A Quasi-Local Method for Instantaneous Frequency Estimation With - - PowerPoint PPT Presentation

A Quasi-Local Method for Instantaneous Frequency Estimation With Application to Structural Magnetic Resonance Images

& & Alvaro Ulloa, Paul Rodriguez, Jingyu Liu, Vince Calhoun, and Marios Pattichis August 30, 2014

A QLM for IF estimation with app to SMRI

Outline

Background Motivation AM-FM decomposition Method comparison AM-FM decomposition of SMRI Results Conclusion

A QLM for IF estimation with app to SMRI

Background

Brain imaging

Magnetic resonance images (MRI) Electroencephalograms (EEG) Magnetoencephalograms (MEG)

Brain metrics

Gray matter concentration, blood

• xygenation level

Electric potential Magnetic field

Computational methods → case-control differences, disease prognosis and diagnosis, lesion detection, etc.

A QLM for IF estimation with app to SMRI

Motivation

New method for analyzing brain texture for mental diseases. Brain images are dominated by strong non-stationary behavior. The brain is formed of peaks and valleys called gyri and sulci Classical methods do not explore gyri and sulci formation, just gray matter concentration

A QLM for IF estimation with app to SMRI

AM-FM decomposition

The AM-FM representation of an image I(x) is expressed as: I(x) =

M

• n=1

an(x) cos(ϕn(x)) (1) where x = (x1, x2, . . . ) : pixel coordinates, M ∈ N : number of components, an > 0 : n-th instantaneous amplitude (IA) function, ϕn : n-th instantaneous phase (IP) function. The IF is defined as the gradient

• f the IP: ∇ϕ(x).

A QLM for IF estimation with app to SMRI

AM-FM demodulation

quasi-local method (QLM) Initially proposed for ω(x) ∈ [0, π

2 ]

Later extended for ω(x) ∈ [ π

2 , π]

We propose ω(x) ∈ [0, π] quasi-eigenfunction approximation (QEA) Initially proposed for ω(x) ∈ [0, π] Compatible with any filter bank design Requires Hilbert pre-processing

A QLM for IF estimation with app to SMRI

Quasi-local demodulation method

QLM for ω(x) ∈ [0, π

2 ]

ω1(x) = cos−1

• R(x) +
• R2(x) + 8

4

• where

R(x) = 2ˇ g(1,1)(x) ˇ g(1,0)(x) + ˇ g(0,1)(x), g(ǫ1,ǫ2) = I(x + ǫ1)I(x − ǫ2), ǫ1, ǫ2 ≥ 0 QLM for ω(x) ∈ [ π

2 , π]

ω2(x) = π − cos−1

• −R(x) +
• R2(x) + 8

4

• A QLM for IF estimation with app to SMRI

New quasi-local demodulation method

QLM for ω(x) ∈ [0, π] If R ∈ (−∞, −1] → ω1(x) = cos−1

• R(x)+√

R2(x)+8 4

• If R ∈ (1, ∞] → ω2(x) = π − cos−1
• −R(x)+√

R2(x)+8 4

• If R ∈ (−1, 1] → ω(x) =
• ω1(x)

if a(f1(x)) > a(f2(x)) ω2(x)

• therwise

Where f1(x) is a low-pass filtered version of the signal and f2(x) is the counterpart.

A QLM for IF estimation with app to SMRI

Method comparison

A QLM for IF estimation with app to SMRI

Method comparison results

• 5 × 10−3

1 × 10−2 1.5 × 10−2 2 × 10−2 0.0 0.1 0.2 0.3

Noise SD

• Gabor

Directional Equirriple

QEA + filter bank

• 5 × 10−4

1 × 10−3 1.5 × 10−3 2 × 10−3 0.0 0.1 0.2 0.3

Noise SD

• Gabor

Directional Equirriple

QLM + filter bank

A QLM for IF estimation with app to SMRI

AM-FM of SMRI

IF angle is orthogonal to edges. IF magnitude is high at rapid variations IF characterizes sulci and gyri

Figure : SMRI IF

A QLM for IF estimation with app to SMRI

Dataset

Table : Demographics of MCIC and COBRE studies.

Site Control/Case Male/Female Age±sd New Mexico 61/53 89/25 36±12.8 Minnesota 19/30 34/15 32.2±10.6 Massachusetts 24/28 32/20 38.7±9.3 Iowa 60/32 59/33 31.3±10 Total 164/143 214/93 34.46±11.4

A QLM for IF estimation with app to SMRI

Results

Voxel-wise two sample t-test of Schizophrenia patients vs healthy controls. Voxels that pass bonferroni correction. Temporal gyrus, parahippocampal gyrus and medial frontal gyrus.

A QLM for IF estimation with app to SMRI

Results

ANOVA by site

A QLM for IF estimation with app to SMRI

Conclusion

Proposed a new AM-FM demodulation method and applied it to the analysis of brain images. IF magnitude as a brain texture measure showed results coherent with previous research while being less affected by scanner settings at different collection sites This information can be used to complement SMRI studies on the effect of neuro-degenerative diseases to sulci and gyri formations.

A QLM for IF estimation with app to SMRI