Non-Gaussian statistical properties of breast images

Craig K. Abbey, Anita Nosrateih, Jascha Sohl-Dickstein, Kai Yang, John M Boone

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Purpose: Several studies have shown that the power spectrum of x-ray breast images is well described by a power-law at lower frequencies where anatomical variability dominates. However, an image generated from a Gaussian process with this spectrum is easily distinguished from an image of actual breast tissue by eye. This demonstrates that higher order non-Gaussian statistical properties of mammograms are readily accessible to the visual system. The authors' purpose is to quantify and characterize non-Gaussian statistical properties of breast images as influenced by processing of a digital mammogram, different imaging modalities, and breast density. Methods: To quantify non-Gaussian statistical properties, the authors consider histograms of filter responses from the interior of a breast image that have similar properties to receptive fields in the early visual system. They quantify departure from a Gaussian distribution by the relative entropy of the histogram compared to a best-fit Gaussian distribution. This entropy is normalized by the relative entropy of a best-fit Laplacian distribution into a measure they refer to as Laplacian fractional entropy (LFE). They test the LFE on a set of 26 patients recalled at screening for which they have available full-field digital mammography (FFDM), digital breast tomosynthesis (DBT), and dedicated breast CT (bCT) images as well as breast density scores and biopsy results. Results: A study of LFE in FFDM comparing the raw for-processing transmission data from the device to log-converted density estimates and the processed for-display data shows that processing mammographic image data enhances the non-Gaussian content of the image. A check of the methodology using a Gaussian process with a power-law power spectrum shows relatively little bias from the finite extent of the region of interests used. A second study comparing LFE across FFDM, DBT, and bCT modalities shows that each maximized the non-Gaussian content of the image for different ranges of spatial frequency. FFDM is optimal at high spatial frequencies (>0.7 mm-1), DBT is optimal at mid-range frequencies (0.3-0.7 mm-1), and bCT is optimal at low spatial frequency (0.3 mm-1). A third study of breast density in FFDM and bCT shows that LFE generally rises slightly going from the low-to moderate density, and then falls considerably at higher densities. Conclusions: Non-Gaussian statistical structure in breast images that is manifest in the responses of Gabor filters similar to receptive fields of the early visual system is dependent on how the image data are processed, the modality used to acquire the image, and the density of the breast tissue being imaged. Higher LFE corresponds with expected improvements from image processing and 3D imaging.

Original languageEnglish (US)
Pages (from-to)7121-7130
Number of pages10
JournalMedical Physics
Volume39
Issue number11
DOIs
StatePublished - Nov 2012

Fingerprint

Entropy
Mammography
Breast
Normal Distribution
Data Display
Visual Fields
X-Rays
Biopsy
Equipment and Supplies
Breast Density

Keywords

  • anatomical noise
  • breast texture
  • image statistics
  • relative entropy

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging

Cite this

Abbey, C. K., Nosrateih, A., Sohl-Dickstein, J., Yang, K., & Boone, J. M. (2012). Non-Gaussian statistical properties of breast images. Medical Physics, 39(11), 7121-7130. https://doi.org/10.1118/1.4761869

Non-Gaussian statistical properties of breast images. / Abbey, Craig K.; Nosrateih, Anita; Sohl-Dickstein, Jascha; Yang, Kai; Boone, John M.

In: Medical Physics, Vol. 39, No. 11, 11.2012, p. 7121-7130.

