# Presentation: 930096

## Image Acquisition Issues 

- Kyle J. Myers, Ph.D.
- NIBIB/CDRH Laboratory for the
- Assessment of Medical Imaging Systems

- Image Acquisition Issues
- in Quantitation Tasks

## Knowledge of the is critical for solving an 

- Knowledge of the is critical for solving an

- Description of the data for a known object

- forward problem

- inverse problem

- Inference about an underlying object from an image

**Notes:**
Major emphasis of our work

## Knowledge of the 

- Knowledge of the

- Description of the data for a known object

- forward problem

- Provides a description of images/data
- Noise, resolution, artifacts,...
- Optimal classification and estimation depend on likelihood of data given underlying object

**Notes:**
Major emphasis of our work

## Object property being imaged

- _Acoustic reflectance_
- Medical ultrasound
- _Concentration_
- Nuclear medicine
- MRI (spin density)
- MRS
- _Field strength_
- Biomagnetic imaging
- _Attenuation_
- Film densitometry
- Transmission x-ray

- _Scattering properties_
- Medical ultrasound
- _Electric, magnetic properties_
- Impedance tomography
- MRI (magnetization
- MRI (spin relaxation)
- _Source strength_
- Fluorescence microscopy
- _Index of refraction_
- Phase-contrast microscopy
- _Gene expression_
- DNA chips, microarrays

## Image acquisition: a mapping from object space to data space

**g**** **= data (         )
**H **=** **the imaging process (mapping)
**f** = tumor/object/patient
- 			(what we want to         )
- Which **H**** ** is best?  What more can we do with possible improvements in **H** ?

- given

- find

- BIROW

- 31 January 2003

## Need models/measures of 
                 H  
  to characterize the data

-                  **H**
-   to characterize the data

- BIROW

- 31 January 2003

## Singular Value Decomposition (SVD): Tool for understanding the forward problem

- Basis functions are found by eigenanalysis of **H**t**H**
- Continuous-Continuous (CC) system
- Linear, shift-invariant (LSIV)
- Fourier theory: Basis functions are wavefunctions
- MTF describes resolution
- NPS describes noise
- Continuous-Discrete (CD) system
**H** is shift-variant
- Resolution and noise depend on location
- Basis functions may be “natural pixels,”
- 	tubes or cones (projection imaging)

**Notes:**
Nonlinear in most general case
More on Fourier

##     Measure the mapping...

- When the object is a point source
-  			*f *(**r**) = (**r **- **r**0)  ,
- The image is the *detector sensitivity function **	*
*	**	**=  a component of the mapping  ***H**.

##      Measuring H on FASTSPECT II at U. of AZ

**Notes:**
This approach is routinely used at the University of Arizona.  A radioactive source is systematically stepped through the object domain; each source location yields approximately 100,000 measurements.  That is, 100,000 measurements for each of about 375,000 source locations, if 2mm object voxels are used!  The system matrix is sparse, though, so only about 2% of the elements must be stored.

## Eigenfunctions of an

- octagonal SPECT system

- Barrett et al.,
- IPMI (1991).

## Null space: H fnull = 0

- If f1 and f2 differ by a null function: **H** f1 – **H** f2 = 0
-  no difference in the image
- CC system: where MTF has zeros
- CD system examples: finite sampling
- Limited-angle tomography
- Temporal sampling
- Spatial sampling (pixel binning)
- All digital systems have null functions
- Can’t recover object uniquely from image

**Notes:**
Lost information – need to know if this is crucial to task performance
Image reconstruction: many algorithms try to put lost information back by using informative priors

## Null functions cause artifacts

- Reconstruction of a brain phantom by filtered
- backprojection.
- (Courtesy of C.K. Abbey)

## Image reconstruction

- Regularization can reduce objectionable artifacts
- Can’t put back what’s lost due to null functions
- Makes noise nonlocal – contributions from entire image

- Sequence of reconstructions of a brain phantom
- by the MLEM algorithm after
- 10, 20, 50, 100, 200, and 400 iterations.
- (Courtesy of D.W. Wilson.)

## Knowing the forward problem means knowing the null space

- Barrett et al.,
- IPMI (1991).

## Classification tasks: Ideal (Bayesian) observer

- Optimal classifier is based
- 	on 	the likelihood ratio:
- Performance is determined by
- 	statistics of  the likelihood ratio
- ROC analysis

- Disease present)

- Disease present)

- BIROW

- 31 January 2003

**Notes:**
By performance, we mean how well the system does at giving information to the observer to perform the task!  For hardware evaluation and optimization we’d like to assess the information content in the raw data in terms of its ability to allow the best possible observer to perform the task.  Thus we make use of the ideal or Bayesian observer.

