Previous reports have shown that the variance in ultrasound attenuation measurements is reduced when spatial and frequency compounding were applied in data acquisition and analysis. This paper investigates factors affecting the efficiency of compound attenuation imaging methods. A theoretical expression is derived that predicts the correlation between attenuation versus frequency slope (β) estimates as a function of the increment between measurement frequencies (Δf ) and the angular separation between beam lines (Δθ). Theoretical results are compared with those from attenuation measurements on tissue-mimicking phantoms and from simulation data. Both predictions and measurement results show that the correlation between β estimates as a function of (Δf ) is independent of the length of the radio frequency (rf) data segment over which β is derived. However, it decreases with an increase in the length of the data segment used in power spectra estimates. In contrast, the correlation between β estimates as a function of Δθ decreases when the rf data segment length is longer or the frequency of the signal is higher.

1.
R.
Kuc
, “
Clinical application of an ultrasound attenuation coefficient estimation technique for liver pathology characterization
,”
IEEE Trans. Biomed. Eng.
27
,
312
319
(
1980
).
2.
Z. F.
Lu
,
J. A.
Zagzebski
, and
F. T.
Lee
, “
Ultrasound backscatter and attenuation in human liver with diffuse disease
,”
Ultrasound Med. Biol.
25
,
1047
1054
(
1999
).
3.
A. T.
Stavros
,
D.
Thickman
,
C. L.
Rapp
,
M. A.
Dennis
,
S. H.
Parker
, and
G. A.
Sisney
, “
Solid breast nodules: use of sonography to distinguish between benign and malignant lesions
,”
Radiology
196
,
123
134
(
1995
).
4.
P. M.
Lamb
,
N. M.
Perry
,
S. J.
Vinnicombe
, and
C. A.
Wells
, “
Correlation between ultrasound characteristics, mammographic findings and histological grade in patients with invasive ductal carcinoma of the breast
,”
Clin. Radiol.
55
,
40
44
(
2000
).
5.
J. G.
Miller
,
J. E.
Perez
,
J. G.
Mottley
,
E. I.
Madaras
,
P. H.
Johnston
,
E. D.
Blodgett
,
L. J. Thomas
III
, and
B. E.
Sobel
, “
Myocardial tissue characterization: an approach based on quantitative backscatter and attenuation
,”
Proc.-IEEE Ultrason. Symp.
83
,
782
793
(
1983
).
6.
S. L.
Bridal
,
P.
Fornes
,
P.
Bruneval
, and
G.
Berger
, “
Parametric (intergrated backscatter and attenuation) images constructed using backscattered radio frequency signals (25-56 MHz) from human aorte in vitro
,”
Ultrasound Med. Biol.
23
,
215
229
(
1997
).
7.
S. W.
Flax
,
N. J.
Pelc
,
G. H.
Glover
,
F. D.
Gutmann
, and
M.
McLachlan
, “
Spectral Characterization and Attenuation Measurements in Ultrasound
,”
Ultrason. Imaging
5
,
95
116
(
1983
).
8.
P.
He
and
J. F.
Greenleaf
, “
Application of stochastic-analysis to ultrasonic echoes—estimation of attenuation and tissue heterogeneity from peaks of echo envelope
,”
J. Acoust. Soc. Am.
79
,
526
534
(
1986
).
9.
E.
Walach
,
A.
Shmulewitz
,
Y.
Itzchak
, and
Z.
Heyman
, “
Local tissue attenuation images based on pulse-echo ultrasound scans
,”
IEEE Trans. Biomed. Eng.
36
,
211
221
(
1989
).
10.
B. S.
Knipp
,
J. A.
Zagzebski
,
T. A.
Wilson
,
F.
Dong
, and
E. L.
Madsen
, “
Attenuation and backscatter estimation using video signal analysis applied to B-mode images
,”
Ultrason. Imaging
19
,
221
233
(
1997
).
