1. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. A two-dimensional sampling lattice. v1 and v2 are the basis vectors. T1 and T2 are the sampling periods in the horizontal and vertical directions. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

2. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Magnitude of the Fourier transform of an interlaced image. Replicas of the spectrum are arranged on a hexagonal pattern that is shown with added dotted lines. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

3. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Image with increasing spatial frequency and subsampled versions using square, interlaced, and hexagonal sampling. Downsampling was done using hyperpixels of 10×10 pixels for the square and interlaced images and 12×10 pixels for the hexagonal image. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

4. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Top: ultrasound image of a hypoechoic lesion in a contrast phantom and its downsampled version by a factor of 10. Bottom: interlaced versions of the images in the top row. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

5. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Neighborhood analysis in rectangular, hexagonal, and interlaced grids. Rectangular pixels can have four or eight neighbors, depending on the definition of connectivity. Hexagonal and interlaced pixels always have six neighbors. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

6. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. 7×7 hexagonal mask. The filter’s output was assigned to the center pixel (shown in white). Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

7. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Hexagonal Laplacian operator. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

8. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Simulated images (a), and filtered versions with the adaptive filter in one iteration (b) and with the diffusion filter in 30 iterations using a value of λ=1/9 (c). Resolution of the original images are 160×160 pixels in the synthetic kidney (top), 350×250 pixels in cyst phantom 1 (middle), and 330×260 pixels in the cyst phantom 2 (bottom). Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

9. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Phantom images (a), and filtered versions with the adaptive filter in one iteration (b) and with the diffusion filter in 30 iterations using a value of λ=1/9 (c). Resolution of the original images are 200×220, 200×200, and 200×200 pixels on top, middle, and bottom images, respectively. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

10. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Heart images (a), and filtered versions with the adaptive filter in one iteration (b) and with the diffusion filter in 30 iterations using a value of λ=1/9 (c). Resolution of the original images are 350×350, 350×350, and 150×150 pixels on top, middle, and bottom images, respectively. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

11. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Three test images showing the regions used to evaluate quality measurements. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

12. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Close up of the aortic root wall. (a) rectangular image. (b) interlaced image. (c) filtered image obtained with the diffusion filter. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022

13. Date of download: 7/9/2016 Copyright © 2016 SPIE. All rights reserved. Simulated image of a cyst phantom zoomed in to observe aliasing artifacts. (a) image on an interlaced grid with axial shifts. (b) image on an interlaced grid with lateral shifts. Figure Legend: From: Hexagonal filters for ultrasound images J. Electron. Imaging. 2014;23(4):043022. doi:10.1117/1.JEI.23.4.043022