## Estimation

- Tumor volume
- Requires delineation of border
- Tracer uptake
- Total or specific activity
- Angiogenesis
- Vessel tortuosity

- Bullitt *et al.,* IEEE TMI (2003).

## Estimation: Basic concepts

-  is *P* –D vector of object parameters
- pris prior probability density; describes underlying randomness in the parameters
- pr(**g**|) = mapping from parameters to data
-               = _likelihood of data given ___
- (**g**)= estimate of parameter vector

- ^

## Estimability

- pr(**g**|1) = pr(**g**|2) implies 1=2
- Closely linked to null functions
- Estimates of pixel values run into
- 	problems of estimability
- See Barrett and Myers, 2004

## Figures of merit

- Bias, variance
- Mean-square error
- Overall fluctuation in the estimate for _particular_ 
- Requires gold standard = true value of parameter
- Only meaningful for estimable parameters
- Limited by measurement noise, anatomical variation, form of the estimator

## Figures of merit – cont’d

- Ensemble MSE (EMSE)
- Need to know prior on 
- Prior information can be statistical or model-based
- Makes problem well-posed

## Family of possible tumors

- Tumor = **t**(******t**)
- Location
- Size
- Shape
- Density
- Some unknowns are nuisance parameters
- Estimate or marginalize
- Key to tractability is knowledge of pr(******t**)

- Courtesy Miguel Eckstein, UCSB

**Notes:**
Order of increasing cost and increasing reality.  Obviously, the SKE and SKEV paradigms are only relevant to classification tasks.
As we shall see, the relationship between SKS and SKEV is known for the ideal observer.
Interestingly, it has been shown that SKEV can be used to predict SKS in experiments involving human observers as well.  Much more to be done on this topic.

## Inhomogeneous backgrounds can mask tumor/margins

- Additional source of
- 	variability 	in the data
- Degrades tumor detectability,
- 	estimation of tumor parameters
- Reduced noise,
- 	increased resolution
- 	may not improve
- 	task performance
- Many models for pr(******b**)
-     to describe random backgrounds

##  No-gold standard estimation

- Use at least 2 modalities
- 	to estimate 
- 	OR
- Use at least 2 estimators
- 	for same data
- Regress the estimates
- 	from all sources
- Requires model for parameter , knowledge of pr(**g**|)

- Hoppin *et al.,* IEEE TMI (2002).

## Estimation results

- Detection results

- Kupinski *et al.*, SPIE 2003

- Optimal acquisition system is task-dependent

**Notes:**
Images from pinhole imagers of various Gaussian blur (single aperture).  Estimation task: determine signal width and amplitude.  Signal is Gaussian blob, background is lumpy and there is additional photon noise. Usual noise vs. resolution trade-off.

Note: optimal system is task-dependent!!!

## Drug response studies using clinical (human) readers

- Beware of reader variability

- TPF *vs  *FPF for 108
- US radiologists in study
- by Beam *et al., (*1996).

## Drug response studies using clinical (human) readers

- Adds to sources of variability in the study
- Need more cases to power the study
- Analyzed via random-effects or multivariate ROC analysis
- Multi-reader multi-case (MRMC) ROC methodology is commonly used in CDRH for determining contribution of variability due to range of reader skill, reader threshold, and case difficulty

## Why consider display image quality?

**Image **
**Processing**

**PACS**

***The diagnostic imaging chain is as effective as its weakest component!***

- Poor display quality can:
- reduce effectiveness of diagnostic or screening test
- lead to misdiagnosis
- cause inconsistent clinical decisions

**Display **
**Processing**

- Courtesy Aldo Badano, CDRH

## Choice of image acquisition system and settings will depend on the answers to these questions:

- What information about the object is desired from the image?
- How will that information be extracted?
- What objects/patients will be imaged?
- What measure of performance will be used?

- BIROW

- 31 January 2003

**Notes:**
Don’t assume that the object is discrete, pixellated.  It is a vector in a Hilbert space.
Noise may be object dependent.
We observe g and use it to classify image or make inferences about underlying parameters of the object.
Framework comes from statistical decision theory

## Summary

- The future: Knowledge of the forward problem will enable well-characterized, patient-specific image-acquisition choices and processing/estimation methods
- For now:
- Make sure the problem is well-posed and the parameters are estimable
- Avoid pixel-based techniques
- Use model-based (low-dimensional) methods
- Try to keep the human out of the loop
- Validate, validate, validate!