Modern problems in trustworthy medical imaging

2026 AI Summer Program

Jeremias Sulam

50 years ago ... 

first CT scan
ELECTRIC & MUSICAL INDUSTRIES

50 years ago ... 

imaging
diagnostics

complete hardware & software description

human expert diagnosis and recommendations

imaging was "simple"

... 50 years forward 

Data

Compute & Hardware

Sensors & Connectivity

Research & Engineering

... 50 years forward 

data-driven  imaging
automatic analysis and rec.
societal implications

Data

Compute & Hardware

Sensors & Connectivity

Research & Engineering

data-driven  imaging
automatic analysis and rec.
societal implications

Problems in trustworthy biomedical imaging

inverse problems

uncertainty quantification

robustness

generalization

demographic fairness

hardware & protocol optimization

model-agnostic interpretability

policy & regulation

monitoring & auditing

data-driven  imaging
automatic analysis and rec.
societal implications

Problems in trustworthy biomedical imaging

inverse problems

uncertainty quantification

robustness

generalization

demographic fairness

hardware & protocol optimization

model-agnostic interpretability

policy & regulation

monitoring & auditing

What is Artificial Intelligence?

1920

What is AI?

1920
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What is AI?

1920
1958
2012

What is AI?

2012
2023
1920
1958

What is AI?

What is AI?

  • Rules (algorithms) that are learned from statistical associations in data
  • These can be obtained by human supervision by means of examples

What is AI?

  • Rules (algorithms) that are learned from statistical associations in data
  • These can be obtained by human supervision by means of examples
radiopedia.org

What is AI?

  • Rules (algorithms) that are learned from statistical associations in data
  • These can be obtained by human supervision by means of examples
  • Can also be obtained
    without supervision
    (e.g. "foundational models") by learning from huge amounts of unlabeled data
data-driven  imaging
automatic analysis and rec.
societal implications

Problems in trustworthy biomedical imaging

inverse problems

uncertainty quantification

robustness

generalization

demographic fairness

hardware & protocol optimization

model-agnostic interpretability

policy & regulation

monitoring & auditing

uncertainty quantification

model-agnostic interpretability

robustness

generalization

policy & regulation

demographic fairness

hardware & protocol optimization

data-driven  imaging
automatic analysis and rec.
societal implications

Problems in trustworthy biomedical imaging

monitoring & auditing

inverse problems

Inverse Problems

\(x:\) phenomenon of interest

\(y = A(x) + v:\) measurements

How do we estimate \(x\) from \(y\)?

Inverse Problems

\(\mathbb{R}^n\)

\(A :  \mathbb{R}^n \to \mathbb{R}^m\)

\(x\)

\(y\)

\(\mathbb{R}^m\)

inversion

  • Computed Tomography

inversion

Inverse Problems

\(A :  \mathbb{R}^n \to \mathbb{R}^m\)

\(\mathbb{R}^n\)

\(x\)

\(y\)

\(\mathbb{R}^m\)

inversion

Inverse Problems

\(A :  \mathbb{R}^n \to \mathbb{R}^m\)

\(\mathbb{R}^n\)

\(x\)

\(y\)

\(\mathbb{R}^m\)

  • Computed Tomography

inversion

  • Imaging

inversion

[Xiang et al, 2024]

Inverse Problems

\(A :  \mathbb{R}^n \to \mathbb{R}^m\)

\(\mathbb{R}^n\)

\(x\)

\(y\)

\(\mathbb{R}^m\)

inversion

Inverse Problems

\(A :  \mathbb{R}^n \to \mathbb{R}^m\)

\(\mathbb{R}^n\)

\(x\)

\(y\)

\(\mathbb{R}^m\)

  • Computed Tomography

inversion

  • Imaging
  • Astronomy

inversion

[Event Horizon Telescope Collaboration, Astrophys. J. Lett. 875 (2019).]

A problem is a well-posed problem if
 

1. (Existence) There exist at least one solution

2. (Uniqueness) There is at most one solution

3. (Stability) The solution depends continuously on the data

Inverse problem

\[\text{find }x \text{ so that }y = A x + v\]

Can we invert the operator \(A\)? 

PART I:  Foundations


\[\text{find }x \text{ so that }y = A x + v\]

(unstable)

 

Error \(\|x - \hat x\|_2 \leq \|A^{-1}\|_2\|v\|_2 \propto \frac{1}{\lambda_n} \|v\|_2\)

 

\[\hat x = A^{-1}y = x + A^{-1}v\]

 

\(1~ \bullet~\) If \(n=m\) and \(A:\) non-singular:

 

 

\(=\)

\(+\)

Inverse Problem

\(2~ \bullet~\) If \(n<m\), then \(A\) cannot span \(\mathbb R^m\).

Thus, \(y \notin \text{span}(A)\), and thus \(\nexists ~ x :  y = Ax\).

(non-existence)

\(=\)

\(+\)

 

\[\hat x = A^{-1}y = x + A^{-1}v\]

 

\(1~ \bullet~\) If \(n=m\) and \(A:\) non-singular:

 

 


\[\text{find }x \text{ so that }y = A x + v\]

Inverse Problem

(non-uniqueness)

\(3~ \bullet~\) If \(n>m\), and \(A:\) full-rank. 

