Euclidean distance matrices (EDMs) are matrices of the squared distances between points. The definition is deceivingly simple; thanks to their many useful properties, they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness, and show how the various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes, and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. The code for all of the described algorithms and to generate the figures in the article is available online at http://lcav.epfl.ch/ivan.dokmanic. Finally, we suggest directions for further research.

/pdf/euclidean-distance-matrices-essential-theory-algorithms-and-19dix74lj3.pdf

Euclidean Distance Matrices: Essential theory, algorithms, and applications

Breast density, as assessed by mammography, reflects breast tissue composition. Breast epithelium and stroma attenuate x-rays more than fat and thus appear light on mammograms while fat appears dark. In this review, we provide an overview of selected areas of current knowledge about the relationship between breast density and susceptibility to breast cancer. We review the evidence that breast density is a risk factor for breast cancer, the histological and other risk factors that are associated with variations in breast density, and the biological plausibility of the associations with risk of breast cancer. We also discuss the potential for improved risk prediction that might be achieved by using alternative breast imaging methods, such as magnetic resonance or ultrasound. After adjustment for other risk factors, breast density is consistently associated with breast cancer risk, more strongly than most other risk factors for this disease, and extensive breast density may account for a substantial fraction of breast cancer. Breast density is associated with risk of all of the proliferative lesions that are thought to be precursors of breast cancer. Studies of twins have shown that breast density is a highly heritable quantitative trait. Associations between breast density and variations in breast histology, risk of proliferative breast lesions, and risk of breast cancer may be the result of exposures of breast tissue to both mitogens and mutagens. Characterization of breast density by mammography has several limitations, and the uses of breast density in risk prediction and breast cancer prevention may be improved by other methods of imaging, such as magnetic resonance or ultrasound tomography.

Breast Tissue Composition and Susceptibility to Breast Cancer

Preface.- 1 Fundamentals of acoustic metamaterials.- 2 Locally resonant structures for low frequency surface acoustic band gap applications.- 3 Band-gap properties of prestressed structures.- 4 Ultrasound transmission through periodically perforated plates.- 5 Novel Ultrasound Imaging Applications.- 6 Subwavelength focussing in metamaterials using far field time reversal.- 7 Anisotropic metamaterials for transformation acoustics and imaging.- 8 Transformation Acoustics.- 9 Acoustic Cloaking Via Homogenization.- 10 Acoustic Cloaking with Plasmonic Shells.- 11 Cloaking Liquid Surface Waves and Plasmon Polaritons.- 12 Transformation elastodynamics and active exterior acoustic cloaking.

Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking

We discuss a bent-ray ultrasound tomography algorithm with total-variation (TV) regularization. We have applied this algorithm to 61 in vivo breast datasets collected with our in-house clinical prototype for imaging sound-speed distributions in the breast. Our analysis showed that TV regularization could preserve sharper lesion edges than the classic Tikhonov regularization. Furthermore, the image quality of our TV bent-ray sound-speed tomograms was superior to that of the straight-ray counterparts for all types of breasts within BI-RADS density categories 1 through 4. Our analysis showed that the improvements for average sharpness (in the unit of (m x s)(-1)) of lesion edges in our TV bent-ray tomograms are between 2.1 to 3.4-fold compared with the straight ray tomograms. Reconstructed sound-speed tomograms illustrated that our algorithm could successfully image fatty and glandular tissues within the breast. We calculated the mean sound-speed values for fatty tissue and breast parenchyma as 1422 +/- 9 m/s (mean +/- SD) and 1487 +/- 21 m/s, respectively. Based on 32 lesions in a cohort of 61 patients, we also found that the mean sound-speed for malignant breast lesions (1548 +/- 17 m/s) was higher, on average, than that of benign ones (1513 +/- 27 m/s) (one-sided p<0.001). These results suggest that, clinically, sound-speed tomograms can be used to assess breast density (and therefore, breast cancer risk), as well as detect and help differentiate breast lesions. Finally, our sound-speed tomograms may also be a useful tool to monitor the clinical response of breast cancer patients to neo-adjuvant chemotherapy.

/pdf/in-vivo-breast-sound-speed-imaging-with-ultrasound-4pm0yiln4l.pdf

In vivo breast sound-speed imaging with ultrasound tomography

Due to parallel advances in signal processing and computer hardware in the last 15 years, quantitative ultrasound techniques have reached maturity, allowing for the construction of quantitative maps or images of soft tissues. This book will focus on 5 modern research topics related to quantitative ultrasound of soft tissues: - Spectral-based methods for tissue characterization, tissue typing, cancer detection, etc.; - Envelope statistics analysis as a means of quantifying and imaging tissue properties; - Ultrasound elastography for quantifying elastic properties of tissues (several clinical ultrasound scanners now display elastography images); - Scanning acoustic microscopy for forming images of mechanical properties of soft tissues with micron resolution (desktop size scanners are now available); and - Ultrasound computer tomography for breast cancer imaging (new ultrasound tomography systems have been developed and are currently under evaluation clinically).

