We are sorry, but NCBI web applications do not support your browser and may not function properly. More information

## Results: 12

1.

2.

3.

Error in reconstruction caused by increasing data-to-background signal level. The percentage error in reconstruction was plotted against the ratio of data-to-background (

*I*_{d}∕*I*_{b}) for all three methods. The percentage error for ratios up to 1 (data equals background) can be seen, where the error increases dramatically as the ratio goes to 1.4.

Dependence of contrast on the curvature correction. The

*I*_{d}∕*I*_{b}ratio is plotted against the normalized standard deviation of the background of the curvature corrected image at a wavelength of 800 nm. Both cases of feature alignment are shown, as well as a comparison of the flat phantom without contrast agents.5.

Curvature correction based on curve fitting on the cylindrical phantom with data (letters). Intensity images are shown before and after curvature correction. Different contrast agents were used with decreasing data-to-background ratios. The different

*I*_{d}∕*I*_{b}ratios are (a) 0.73, (b) 0.51, and (c) 0.39. The figure qualitatively shows the dependence of data-to-background ratio on the correction performance.6.

Effect of multiple iterations on the goodness of fit of curvature is shown in this graph. (a) shows a cross section through the curvature fit for all six iterations. Black arrows indicate the location of veins. It can be seen that the effect of veins disappear after several iterations, leaving a smooth curvature. The L-curve in (b) shows the squared error against number of iterations.

7.

Curvature correction based on curve fitting on the cylindrical phantom without data content and compared to the flat phantom. (a) shows the curvature uncorrected intensity image, (b) the curvature corrected intensity image, and (c) shows the flat phantom. (d) shows the averaged cross section of (a), (b), and (c) with error bars given by the standard deviation over all rows.

8.

(a) Dependence of polynomial order on the fitting quality. The averaged, normalized cross section through the cylinder (along the

*y*axis) is plotted for each polynomial order tested. Order five and six fit the object shape accurately, leaving only minor residuals (<2%) at the edges of the cylinder. (b) shows the dependence of the polynomial order on normalized standard deviation of the curvature corrected cylinder, illustrated by the L-curves.9.

(a) Data wave (a sine grating), superimposed on [(b), left] a cylindrical object without noise and [(b), right] with 50% noise. Three different approaches for curvature removal were tested; (c) exact kernel deconvolution, (d) horizontal and vertical averaging, and (e) curve fitting. Qualitatively all three approaches perform equally well in the noise-free scenario (left), as well as in the noise scenario (middle). The point-wise percentage error for the noise case is shown in the right column.

10.

Effect of curvature correction on quantification of (a) and (c) fraction blood oxygenation and (b) and (c) fraction blood volume. Reconstruction results (a) and (b) before curvature correction are clearly biased by it. Results after correction (c) and (d) do not show this effect, which can be seen in more detail in the cross sectional plots shown in (e) and (f), with uncorrected in blue and corrected in green. The cross sections shown are indicated by the dotted line in (a). Detailed assessment of tissue chromophore concentration was made possible. (Color online only.)

11.

(a) Gradual degradation of the curvature correction using the curve fitting approach when data with decreasing spatial frequencies (top to bottom) are applied. The left column shows the data waves and the right column the deconvolved ones. (b) Error in reconstruction caused by low spatial frequencies in data. The dependence of spatial frequency of the data wave for the curve fitting approach is pointed out by plotting the average error in reconstruction against the number of cycles of the sine grating in the data wave. As expected, the averaging approach is not affected by the varying spatial frequency.

12.

(a) Error in reconstruction caused by rotation of the object from the image axis. The cylindrical object was rotated 90 deg in 5-deg steps. The average error in reconstruction is plotted against the angle of rotation for all three methods. The averaging method highly depends on the orientation of the object axis to the image axis, whereas the curve fitting method does not. (b) Error due to varying curvature. There are changes in the radius, therefore maximum angles of the cylinder were evaluated. The error displayed has units of the data signal of the order of 0.01. The curve fitting method shows an error greater than the data for angles between 85 and 35 deg, and breaks down at angles >85 deg. At angles smaller than 35 deg, the error is smaller than the data signal. The averaging method is not affected by the angle.