Machine learning holography for particle field imaging

1. A method for particle/tracer localization or particle field imaging, the method comprising:

obtaining input data, the input data comprising at least one of a hologram of a 3-dimensional (3D) particle field, a depth map of the 3D particle field, or a maximum phase projection of the 3D particle field; and

applying a U-net convolutional neural network (CNN) to the input data to generate output data, wherein:

the U-net CNN comprises a set of one or more encoder blocks and a set of one or more decoder blocks,

for each respective encoder block of the set of encoder blocks, the respective encoder block has a residual connection between a first layer of the respective encoder block and a second layer of the respective encoder block that skips over a convolution layer of the respective encoder block between the first layer of the respective encoder block and the second layer of the respective encoder block,

for each respective decoder block of the set of decoder blocks, the respective decoder block has a residual connection between a first layer of the respective decoder block and a second layer of the respective decoder block that skips over a convolution layer of the respective decoder block between the first layer of the respective decoder block and the second layer of the respective decoder block,

output of a last-occurring encoder block of the set of encoder blocks is input to a first-occurring decoder block of the set of decoder blocks, and

the output data includes a first output image and a second output image, the first output image comprising a channel in which pixel intensity corresponds to relative depth of particles in the 3D particle field, and the second output image indicating locations of centroids of the particles in the 3D particle field.

2. The method of claim 1 , wherein applying the U-net CNN comprises:

for each respective encoder block of the set of encoder blocks, applying a Swish activation function between layers of the respective encoder block; and

applying the Swish activation function between each layer of each decoder block of the set of decoder blocks aside from before a last layer of a last decoder block of the set of decoder blocks.

3. The method of claim 2 , wherein applying the U-net CNN comprises:

applying a Sigmoid activation function before the last layer of the last decoder block of the set of decoder blocks.

4. The method of claim 1 , further comprising generating the depth map and maximum phase projection from the hologram.

5. The method of claim 1 , further comprising training the U-net CNN, wherein training the U-net CNN comprises:

calculating a first loss value by applying, to the first output image, a Huber loss function;

calculating a second loss value by applying, to the second output image, a Mean Square Error (MSE) loss function regularized by a total variation of the second output image; and

modifying parameters of the U-net CNN based on the first loss value and the second loss value.

6. A method for particle segmentation, the method comprising:

obtaining input data, the input data comprising at least one of a hologram of a 3-dimensional (3D) particle field, an image reconstructed from the hologram to a longitudinal location, or a minimum intensity projection in a longitudinal direction from a reconstructed optical field of the hologram; and

applying a U-net convolutional neural network (CNN) to the input data to generate output data, wherein:

the U-net CNN comprises a set of one or more encoder blocks and a set of one or more decoder blocks,

for each respective encoder block of the set of encoder blocks, the respective encoder block has a residual connection between a first layer of the respective encoder block and a second layer of the respective encoder block that skips over a convolution layer of the respective encoder block between the first layer of the respective encoder block and the second layer of the respective encoder block,

for each respective decoder block of the set of decoder blocks, the respective decoder block has a residual connection between a first layer of the respective decoder block and a second layer of the respective decoder block that skips over a convolution layer of the respective decoder block between the first layer of the respective decoder block and the second layer of the respective decoder block,

output of a last-occurring encoder block of the set of encoder blocks is input to a first-occurring decoder block of the set of decoder blocks, and

the output data includes a first output image and a second output image, the first output image comprising a particle size map for particles in the 3D particle field, and the second output image indicating locations of centroids of the particles in the 3D particle field.

7. The method of claim 6 , wherein applying the U-net CNN comprises:

for each respective encoder block of the set of encoder blocks, applying a Swish activation function between layers of the respective encoder block; and

applying the Swish activation function between each layer of each decoder block of the set of decoder blocks aside from before a last layer of a last decoder block of the set of decoder blocks.

8. The method of claim 7 , wherein applying the U-net CNN comprises:

applying a Sigmoid activation function before the last layer of the last decoder block of the set of decoder blocks.

9. The method of claim 6 , further comprising training the U-net CNN, wherein training the U-net CNN comprises:

calculating a first loss value by applying, to the first output image, a generalized dice loss (GDL) loss function;

calculating a second loss value by applying, to the second output image, a Mean Square Error (MSE) loss function regularized by a total variation of the second output image; and

modifying parameters of the U-net CNN based on the first loss value and the second loss value.

