Mammogram Diagnostics via 2-D Complex Wavelet-based Self-similarity Measures

Jeon, Seonghye; Nicolis, Orietta; Vidaković, Brani

doi:10.11606/issn.2316-9028.v8i2p265-284

Cited by 20 publications

(31 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For fractional Brownian motion, we observe that our method achieves gains in mean square error, albeit at a cost of a decrease in bias performance. These results agree with other studies using complex-valued wavelet methodology, which is shown to outperform its real-valued counterpart in a variety of applications, from denoising (Barber and Nason 2004 to Hurst estimation in the (real-valued) image context (Nelson and Kingsbury 2010;Jeon et al 2014;Nafornita et al 2014). This is due to the use of two rather than just one filter, thus eliciting more information from the signal under analysis.…”

Section: Simulated Performance Of Clompesupporting

confidence: 89%

“…Recent works that deal with long memory estimation in various settings are Vidakovic et al (2000), Shi et al (2005), Hsu (2006), Jung et al (2010) and Coeurjolly et al (2014). Some authors have recently considered Hurst estimation using complexvalued wavelets in the regularly spaced real-valued image context; see Nelson and Kingsbury (2010), Jeon et al (2014) and Nafornita et al (2014). Reviews comparing several techniques for Hurst exponent estimation (for real-valued series) can be found in, for example, Taqqu et al (1995).…”

Section: Long Memory and Its Estimationmentioning

confidence: 99%

See 1 more Smart Citation

Long memory estimation for complex-valued time series

Knight

Nunes

2018

Stat Comput

View full text Add to dashboard Cite

Long memory has been observed for time series across a multitude of fields, and the accurate estimation of such dependence, for example via the Hurst exponent, is crucial for the modelling and prediction of many dynamic systems of interest. Many physical processes (such as wind data) are more naturally expressed as a complex-valued time series to represent magnitude and phase information (wind speed and direction). With data collection ubiquitously unreliable, irregular sampling or missingness is also commonplace and can cause bias in a range of analysis tasks, including Hurst estimation. This article proposes a new Hurst exponent estimation technique for complex-valued persistent data sampled with potential irregularity. Our approach is justified through establishing attractive theoretical properties of a new complex-valued wavelet lifting transform, also introduced in this paper. We demonstrate the accuracy of the proposed estimation method through simulations across a range of sampling scenarios and complex-and real-valued persistent processes. For wind data, our method highlights that inclusion of the intrinsic correlations between the real and imaginary data, inherent in our complex-valued approach, can produce different persistence estimates than when using real-valued analysis. Such analysis could then support alternative modelling or policy decisions compared with conclusions based on real-valued estimation. Keywords Complex-valued time series • Hurst exponent • Irregular sampling • Long-range dependence • Wavelets 1 Introduction Complex-valued time series arise in many scientific fields of interest, for example digital communication and signal processing (Curtis 1985; Martin 2004), environmental series (Gonella 1972; Lilly and Gascard 2006; Adali et al. 2011) and physiology (Rowe 2005). Modelling and analysis of such series in the complex domain is not only natural, but also convenient. In addition, complex-valued time series models are often able to represent more realistic behaviour in observed physical processes; see, for example, Mandic and Goh (2009) and Sykulski et al. (2017). A particular modelling Electronic supplementary material The online version of this article (

show abstract

Section: Simulated Performance Of Clompesupporting

confidence: 89%

Section: Long Memory and Its Estimationmentioning

confidence: 99%

Long memory estimation for complex-valued time series

Knight

Nunes

2018

Stat Comput

View full text Add to dashboard Cite

show abstract

“…Extensions of wavelet estimators to other settings, for example the presence of observational noise, can be found in Stoev et al (2006), Gloter and Hoffmann (2007). Other recent works concerning long-memory estimation including multiscale approaches are Vidakovic et al (2000), Shi et al (2005), Hsu (2006), Jung et al (2010), Coeurjolly et al (2014) and Jeon et al (2014). Reviews comparing several techniques for Hurst exponent estimation can be found in e.g.…”

Section: Review Of Long-range Dependence Its Estimation Wavelets Anmentioning

confidence: 99%

A wavelet lifting approach to long-memory estimation

2016

View full text Add to dashboard Cite

Reliable estimation of long-range dependence parameters is vital in time series. For example, in environmental and climate science such estimation is often key to understanding climate dynamics, variability and often prediction. The challenge of data collection in such disciplines means that, in practice, the sampling pattern is either irregular or blighted by missing observations. Unfortunately, virtually all existing Hurst parameter estimation methods assume regularly sampled time series and require modification to cope with irregularity or missing data. However, such interventions come at the price of inducing higher estimator bias and variation, often worryingly ignored. This article proposes a new Hurst exponent estimation method which naturally copes with data sampling irregularity. The new method is based on a multiscale lifting transform exploiting its ability to produce wavelet-like coefficients on irregular data and, simultaneously, to effect a necessary powerful decorrelation of those coefficients. Simulations show that our method is accurate and effective, performing well against competitors

show abstract

“…A 2014 study using the discrete complex wavelet transform on mammogram images obtained a classification procedure based on the spectral slopes and phase variance of mammograms with and without cancer with an accuracy rate of nearly 86% [8]. However, it was later discovered that the mammograms of the cases were performed on a different mammography unit than the mammograms of the controls.…”

Section: Introductionmentioning

confidence: 99%

Wavelet-based scaling indices for breast cancer diagnostics

et al. 2017

View full text Add to dashboard Cite

Mammography is routinely used to screen for breast cancer (BC). However, the radiological interpretation of mammogram images is complicated by the heterogeneous nature of normal breast tissue and the fact that cancers are often of the same radiographic density as normal tissue. In this work, we use wavelets to quantify spectral slopes of BC cases and controls and demonstrate their value in classifying images. In addition, we propose asymmetry statistics to be used in forming features which improve the classification result. For the best classification procedure, we achieve approximately 77% accuracy (sensitivity=73%, specificity=84%) in classifying mammograms with and without cancer.

show abstract

Mammogram Diagnostics via 2-D Complex Wavelet-based Self-similarity Measures

Cited by 20 publications

References 29 publications

Long memory estimation for complex-valued time series

Long memory estimation for complex-valued time series

A wavelet lifting approach to long-memory estimation

Wavelet-based scaling indices for breast cancer diagnostics

Contact Info

Product

Resources

About