Data pre-processing

Prior to image reconstruction, the raw TPSFs are temporally calibrated, corrected, and reduced to so-called data type values. These procedures are largely being developed and implemented by Elizabeth Hillman.

8.1.3.1 Data types

As a consequence of the desire to reduce data redundancy and minimise the forward model calculation in the reconstruction scheme, the imaging algorithm is provided with data in the form of a basis consisting of various characteristics of the TPSFs. These so-called data (or measurement) types can currently consist of any combination of integrated intensity, temporal moments (around zero), central moments (around the mean), and normalised Laplace transforms [Schweiger 1999a], If r(r) represents the TPSF, these can be expressed as: integrated intensity: (8.1) 0 n* temporal moment: = (8.2) 0 n* central moment: ^c”^ = £ " '^ J ( t- ( t) ) ”r(r) (8.3)

normalised Laplace transform: L(s) = E ^ j g _(8.4)

The integrated intensity, E, equals the area under the curve, and is equivalent to the average measured intensity. The mean time, <r> is the average flight time of photons through tissue, and is related to the phase shift in frequency domain systems. The variance about the mean, <c^>, depends on the shape (e.g. width) of the TPSF, while the normalised Laplace transform L(s), because of the exponential term, is particularly sensitive to early light (c.f. time gating). Some conunon data types are illustrated in Figure 8-4.

r(t) _{TPSF r(t)}

variance <c > _{integrated intensity E}

If +1

t

mean time <t>

Figure 8 -4 Plot illustrating the integrated intensity, mean time and variance of a TPSF. An appropriate choice of data types is required for simultaneously reconstructing separate absorption and scattering profiles [Arridge 1998]. Usually the mean flight time, variance, and Laplace transform (with a coefficient of 0.005 ps'^) were chosen for the image reconstructions presented here. The exact combination used in each of the experiments described below largely depends on the quality of the measurement data. Figure 8-10 shows some sample data obtained from a phantom imaging experiment.

8.1.3.2 Calibration and correction procedures

As discussed in the previous chapter on system performance aspects, noise, reflections, cross talk, the finite width and asymmetry of the IRF and other effects all produce system­ atic errors in the recorded TPSFs and consequently contaminate the derived data types. In order to reduce systematic errors in the raw data the following pre-processing methods are performed, a full description of which is provided by [Hillman 2000].

Windowing and background subtraction

A suitable temporal window (i.e. part of the full data acquisition span) is chosen from which the data types are computed. Thereby the pre-peak due to the ‘source cross talk’.

discussed in section 7.4.2, can be effectively removed and it is ensured that a consistent region is sampled for all TPSFs. Any uncorrelated background noise is subsequently subtracted.

Calibration and IRF correction

Calibration and correction for the finite temporal response of the system is dependent on the data type being calculated. For mean time data the full set of temporal response measurements for all sources and detectors (as described in section 8.1.1) allows the calibration of the temporal offset due to differences in fibre and cable lengths, etc. The same measurements are also used to correct errors in the mean time due to the particular IRF characteristics, such as asymmetry and reflection peaks. Similarly, these IRF charac­ teristics also affect the variance, and are corrected for by using calibration values derived from the variances of the IRFs. The Laplace Transform data are calculated relative to the zero-time.

On some occasions individual detector channels were found to exhibit evidence of temporal instability. These ‘bad’ channels are likely to produce artefacts in the recon­ structed image, and the corresponding data were therefore rejected.

2D/3D correction

While the image reconstruction software is, in principle, capable of performing full 3D reconstructions, it is computationally much more efficient to employ a 2D model. However, diffusely scattered photons migrate in all three dimensions. Therefore an approximate correction is performed on the measurement data to account for the fact that the image reconstruction is based on a 2D forward model of the object. A correction factor specific to each data type and source-detector separation is used to re-scale the experimental values in order to match the simulated 2D forward data in the image reconstruction algorithm more closely. The scaling factors are equal to the ratio of data types computed either analytically using infinite space 2D and 3D Green’s functions, or from 2D and 3D diffusion model based finite-element simulations using a homogenous object with the same physical geometry and average optical properties. One benefit of the 2D/3D correction is that it reduces ring artefacts in the reconstructed images. However, since boundary measurements taken in a single plane are sensitive to off-plane structures, it is not, of course, possible to correct for the influence these structures have on in-plane measurements. This concept has previously been investigated using data simulated with a 3D FEM model, which also

yielded improved results exhibiting fewer artefacts as compared to those generated with uncorrected data [Schweiger 1998]. The development of 2D/3D correction methods is continuing, and recently improved techniques are described by [HiUman 2000].