/pdf/quantitative-ultrasound-in-soft-tissues-2tpw0mphzl.pdf

Quantitative Ultrasound in Soft Tissues

Although mammography is the gold standard for breast imaging, its limitations result in a high rate of biopsies of benign lesions and a significant false negative rate for women with dense breasts. In response to this imaging performance gap we have been developing a clinical breast imaging methodology based on the principles of ultrasound tomography. The Computed Ultrasound Risk Evaluation (CURE) system has been designed with the clinical goals of whole breast, operator-independent imaging, and differentiation of breast masses. This paper describes the first clinical prototype, summarizes our initial image reconstruction techniques, and presents phantom and preliminary in vivo results. In an initial assessment of its in vivo performance, we have examined 50 women with the CURE prototype and obtained the following results. (1) Tomographic imaging of breast architecture is demonstrated in both CURE modes of reflection and transmission imaging. (2) In-plane spatial resolution of 0.5 mm in reflection and 4 mm in transmission is achieved. (3) Masses > 15 mm in size are routinely detected. (4) Reflection, sound speed, and attenuation imaging of breast masses are demonstrated. These initial results indicate that operator-independent, whole-breast imaging and the detection of breast masses are feasible. Future studies will focus on improved detection and differentiation of masses in support of our long-term goal of increasing the specificity of breast exams, thereby reducing the number of biopsies of benign masses.

Detection of breast cancer with ultrasound tomography: First results with the Computed Ultrasound Risk Evaluation (CURE) prototype

Women with high mammographic breast density have a four- to fivefold increased risk of developing breast cancer compared to women with fatty breasts. Many preventative strategies have attempted to correlate changes in breast density with response to interventions including drugs and diet. The purpose of this work is to investigate the feasibility of assessing breast density with acoustic velocity measurements with ultrasoundtomography, and to compare the results with existing measures of mammographic breast density. An anthropomorphic breast tissue phantom was first imaged with our computed ultrasoundtomography clinical prototype. Strong positive correlations were observed between sound speed and material density, and sound speed and computed tomography number (Pearson correlation coefficients = 0.87 and 0.91, respectively). A cohort of 48 women was then imaged. Whole breast acoustic velocity was determined by creating image stacks and evaluating the sound speed frequency distribution. The acoustic measures of breast density were evaluated by comparing these results to two mammographic density measures: (1) qualitative estimates determined by a certified radiologist using the BI-RADS Categorical Assessment based on a 1 (fatty) to 4 (dense) scale, and (2) quantitative measurements via digitization and computerized analysis of archival mammograms. A one-way analysis of variance showed that a significant difference existed between the mean values of sound speed according to BI-RADS category, while post hoc analyses using the Scheffe criterion for significance indicated that BI-RADS 4 (dense) patients had a significantly higher sound speed than BI-RADS 1, 2, and 3 at an alpha level of 0.05. Using quantitative measures of breast density, a direct correlation between the mean acoustic velocity and calculated mammographic percent breast density was demonstrated with correlation coefficients ranging from 0.75 to 0.89. The results presented here support the hypothesis that sound speed can be used as an indicator of breast tissue density. Noninvasive, nonionizing monitoring of dietary and chemoprevention interventions that affect breast density are now possible.

Novel approach to evaluating breast density utilizing ultrasound tomography

Purpose: Previous ultrasoundtomography work conducted by our group showed a direct correlation between measuredsound speed and physical density in vitro, and increased in vivosound speed with increasing mammographic density, a known risk factor for breast cancer. Building on these empirical results, we investigated the use of volumetric ultrasound percent density (USPD) for breast density estimation. Method and Materials: A breast phantom comprised of fat inclusions embedded in fibroglandular tissue was scanned four times with both ultrasoundtomography and CT. The coronal transmission tomograms and corresponding CTimages were analyzed using a semi‐automatic segmentation routine. Next, a cohort of ∼100 patients was imaged encompassing the entire breast volume (50–75 tomograms/patient). USPD was determined by segmenting high sound speed areas from each slice using a k‐means clustering routine, integrating these results over the entire breast, and dividing by total breast area. USPD was evaluated using two mammographic density measures: (1) qualitative, as determined by a radiologist's visual assessment using BI‐RADS Criteria and (2) quantitative, via digitization and semi‐automatic segmentation of craniocaudal and medio‐lateral oblique mammograms.Results: The integrated areas of the phantom's fat inclusions were compared using both transmission ultrasound and CT for four repeated scans. The average variability for inclusion segmentation was ∼2% and ∼10%, respectively, and a close correlation was observed in the integrated areas between the two modalities. A strong positive association between BI‐RADS category and USPD was demonstrated. Furthermore, comparing USPD to calculated mammographic density yielded moderate to strong positive associations (Pearson r = 0.76–0.84) for MLO and CC views, respectively. Conclusion: These results support the hypothesis that utilizing USPD as an analogue to mammographic breast density is feasible. USPD has the potential to provide a non‐ionizing, whole‐breast analysis of breast density, which may better elucidate the relationship between breast density and breast cancer risk.

TH-E-L100J-07: Comparison of Mammographic Percent Density and Volumetric Percent Density Determined From Ultrasound Tomography Images

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Detection of breast cancer with ultrasound tomography: First results with the Computed Ultrasound Risk Evaluation (CURE) prototype

Novel approach to evaluating breast density utilizing ultrasound tomography

TH-E-L100J-07: Comparison of Mammographic Percent Density and Volumetric Percent Density Determined From Ultrasound Tomography Images