Research output: Contribution to journalArticle

Abbey, CK, Nosrateih, A, Sohl-Dickstein, J, Yang, K & Boone, JM 2012, 'Non-Gaussian statistical properties of breast images', Medical Physics, vol. 39, no. 11, pp. 7121-7130. https://doi.org/10.1118/1.4761869
Abbey CK, Nosrateih A, Sohl-Dickstein J, Yang K, Boone JM. Non-Gaussian statistical properties of breast images. Medical Physics. 2012 Nov;39(11):7121-7130. https://doi.org/10.1118/1.4761869
Abbey, Craig K. ; Nosrateih, Anita ; Sohl-Dickstein, Jascha ; Yang, Kai ; Boone, John M. / Non-Gaussian statistical properties of breast images. In: Medical Physics. 2012 ; Vol. 39, No. 11. pp. 7121-7130.
@article{c2d6c78596a24553863c687b61e32712,
title = "Non-Gaussian statistical properties of breast images",
abstract = "Purpose: Several studies have shown that the power spectrum of x-ray breast images is well described by a power-law at lower frequencies where anatomical variability dominates. However, an image generated from a Gaussian process with this spectrum is easily distinguished from an image of actual breast tissue by eye. This demonstrates that higher order non-Gaussian statistical properties of mammograms are readily accessible to the visual system. The authors' purpose is to quantify and characterize non-Gaussian statistical properties of breast images as influenced by processing of a digital mammogram, different imaging modalities, and breast density. Methods: To quantify non-Gaussian statistical properties, the authors consider histograms of filter responses from the interior of a breast image that have similar properties to receptive fields in the early visual system. They quantify departure from a Gaussian distribution by the relative entropy of the histogram compared to a best-fit Gaussian distribution. This entropy is normalized by the relative entropy of a best-fit Laplacian distribution into a measure they refer to as Laplacian fractional entropy (LFE). They test the LFE on a set of 26 patients recalled at screening for which they have available full-field digital mammography (FFDM), digital breast tomosynthesis (DBT), and dedicated breast CT (bCT) images as well as breast density scores and biopsy results. Results: A study of LFE in FFDM comparing the raw for-processing transmission data from the device to log-converted density estimates and the processed for-display data shows that processing mammographic image data enhances the non-Gaussian content of the image. A check of the methodology using a Gaussian process with a power-law power spectrum shows relatively little bias from the finite extent of the region of interests used. A second study comparing LFE across FFDM, DBT, and bCT modalities shows that each maximized the non-Gaussian content of the image for different ranges of spatial frequency. FFDM is optimal at high spatial frequencies (>0.7 mm-1), DBT is optimal at mid-range frequencies (0.3-0.7 mm-1), and bCT is optimal at low spatial frequency (0.3 mm-1). A third study of breast density in FFDM and bCT shows that LFE generally rises slightly going from the low-to moderate density, and then falls considerably at higher densities. Conclusions: Non-Gaussian statistical structure in breast images that is manifest in the responses of Gabor filters similar to receptive fields of the early visual system is dependent on how the image data are processed, the modality used to acquire the image, and the density of the breast tissue being imaged. Higher LFE corresponds with expected improvements from image processing and 3D imaging.",
keywords = "anatomical noise, breast texture, image statistics, relative entropy",
author = "Abbey, {Craig K.} and Anita Nosrateih and Jascha Sohl-Dickstein and Kai Yang and Boone, {John M}",
year = "2012",
month = "11",
doi = "10.1118/1.4761869",
language = "English (US)",
volume = "39",
pages = "7121--7130",
journal = "Medical Physics",
issn = "0094-2405",
publisher = "AAPM - American Association of Physicists in Medicine",
number = "11",

}

TY - JOUR

T1 - Non-Gaussian statistical properties of breast images

AU - Abbey, Craig K.

