Ordinator

Combinatorial optimization to find permutation maximizing sparsity.

mr_utils.cs.ordinator.get_xhat(locs, N, k, inverse, pdf_ref, pdf, pdf_metric)[source]

Compute xhat for given coefficient locs using basinhopping.

Parameters:
  • locs (array_like) – Coefficient location indices.
  • N (int) – Length of the desired signal (also number of coefficients in total).
  • k (int) – Desired sparsity level.
  • inverse (callable) – Inverse sparsifying transform.
  • pdf_ref (array_like) – Reference pdf of the prior to compare against.
  • pdf (callable) – Function that estimates pixel intensity distribution.
  • pdf_metric (callable) – Function that returns the distance between pdfs.
Returns:

  • xhat (array_like) – Inverse transform of coeffs.
  • locs (array_like) – Indices of non-zero coefficients.
  • coeffs (array_like) – Coefficients of xhat.
mr_utils.cs.ordinator.obj(ck, N, locs, inverse, pdf_ref, pdf, pdf_metric)[source]

Objective function for basinhopping.

mr_utils.cs.ordinator.ordinator1d(prior, k, forward, inverse, chunksize=10, pdf=None, pdf_metric=None, sparse_metric=None, disp=False)[source]

Find permutation that maximizes sparsity of 1d signal.

Parameters:
  • prior (array_like) – Prior signal estimate to base ordering.
  • k (int) – Desired sparsity level.
  • forward (callable) – Sparsifying transform.
  • inverse (callable) – Inverse sparsifying transform.
  • chunksize (int, optional) – Chunk size for parallel processing pool.
  • pdf (callable, optional) – Function that estimates pixel intensity distribution.
  • pdf_metric (callable, optional) – Function that returns the distance between pdfs.
  • sparse_metric (callable, optional) – Metric to use to measure sparsity. Uses l1 norm by default.
  • disp (bool, optional) – Whether or not to display coefficient plots at the end.
Returns:

Reordering indices.
Return type:

array_like
Raises:

ValueError – If disp=True and forward function is not provided.

Notes

pdf_method=None uses histogram. pdf_metric=None uses l2 norm. If disp=True then forward transform function must be provided. Otherwise, forward is not required, only inverse.

pdf_method should assume the signal will be bounded between (-1, 1). We do this by always normalizing a signal before computing pdf or comparing.

class mr_utils.cs.ordinator.pdf_default(prior)[source]

Picklable object for computing pdfs.

Uses histogram to estimate pdf.

N

Size of signal.

Type:int
lims

Upper and lower bounds for range of histogram.

Type:array_like or tuple
pdf_ref

pdf estimate of prior. Used to compare to pdf(xhat).

Type:array_like
bins

bin locations used for construction of pdf_ref.

Type:array_like
pdf(x)[source]

Estimate the pdf of x.

Parameters:x (array_like) – Signal to get pdf estimate of.
Returns:Histogram of x.
Return type:array_like

Notes

Will report when xhat has a value outside of range of pdf_ref.

mr_utils.cs.ordinator.pdf_metric_default(x, y)[source]

Default pdf metric, l2 norm.

Parameters:
  • x (array_like) – First pdf.
  • y (array_like) – Second pdf.
Returns:

l2 norm between x and y.
Return type:

float
mr_utils.cs.ordinator.search_fun(locs, N, k, inverse, pdf_ref, pdf, pdf_metric)[source]

Return function for parallel loop.

Parameters:
  • locs (array_like) – Coefficient location indices.
  • N (int) – Length of the desired signal (also number of coefficients in total).
  • k (int) – Desired sparsity level.
  • inverse (callable) – Inverse sparsifying transform.
  • pdf_ref (array_like) – Reference pdf of the prior to compare against.
  • pdf (callable) – Function that estimates pixel intensity distribution.
  • pdf_metric (callable) – Function that returns the distance between pdfs.
Returns:

  • locs (array_like) – Indices of non-zero coefficients.
  • vals (array_like) – Values of coefficients at locations given by locs.
  • float – Measure of difference between pdf_ref and pdf(xhat).