\(=\)

\(+\)

\(2~ \bullet~\) If \(n<m\), then \(A\) cannot span \(\mathbb R^m\).

Thus, \(y \notin \text{span}(A)\), and thus \(\nexists ~ x :  y = Ax\).

 

\[\hat x = A^{-1}y = x + A^{-1}v\]

 

\(1~ \bullet~\) If \(n=m\) and \(A:\) non-singular:

 

 


\[\text{find }x \text{ so that }y = A x + v\]

Inverse Problem

(non-uniqueness)

\(3~ \bullet~\) If \(n>m\), and \(A:\) full-rank. 

\(=\)

\(+\)

\[\min_x ~R(x) ~~ \text{s.t.}~~ y = Ax\]

Strategy: define a new criteria, \(R(x): \mathbb R^n \to \mathbb R\)


\[\text{find }x \text{ so that }y = A x + z\]

Inverse Problem

Signal and Image Models

Signal and Image Models

Signal and Image Models

Signal and Image Models

Signal and Image Models

How can we combine powerful data-driven models with mathematical analysis and guarantees?

Signal and Image Models

\bar{M} = \chi \bar{H}

degree to which a material is magnetized when placed in a magnetic field

[from talk by S. Bollmann]

  • Heme Iron (in RBC)
    paramagnetic

     
  • Myelin
    diamagnetic
  • Very important implications for neurodegenerative disorders

[Li et al, 2012]

Inverse Problems

in Magnetic Susceptibility Imaging

Inverse Problems

in Magnetic Susceptibility Imaging

Calculation of susceptibility through multiple orientation sampling (COSMOS)
[Liu et al, 2009]

As close as possible to "ground truth" in vivo

Impractical in the clinic

A{x} + v = y :
A'x + v' = y' :
A'x + v'' = y'' :

Inverse Problems

in Magnetic Susceptibility Imaging

Calculation of susceptibility through multiple orientation sampling (COSMOS)
[Liu et al, 2009]

As close as possible to "ground truth" in vivo

Impractical in the clinic

A'x + v' = y' :
A'x + v'' = y'' :
A{x} + v = y :

Can we estimate susceptibility from a single orientation?

f_\theta
f_\theta
f_\theta
f_\theta

[Lai, Aggarwal, van Zijl, Li, Sulam, Learned Proximal Networks for Quantitative Susceptibility Mapping, MICCAI 2020]

Single Phase Quantitative Susceptibility Mapping 

Single Phase Quantitative Susceptibility Mapping 

uncertainty quantification

model-agnostic interpretability

robustness

generalization

policy & regulation

demographic fairness

hardware & protocol optimization

data-driven  imaging
automatic analysis and rec.
societal implications

Problems in trustworthy biomedical imaging

monitoring & auditing

inverse problems

Demographic Fairness

Demographic Fairness

  • Group/Associative Fairness
           Predictors should not have very different (error) rates among groups
         [Calders et al, '09][Zliobaite, '15][Hardt et al, '16]
  • Individual Fairness
           Similar individuals/patients should have similar outputs
           [Dwork et al, '12][Fleisher, '21][Petersen et al, '21]
  • Causal Fairness
           Predictors should be fair in a counter-factual world
          [Nabi & Shpitser, '18][Nabi et al, '19][Plecko & Bareinboim, '22]
  • Multiaccuracy/Multicalibration
           Predictors should be approximately unbiased/calibrated for every group
           [Kim et al, '20][Hebert-Johnson et al, '18][Globus-Harris et at, 22]

Multiaccuracy:

Similar accuracy across different groups

Example: Predicting abnormal findings in chest X-rays

Demographic Fairness

Multiaccuracy:

Similar accuracy across different groups

Example: Predicting abnormal findings in chest X-rays

Demographic Fairness

Problem: This is not always possible...

Problem: This is not always possible...

sex and race attributes missing

Problem: This is not always possible...

Demographic Fairness through Proxy Attributes

not computable
computable gaurantee

Demographic Fairness through Proxy Attributes

not computable
computable gaurantee
correcting multi-group accuracy

Demographic Fairness through Proxy Attributes

Problems in trustworthy biomedical imaging

Problems in trustworthy biomedical imaging

inverse problems

uncertainty quantification

robustness

generalization

demographic fairness

hardware & protocol optimization

model-agnostic interpretability

policy & regulation

monitoring & auditing

uncertainty quantification

hardware & protocol optimization

Problems in trustworthy biomedical imaging

inverse problems

uncertainty quantification

robustness

generalization

demographic fairness

hardware & protocol optimization

model-agnostic interpretability

policy & regulation

monitoring & auditing

uncertainty quantification

policy & regulation

hardware & protocol optimization

robustness

generalization

data-driven  imaging
automatic analysis and rec.
societal implications

Interpretability

Formal frameworks for interpretability for decision making
Understanding social implications of algorithms in the wild
Efficient and robust generative AI

uncertainty quantification

Generative Modeling

ML for Science

Biomarker discovery through AI

Societal Constraints

many open questions...

policy & regulation

robustness

generalization

uncertainty quantification