11.
R.
Kuc
and
M.
Schwartz
, “
Estimating the acoustic attenuation coefficient slope for liver from reflected ultrasound signals
,”
IEEE Trans. Sonics Ultrason.
SU-26
,
353
362
(
1979
).
12.
M. J. T. M.
Cloostermans
and
J. M.
Thijssen
, “
A beam corrected estimation of the frequency dependent attenuation of biological tissues from backscattered ultrasound
,”
Ultrason. Imaging
5
,
136
147
(
1983
).
13.
L. X.
Yao
,
J. A.
Zagzebski
, and
E. L.
Madsen
, “
Backscatter coefficient measurements using a reference phantom to extract depth-dependent instrumentation factors
,”
Ultrason. Imaging
12
,
58
70
(
1990
).
14.
M.
Fink
,
F.
Hottier
, and
J. F.
Cardoso
, “
Ultrasonic signal processing for in vivo attenuation measurement: Short time Fourier analysis
,”
Ultrason. Imaging
5
,
117
135
(
1983
).
15.
H.
Tu
,
T.
Varghese
,
E. L.
Madsen
,
Q.
Chen
, and
J. A.
Zagzebski
, “
Ultrasound attenuation imaging using compound acquistion and processing
,”
Ultrason. Imaging
25
,
245
261
(
2003
).
16.
L. X.
Yao
,
J. A.
Zagzebski
, and
E. L.
Madsen
, “
Statistical uncertainty inultrasonic backscatter and attenuation coefficients determined with a reference phantom
,”
Ultrasound Med. Biol.
17
,
187
194
(
1991
).
17.
R. F.
Wagner
,
S. W.
Smith
,
J. M.
Sandrick
, and
H.
Lopez
, “
Statistics of speckle in ultrasound B-scans
,”
IEEE Trans. Sonics Ultrason.
30
,
156
163
(
1983
).
18.
R. R.
Entrekin
,
B. A.
Porter
,
H. H.
Sillesen
,
A. D.
Wong
,
P. L.
Cooperberg
, and
C. H.
Fix
, “
Real-time spatial compound imaging: application to breast, vascular, and musculoskeletal ultrasound
,”
Semin Ultrasound CT MR
22
,
50
64
(
2001
).
19.
A. L.
Gerig
,
T.
Varghese
, and
J. A.
Zagzebski
, “
Improved parametric imaging of scatterer size estimates using angular compounding
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
51
,
708
715
(
2004
).
20.
P. A.
Magnin
,
O. T.
von Ramm
, and
F. L.
Thurstone
, “
Frequency compounding for speckle contrast reduction in phased-array Images
,”
Ultrason. Imaging
4
,
267
281
(
1982
).
21.
G. E.
Trahey
,
J. W.
Allison
,
S. W.
Smith
, and
O. T.
von Ramm
, “
A quantitative approach to speckle reduction via frequency compounding
,”
Ultrason. Imaging
8
,
151
164
(
1986
).
22.
M.
O’Donnell
and
S. D.
Silverstein
, “
Optimum displacement for compound image generation in medical ultrasound
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
35
,
470
476
(
1988
).
23.
A. L.
Gerig
,
Q.
Chen
, and
J. A.
Zagzebski
, “
Correlation of ultrasonic scatterer size estimates for the statistical analysis and optimization of angular compounding
,”
J. Acoust. Soc. Am.
116
,
1832
1841
(
2004
).
24.
P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).
25.
A. L.
Gerig
,
J. A.
Zagzebski
, and
T.
Varghese
, “
Statistics of ultrasonic scatterer size estimation with a reference phantom
,”
J. Acoust. Soc. Am.
113
,
3430
3437
(
2002
).
26.
P.
Chaturvedi
and
M. F.
Insana
, “
Error bounds on ultrasonic scatter size estimates
,”
J. Acoust. Soc. Am.
100
,
392
399
(
1996
).
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