Fast acquisition and reconstruction of optical coherence tomography images via sparse representation

Abstract

In this paper, we present a novel technique, based on compressive sensing principles, for reconstruction and enhancement of multi-dimensional image data. Our method is a major improvement and generalization of the multi-scale sparsity based tomographic denoising (MSBTD) algorithm we recently introduced for reducing speckle noise. Our new technique exhibits several advantages over MSBTD, including its capability to simultaneously reduce noise and interpolate missing data. Unlike MSBTD, our new method does not require an a priori high-quality image from the target imaging subject and thus offers the potential to shorten clinical imaging sessions. This novel image restoration method, which we termed sparsity based simultaneous denoising and interpolation (SBSDI), utilizes sparse representation dictionaries constructed from previously collected datasets. We tested the SBSDI algorithm on retinal spectral domain optical coherence tomography images captured in the clinic. Experiments showed that the SBSDI algorithm qualitatively and quantitatively outperforms other state-of-the-art methods.

Fig. 1

Process schematic for creating an HH SDOCT image and its LL counterpart.

Fig. 2

Selection of patches from the LL and HH images to construct their corresponding dictionaries of basis functions. Since the patch positions in these two images are known, the constructed dictionaries can be strictly matched. In mathematical representation, both LL and HH patches are lexicographically ordered as columns (atoms) of the corresponding dictionary.

Fig. 3

Illustration of the sparse coefficients α_L,L and α_H,H obtained by the decomposition of LL patch x_L,L and HH patch x_H,H over dictionaries D_L,L and D_H,H with OMP algorithm. The positions of the nonzeros coefficients in α_L,L and α_H,H are identical while their values might be different.

Fig. 4

Dictionary and mapping learning algorithm.

Fig. 5

SDOCT B-scan acquired from the fovea (d) often have more complex structures than those in periphery regions (b), (c), (e), (f). (a) Summed-voxel projection [51] (SVP) en face SDOCT image of a nonneovascular age-related macular degeneration (AMD) patient. (b), (c), (e), (f) B-scans acquired from the green, yellow, blue, and purple lines (periphery regions). (d) B-scan acquired from the red line (fovea region).

Fig. 6

Algorithmic flowchart illustrating learning processes for structural dictionaries and mapping functions.

Fig. 7

Outline of the SBSDI framework.

Fig. 8

Two types of sampling patterns and their reconstruction results by CS-recovery [62], Bicubic, Tikhonov [63], BM3D [64]+Bicubic, ScSR [32], 2-D-SBSDI-nomap, 2-D-SBSDI, and our SBSDI method. (a) Randomly sampled image with 50% data missing. (b) Image (a) reconstructed by CS-recovery [62] (PSNR = 19.46). (c) Regularly sampled image with 50% data missing. (d) Image (c) reconstructed by CS-recovery [62] (PSNR = 19.01). (e) Image (c) reconstructed by Bicubic (PSNR = 17.77). (f) Image (c) reconstructed by Tikhonov [63] (PSNR = 22.23). (g) Image (c) reconstructed by BM3D [64] +Bicubic (PSNR = 23.26). (h) Image (c) reconstructed by ScSR (PSNR = 22.11). (i) Image (c) reconstructed by 2-D-SBSDI-nomap (PSNR = 23.05). (j) Image (c) reconstructed by 2-D-SBSDI (PSNR = 23.96). (k) Image (c) reconstructed by SBSDI (PSNR = 24.56). (l) Registered and averaged image which was acquired 80 times slower than the image in (i)–(k).

Fig. 9

Two types of sampling patterns and their reconstruction results by CS-recovery [62], Bicubic, Tikhonov [63], BM3D [64]+Bicubic, ScSR [32], 2-D-SBSDI-nomap, 2-D-SBSDI, and our SBSDI method. (a) Randomly sampled image with 75% data missing. (b) Image (a) reconstructed by CS-recovery [62] (PSNR = 20.83). (c) Regularly sampled image with 75% data missing. (d) Image (c) reconstructed by CS-recovery [62] (PSNR = 20.67). (e) Image (c) reconstructed by Bicubic (PSNR = 17.75). (f) Image (c) reconstructed by Tikhonov [63] (PSNR = 22.68). (g) Image (c) reconstructed by BM3D [64] +Bicubic (PSNR = 23.28). (h) Image (c) reconstructed by ScSR (PSNR = 23.09). (i) Image (c) reconstructed by 2-D-SBSDI-nomap (PSNR = 23.68). (j) Image (c) reconstructed by 2-D-SBSDI (PSNR = 23.99). (k) Image (c) reconstructed by SBSDI (PSNR = 24.58). (l) Registered and averaged image which was acquired 160 times slower than the image in (i)–(k).

Fig. 10

An example real experimental dataset with results reconstructed by Tikhonov [63], Bicubic, BM3D [64]+Bicubic, 2-D-SBSDI-nomap, 2-D-SBSDI, and SBSDI method. The left and right columns show images from the fovea and 1.5 mm below the fovea area, respectively. (a) Original images (b) bicubic reconstruction (Left: PSNR = 18.51, Right: PSNR = 17.84). (c) Tikhonov [63] reconstruction (Left: PSNR = 23.07, Right: PSNR = 21.99). (d) BM3D [64]+Bicubic reconstruction (Left: PSNR = 26.33, Right: PSNR = 23.24). (e) 2-D-SBSDI-nomap reconstruction (Left: PSNR = 25.06, Right: PSNR = 22.46). (f) 2-D-SBSDI reconstruction (Left: PSNR = 26.20, Right: PSNR = 23.10). (g) SBSDI reconstruction (Left: PSNR = 26.77, Right: PSNR = 23.52). (h) Registered and averaged images which were acquired 80 times slower than the image in (g).

Fig. 11

A real experimental dataset from a mouse optic nerve with results reconstructed by Bicubic, BM3D [64]+Bicubic, and SBSDI methods. We intentionally selected a suboptimal training set for the SBSDI method based on human images captured on a different SDOCT system to evaluate robustness of the SBSDI algorithm with respect to training sets. (a) Average image. (b) Top Left: Test image (with no subsampling). Top Right: Bicubic reconstruction, PSNR = 28.63, CNR = 0.85, MSR = 3.12. Bottom Left: BM3D+Bicubic reconstruction, PSNR = 31.89, CNR = 2.26, MSR = 11.15. Bottom Right: SBSDI reconstruction, PSNR = 32.69, CNR = 2.64, MSR = 13.69. (c) Top Left: Test image (with 50% data missing). Top Right: Bicubic reconstruction, PSNR = 28.43, CNR = 0.77, MSR = 3.31. Bottom Left: BM3D+Bicubic reconstruction, PSNR = 31.27, CNR = 2.03, MSR = 11.36. Bottom Right: SBSDI reconstruction, PSNR = 32.48, CNR = 2.33, MSR = 13.72. (d) Top Left: Test image (with 75% data missing). Top Right: Bicubic reconstruction, PSNR = 29.18, CNR = 0.69, MSR = 3.30. Bottom Left: BM3D+Bicubic reconstruction, PSNR = 33.26, CNR = 2.06, MSR = 19.50. Bottom Right: SBSDI reconstruction, PSNR = 32.93, CNR = 2.47, MSR = 20.96.