Public Discussion of the Research ativity

May, 27 2021

Academic Path:

  • [2012] MD in Mathematics, thesis on CT/SPECT image reconstruction from projection data.
  • [2017] PhD in Medical, Clinical and Experimental Sciences (Neurosciences curriculum). Research on PET/MRI neuroimaging and data analysis in MS, AD, Brain Tumour, PD.
  • In this moment Third-year PostDoc at the PNC - Padova Neuroscience Center. Research on interpolation of discontinuous data w/ application to medical imaging, and PET/MRI-based clinical type prediction.

Collaborations:

  • CAA: Padova-Verona research group on
    "Constructive Approximation and Applications".

  • CeSMuV (Centro Sclerosi Multipla del Veneto).
  • Nuclear Medicine Unit, Hospital of Padova.

  • Dorian Technologies - Diagnosis ORIented ANalysis (spin-off INFN, Genova).

Membership

Rete ITaliana di

Approssiamzione (GNCS)

Teoria dell'Approssimazione

e Applicazioni (UMI)

Voting member of the PSF - Python Software Foundation

Scores

Scopus

Google Scholar

Neuroimaging

  • Acknowledge the system's limits.

from

D. Cecchin, D. Poggiali, L. Riccardi, P. Turco, F. Bui, S. De Marchi, Analytical and experimental FWHM of a gamma camera: theoretical and practical issues, PeerJ, doi:10.7717/peerj.722.

What does a numerical analyst do in clinical studies?

  • Awareness of neuroimaging algorithms and their applicability in different context.
  • Pipelining and automation.

from

M. Margoni, D. Poggiali, S. Zywicki, M. Rubin, A. Lazzarotto, S. Franciotta, M. G. Anglani, F. Causin, F. Rinaldi, P. Perini, M. Filippi, P. Gallo, Early red nucleus atrophy in relapse‐onset multiple sclerosis, HBM doi:10.1002/hbm.25213

  • Preliminary statistic for feasibility of a study.
  • Dataviz.

from

  • D. Cecchin, H. Barthel, D. Poggiali, A. Cagnin, S. Tiepolt, P. Zucchetta, P. Turco, P. Gallo, A.C. Frigo, O. Sabri, F. Bui, A new integrated dual time-point amyloid PET/MRI data analysis method, EJNMMI, doi:10.1007/s00259-017-3750-0.

  • Mathematical modelling.
  • Statistical analysis/Machine Learning.

from the Supplementary Materials of

  • D. Cecchin, H. Barthel, D. Poggiali, A. Cagnin, S. Tiepolt, P. Zucchetta, P. Turco, P. Gallo, A.C. Frigo, O. Sabri, F. Bui, A new integrated dual time-point amyloid PET/MRI data analysis method, EJNMMI, doi:10.1007/s00259-017-3750-0.

  • Automated fingerprinting of clinical type/subtype from imaging for differential diagnosis.

(work in progress)

Numerical approximation and applications

Main topics of research:

  • Fake nodes interpolation.
  • Quadrature on Fake nodes.
  • Applications on imaging.

What is Fake Nodes interpolation?

Instead of interpolating on the nodes x you define a mapping function S and interpolate over the fake nodes S(x).

f = lambda x: np.log(x**2+1)
x = np.linspace(-1,1,10)
y = f(x)
xx = np.linspace(-1,1,100)



yy = my_fancy_interpolator(x,y,xx)
f = lambda x: np.log(x**2+1)
x = np.linspace(-1,1,10)
y = f(x)
xx = np.linspace(-1,1,100)

S = lambda x: -np.cos(np.pi * .5 * (x+1))

yy = my_fancy_interpolator(S(x),y,S(xx))

Given a function

f: \Omega \subseteq \mathbb{R}^d \longrightarrow \mathbb{R}\;\;\;\;\; {d \in \mathbb{N}},

a set of distinct nodes

X = \{ x_0, \dots, x_N\} \subset \Omega,

and a set of basis functions

\mathcal{B} = \{ b_i: \Omega \longrightarrow \mathbb{R} \}_{i = 0, \ldots, N}

The interpolant is given by a function

\displaystyle \mathcal{P}(\bm{x}) = \sum_{i=0}^{N} c_i b_i(\bm{x})

s.t.

\mathcal{P}(\bm{x}_i)=y_i:=f(\bm{x}_i) \;\;\forall i
\mathcal{B} = \{ b_i \circ S: \Omega \longrightarrow \mathbb{R}^d \}_{i = 0, \ldots, N}
\displaystyle \mathcal{R}^s(\bm{x}) = \sum_{i=0}^{N} c_i b_i(S(\bm{x}))
\mathcal{R}^s(\bm{x}_i)=y_i:=f(\bm{x}_i) \;\;\forall i

This process can be seen equivalently as:

1. Interpolation over the mapped basis

\[\mathcal{B}^s = \{b_i \circ S \}_{i=0, \dots, N}.\]

2. Interpolation over the original basis \(\mathcal{B}\) of a function \(g: S(\Omega) \longrightarrow\mathbb{R}\)

at the fake nodes 

\[S(X) = \{S(x_i) \}_{i=0, \dots, N}.\]

 \(g\in C^s\) must satisfy \(g(S(x_i)) = f(x_i)\;\;\forall i\).

If \(\mathcal{P} \approx g \) on \(S(X)\) with the original basis,

then \(\mathcal{R}^s = \mathcal{P} \circ S \approx f \)  on \(X\).

This allow to treat Gibbs Effect...

from

  • S. De Marchi, F. Marchetti, E. Perracchione, D. Poggiali, Polynomial interpolation via mapped bases without resampling, JCAM, doi:10.1016/j.cam.2019.112347.

  • S. De Marchi, F. Marchetti, E. Perracchione, D. Poggiali, Multivariate approximation at fake nodes, AMC, doi:0.1016/j.amc.2020.125628

...and Runge Effect, with consequences on MPI reconstruction.

from

  • S. De Marchi, F. Marchetti, E. Perracchione, D. Poggiali, Polynomial interpolation via mapped bases without resampling, JCAM, doi:10.1016/j.cam.2019.112347.

  • S. De Marchi, W. Erb, E. Francomano, F. Marchetti, E. Perracchione, D. Poggiali, Fake Nodes approximation for Magnetic Particle Imaging, Conference paper, MELECON 2020 doi:10.1109/MELECON48756.2020.914058

Consequences in 3D multimodal image resampling are currently under examination.

from the Preprint

Programming experience

I like to write (mostly in Python), share as Open Source, and maintain my own code whenever it is possible. This makes my work:

  • Accessible to anyone;
  • Verifiable by anyone;
  • Reproducible;
  • More visible (and hopefully cited).

For instance, the RainCloud plot publication began as an open source project.

Teaching experience

[2021] Professor of "Introduction to Numerical Calculus" for Astronomy, 6CFU.

[2020] Lab Professor of "Numerical Calculus" for Mechanical Engineering (tracks 1 and 2); Main Teacher: Prof S. De Marchi, 6CFU.

[2019] Lab Professor of "Numerical Calculus" for Energy Engineering; Main Teacher: Prof A. Sommariva, 1CFU.

[2018] Professor of "Introduction to Python" for the Data Science Summer School, University of Trento, 6 CFU.

 

[2012-19] Teaching Assistant (TA) in Numerical Calculus for 8 courses.

[2019] Acquired the 24 CFU for High school teaching.

 

[2017-2019] High school Math/Physics substitute teacher. Total time: 18 months.

Thanks for listening!

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