....

[...]

8,153 citations