AU - Nosrateih, Anita

AU - Sohl-Dickstein, Jascha

AU - Yang, Kai

AU - Boone, John M

PY - 2012/11

Y1 - 2012/11

N2 - Purpose: Several studies have shown that the power spectrum of x-ray breast images is well described by a power-law at lower frequencies where anatomical variability dominates. However, an image generated from a Gaussian process with this spectrum is easily distinguished from an image of actual breast tissue by eye. This demonstrates that higher order non-Gaussian statistical properties of mammograms are readily accessible to the visual system. The authors' purpose is to quantify and characterize non-Gaussian statistical properties of breast images as influenced by processing of a digital mammogram, different imaging modalities, and breast density. Methods: To quantify non-Gaussian statistical properties, the authors consider histograms of filter responses from the interior of a breast image that have similar properties to receptive fields in the early visual system. They quantify departure from a Gaussian distribution by the relative entropy of the histogram compared to a best-fit Gaussian distribution. This entropy is normalized by the relative entropy of a best-fit Laplacian distribution into a measure they refer to as Laplacian fractional entropy (LFE). They test the LFE on a set of 26 patients recalled at screening for which they have available full-field digital mammography (FFDM), digital breast tomosynthesis (DBT), and dedicated breast CT (bCT) images as well as breast density scores and biopsy results. Results: A study of LFE in FFDM comparing the raw for-processing transmission data from the device to log-converted density estimates and the processed for-display data shows that processing mammographic image data enhances the non-Gaussian content of the image. A check of the methodology using a Gaussian process with a power-law power spectrum shows relatively little bias from the finite extent of the region of interests used. A second study comparing LFE across FFDM, DBT, and bCT modalities shows that each maximized the non-Gaussian content of the image for different ranges of spatial frequency. FFDM is optimal at high spatial frequencies (>0.7 mm-1), DBT is optimal at mid-range frequencies (0.3-0.7 mm-1), and bCT is optimal at low spatial frequency (0.3 mm-1). A third study of breast density in FFDM and bCT shows that LFE generally rises slightly going from the low-to moderate density, and then falls considerably at higher densities. Conclusions: Non-Gaussian statistical structure in breast images that is manifest in the responses of Gabor filters similar to receptive fields of the early visual system is dependent on how the image data are processed, the modality used to acquire the image, and the density of the breast tissue being imaged. Higher LFE corresponds with expected improvements from image processing and 3D imaging.

AB - Purpose: Several studies have shown that the power spectrum of x-ray breast images is well described by a power-law at lower frequencies where anatomical variability dominates. However, an image generated from a Gaussian process with this spectrum is easily distinguished from an image of actual breast tissue by eye. This demonstrates that higher order non-Gaussian statistical properties of mammograms are readily accessible to the visual system. The authors' purpose is to quantify and characterize non-Gaussian statistical properties of breast images as influenced by processing of a digital mammogram, different imaging modalities, and breast density. Methods: To quantify non-Gaussian statistical properties, the authors consider histograms of filter responses from the interior of a breast image that have similar properties to receptive fields in the early visual system. They quantify departure from a Gaussian distribution by the relative entropy of the histogram compared to a best-fit Gaussian distribution. This entropy is normalized by the relative entropy of a best-fit Laplacian distribution into a measure they refer to as Laplacian fractional entropy (LFE). They test the LFE on a set of 26 patients recalled at screening for which they have available full-field digital mammography (FFDM), digital breast tomosynthesis (DBT), and dedicated breast CT (bCT) images as well as breast density scores and biopsy results. Results: A study of LFE in FFDM comparing the raw for-processing transmission data from the device to log-converted density estimates and the processed for-display data shows that processing mammographic image data enhances the non-Gaussian content of the image. A check of the methodology using a Gaussian process with a power-law power spectrum shows relatively little bias from the finite extent of the region of interests used. A second study comparing LFE across FFDM, DBT, and bCT modalities shows that each maximized the non-Gaussian content of the image for different ranges of spatial frequency. FFDM is optimal at high spatial frequencies (>0.7 mm-1), DBT is optimal at mid-range frequencies (0.3-0.7 mm-1), and bCT is optimal at low spatial frequency (0.3 mm-1). A third study of breast density in FFDM and bCT shows that LFE generally rises slightly going from the low-to moderate density, and then falls considerably at higher densities. Conclusions: Non-Gaussian statistical structure in breast images that is manifest in the responses of Gabor filters similar to receptive fields of the early visual system is dependent on how the image data are processed, the modality used to acquire the image, and the density of the breast tissue being imaged. Higher LFE corresponds with expected improvements from image processing and 3D imaging.

KW - anatomical noise

KW - breast texture

KW - image statistics

KW - relative entropy

UR - http://www.scopus.com/inward/record.url?scp=84868586632&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868586632&partnerID=8YFLogxK

U2 - 10.1118/1.4761869

DO - 10.1118/1.4761869

M3 - Article

VL - 39

SP - 7121

EP - 7130

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 11

ER -