Applications of compressive sensing in spatial frequency domain imaging

Abstract

Significance: Spatial frequency domain imaging (SFDI) is an imaging modality that projects spatially modulated light patterns to determine optical property maps for absorption and reduced scattering of biological tissue via a pixel-by-pixel data acquisition and analysis procedure. Compressive sensing (CS) is a signal processing methodology which aims to reproduce the original signal with a reduced number of measurements, addressing the pixel-wise nature of SFDI. These methodologies have been combined for complex heterogenous data in both the image detection and data analysis stage in a compressive sensing SFDI (cs-SFDI) approach, showing reduction in both the data acquisition and overall computational time.

Aim: Application of CS in SFDI data acquisition and image reconstruction significantly improves data collection and image recovery time without loss of quantitative accuracy.

Approach: cs-SFDI has been applied to an increased heterogenic sample from the AppSFDI data set (back of the hand), highlighting the increased number of CS measurements required as compared to simple phantoms to accurately obtain optical property maps. A novel application of CS to the parameter recovery stage of image analysis has also been developed and validated.

Results: Dimensionality reduction has been demonstrated using the increased heterogenic sample at both the acquisition and analysis stages. A data reduction of 30% for the cs-SFDI and up to 80% for the parameter recover was achieved as compared to traditional SFDI, while maintaining an error of <10 % for the recovered optical property maps.

Conclusion: The application of data reduction through CS demonstrates additional capabilities for multi- and hyperspectral SFDI, providing advanced optical and physiological property maps.

Keywords: compressive sensing; data reduction; spatial frequency domain imaging.

Fig. 1

SFDI analysis workflows. (a) Traditional three-stage workflow. (b) cs-SFDI based workflow, here, raw images are compressed and reconstructed to simulate single-pixel detection, before following the traditional workflow. (c) CS-based parameter recovery algorithm, here, the demodulated images are compressed before both calibration and optical fitting are performed in the compressed space, before image reconstruction to generate the optical property maps.

Fig. 2

Representation of Eq. (5). The measurement vector $y$ is calculated by multiplying the sensing matrix, ${\mathrm{\Phi }}_{M\times N}$, by the image vector $x$, reducing the dimensionality of the data to $M\ll N$ values.

Fig. 3

cs-SFDI image panel. Comparison between the original data and reconstructed images for increasing pattern numbers.

Fig. 4

cs-SFDI RMS error results. RMS error for each optical property map obtained using the cs-SFDI algorithm, compared to the non-compression based ground truth results.

Fig. 5

Analytical anomaly ground truth maps for the CS parameter recovery phantom test.

Fig. 6

Simulated data CS parameter recovery algorithm image panel. Comparison between the original data and reconstructed images for increasing pattern numbers.

Fig. 7

Simulated data CS parameter recovery algorithm RMS error results. RMS error for each optical property map obtained using the data CS parameter recovery algorithm, compared to the non-compression based ground truth results.

Fig. 8

AppSFDI CS parameter recovery algorithm image panel. Comparison between the original data and reconstructed images for increasing pattern numbers.

Fig. 9

AppSFDI CS-based parameter recovery algorithm RMS errors. RMS error for each optical property map for the CS-based parameter recovery algorithm, compared to the non-compression–based ground truth results.

Fig. 10

Pixel-wise RMS error for 50% measurement reduction using the CS parameter recovery algorithm.