Super-resolution method for arbitrary retrospective sampling in fluorescence tomography with raster scanning photodetectors

Abstract

Dense spatial sampling is required in high-resolution optical imaging and many other biomedical optical imaging methods, such as diffuse optical imaging. Arrayed photodetectors, in particular charge coupled device cameras are commonly used mainly because of their high pixel count. Nonetheless, discrete-element photodetectors, such as photomultiplier tubes, are often desirable in many performance-demanding imaging applications. However, utilization of the discrete-element photodetectors typically requires raster scan to achieve arbitrary retrospective sampling with high density. Care must be taken in using the relatively large sensitive areas of discrete-element photodetectors to densely sample the image plane. In addition, off-line data analysis and image reconstruction often require full-field sampling. Pixel-by-pixel scanning is not only slow but also unnecessary in diffusion-limited imaging. We propose a super-resolution method that can recover the finer features of an image sampled with a coarse-scale sensor. This generalpurpose method was established on the spatial transfer function of the photodetector-lens system, and achieved super-resolution by inversion of this linear transfer function. Regularized optimization algorithms were used to achieve optimized deconvolution. Compared to the uncorrected blurred image, the proposed super-resolution method significantly improved image quality in terms of resolution and quantitation. Using this reconstruction method, the acquisition speed with a scanning photodetector can be dramatically improved without significantly sacrificing sampling density or flexibility.

Keywords: Fluorescence tomography; data sampling; deconvolution; diffuse optical imaging; motion deblurring; reconstruction; super-resolution.

Figure 1

Schematics of the scan pattern and device timing. (a) Bi-directional raster scan, where the gray area represents the region of interest within the image plane, and the folded arrow-line represents the trajectory of the scan head. (b) Schematics of device timing of the linear actuators and the photodetector: t₁ – experiment starts, t₂ – data acquisition and raster scan start, t₃ – data acquisition ends, and t₄ – experiment ends. During data acquisition, the x-actuator moves continuously and the y-actuator moves at discrete steps.

Figure 2

Comparison of the true, blurred, and de-blurred images of two synthesized imaging targets to characterize resolution and quantitation of the proposed super-resolution method. Top raw (a-c): the binary imaging target tests the performance in resolution and qualitative image quality. Bottom raw (d-f): the multi-level imaging target tests the performance in quantitative sampling accuracy. Left column (a and d): the true images. Middle column (b and e): the blurred images. Right column (c and f): reconstruction results using the proposed super-resolution method.

Figure 3

Comparison of the cross-sectional plots across the fine features in the true, blurred, and reconstructed images, drawn along the yellow line near the bottom in Figures 2(d-f). Compared to the blurred image, the reconstruction produced improved results in terms of spatial resolution and quantitative accuracy.

Figure 4

Comparison of the blurred and reconstructed images against the true image using histograms. Top raw (a-c): the binary imaging phantom. Bottom raw (d-f): the multi-level imaging phantom. Left column (a and d): the true images. Middle column (b and e): the blurred images. Right column (c and f): the reconstructed images.

Figure 5

Three-dimensional slab geometry for validating the proposed method in diffuse optical imaging. The slab is homogeneous with significantly larger size in the x-/y-dimensions than in the z-dimension. A grid of 5×5 inclusions were positioned midway between the top and bottom surfaces to simulate fluorophores.

Figure 6

a) The true, (b) blurred, and (c) reconstructed images of transmittance from the simulated diffuse optical imaging using the geometry shown in Figure 5. (d) Quantitative comparison across the centerline, the yellow broken line within the white rectangles in (a-c), revealed the differences of the images. (e) Relative error images (defined by the ratio of the image in question to the true image, minus one) of the blurred and reconstructed images, respectively left and right, showed significant improvement of reconstruction (relative error of 17±4% vs. 1±1%, respectively).