10. A system comprising:

processing circuitry; and

a computer-readable storage medium coupled to the at least one processor, the computer-readable storage medium configured to store instructions that configure the processing circuitry to:

obtain input data, the input data comprising at least one a hologram of a 3-dimensional (3D) particle field, a depth map of the 3D particle field, or a maximum phase projection of the 3D particle field; and

apply a U-net convolutional neural network (CNN) to the input data to generate output data, wherein:

the U-net CNN comprises a set of one or more encoder blocks and a set of one or more decoder blocks,

for each respective encoder block of the set of encoder blocks, the respective encoder block has a residual connection between a first layer of the respective encoder block and a second layer of the respective encoder block that skips over a convolution layer of the respective encoder block between the first layer of the respective encoder block and the second layer of the respective encoder block,

for each respective decoder block of the set of decoder blocks, the respective decoder block has a residual connection between a first layer of the respective decoder block and a second layer of the respective decoder block that skips over a convolution layer of the respective decoder block between the first layer of the respective decoder block and the second layer of the respective decoder block,

output of a last-occurring encoder block of the set of encoder blocks is input to a first-occurring decoder block of the set of decoder blocks, and

the output data includes a first output image and a second output image, the first output image comprising a channel in which pixel intensity corresponds to relative depth of particles in the 3D particle field, and the second output image indicating locations of centroids of the particles in the 3D particle field.

11. The system of claim 10 , wherein the processing circuitry is configured such that, as part of applying the U-net CNN, the processing circuitry:

for each respective encoder block of the set of encoder blocks, applies a Swish activation function between layers of the respective encoder block; and

applies the Swish activation function between each layer of each decoder block of the set of decoder blocks aside from before a last layer of a last decoder block of the set of decoder blocks.

12. The system of claim 11 , wherein the processing circuitry is configured such that, as part of applying the U-net CNN, the processing circuitry:

applies a Sigmoid activation function before the last layer of the last decoder block of the set of decoder blocks.

13. The system of claim 10 , wherein the processing circuitry is further configured to generate the depth map and maximum phase projection from the hologram.

14. The system of claim 10 , wherein the processing circuitry is further configured to train the U-net CNN, wherein the processing circuitry is configured such that, as part of training the U-net CNN, the processing circuitry:

calculates a first loss value by applying, to the first output image, a Huber loss function; and

calculates a second loss value by applying, to the second output image, a Mean Square Error (MSE) loss function regularized by a total variation of the second output image; and

modifies parameters of the U-net CNN based on the first loss value and the second loss value.

15. The system of claim 10 , further comprising an imaging apparatus configured to generate the hologram of the 3D particle field.

16. An imaging system comprising:

processing circuitry; and

a computer-readable storage medium coupled to the at least one processor, the computer-readable storage medium configured to store instructions that configure the processing circuitry to:

obtain input data, the input data comprising a hologram, a depth map of the 3D particle field, and a maximum phase projection of the 3D particle field; and

apply a U-net convolutional neural network (CNN) to the input data to generate output data, wherein:

the U-net CNN comprises a set of one or more encoder blocks and a set of one or more decoder blocks,

for each respective encoder block of the set of encoder blocks, the respective encoder block has a residual connection between a first layer of the respective encoder block and a second layer of the respective encoder block that skips over a convolution layer of the respective encoder block between the first layer of the respective encoder block and the second layer of the respective encoder block,

for each respective decoder block of the set of decoder blocks, the respective decoder block has a residual connection between a first layer of the respective decoder block and a second layer of the respective decoder block that skips over a convolution layer of the respective decoder block between the first layer of the respective decoder block and the second layer of the respective decoder block,

output of a last-occurring encoder block of the set of encoder blocks is input to a first-occurring decoder block of the set of decoder blocks, and

the output data includes a first output image and a second output image, the first output image comprising a channel in which pixel intensity corresponds to relative depth of particles in the 3D particle field, and the second output image indicating locations of centroids of the particles in the 3D particle field.

17. The system of claim 16 , wherein the processing circuitry is configured such that, as part of applying the U-net CNN, the processing circuitry:

for each respective encoder block of the set of encoder blocks, applies a Swish activation function between layers of the respective encoder block; and

applies the Swish activation function between each layer of each decoder block of the set of decoder blocks aside from before a last layer of a last decoder block of the set of decoder blocks.

18. The system of claim 17 , wherein the processing circuitry is configured such that, as part of applying the U-net CNN, the processing circuitry:

applies a Sigmoid activation function before the last layer of the last decoder block of the set of decoder blocks.

19. The system of claim 16 , wherein the processing circuitry is further configured to train the U-net CNN, wherein the processing circuitry is configured such that, as part of training the U-net CNN, the processing circuitry:

calculate a first loss value by applying, to the first output image, a generalized dice loss (GDL) loss function;

calculates a second loss value by applying, to the second output image, a Mean Square Error (MSE) loss function regularized by a total variation of the second output image;

modifies parameters of the U-net CNN based on the first loss value and the second loss value.

20. The system of claim 16 , further comprising an imaging apparatus configured to generate the hologram of the 3D particle field.