Description Usage Arguments Value Author(s) References

The distribution of image intensity values *S_i* divided by the noise standard deviation in *K*-space *σ*
in dMRI experiments is assumed
to follow a non-central chi-distribution with *2L* degrees of freedom and noncentrality parameter *η*, where *L* refers to the number of receiver
coils in the system and *σ η* is the signal of interest. This is an idealization in the sense that
each coil is assumed to have the same contribution at each location. For realistic modeling *L* should
be a locally smooth function in voxel space that reflects the varying local influence of the receiver coils in the
the reconstruction algorithm used.

The functions assume *L* to be known and estimate either a local
(function `awslsigmc`

) or global ( function `awssigmc`

)
*σ* employing an assumption of local homogeneity for
the noncentrality parameter *η*.

Function `afsigmc`

implements estimates from Aja-Fernandez (2009).
Function `aflsigmc`

implements the estimate from Aja-Fernandez (2013).

1 2 3 4 5 6 7 8 9 10 | ```
awssigmc(y, steps, mask = NULL, ncoils = 1, vext = c(1, 1), lambda = 20,
h0 = 2, verbose = FALSE, sequence = FALSE, hadj = 1, q = 0.25,
qni = .8, method=c("VAR","MAD"))
awslsigmc(y, steps, mask = NULL, ncoils = 1, vext = c(1, 1), lambda = 5, minni = 2,
hsig = 5, sigma = NULL, family = c("NCchi"), verbose = FALSE,
trace=FALSE, u=NULL)
afsigmc(y, level = NULL, mask = NULL, ncoils = 1, vext = c( 1, 1),
h = 2, verbose = FALSE, hadj = 1,
method = c("modevn","modem1chi","bkm2chi","bkm1chi"))
aflsigmc(y, ncoils, level = NULL, mask = NULL, h=2, hadj=1, vext = c( 1, 1))
``` |

`y` |
3D array, usually obtained from an object of class |

`steps` |
number of steps in adapive weights smoothing, used to reveal the unerlying mean structure. |

`mask` |
restrict computations to voxel in mask, if |

`ncoils` |
number of coils, or equivalently number of effective degrees of freedom of non-central chi distribution divided by 2. |

`vext` |
voxel extentions |

`lambda` |
scale parameter in adaptive weights smoothing |

`h0` |
initial bandwidth |

`verbose` |
if |

`trace` |
if |

`sequence` |
if |

`hadj` |
adjustment factor for bandwidth (chosen by |

`q` |
quantile to be used for interquantile-differences. |

`qni` |
quantile of distribution of actual sum of weights |

`method` |
in case of function |

`level` |
threshold for background separation. Used if |

`h` |
bandwidth for local avaeraging |

`minni` |
Minimum sum of weights for updating values of |

`hsig` |
Bandwidth of the median filter. |

`sigma` |
Initial estimate for |

`family` |
One of |

`u` |
if |

a list with components

`sigma` |
either a scalar or a vector of estimated noise standard deviations. |

`theta` |
the estimated mean structure |

J\"org Polzehl [email protected]

K. Tabelow and J. Polzehl (2013). Estimating the noise level in MRI using structural adaptive smoothing. Manuscript in preparation.

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