Task-specific sensor optical designs

1. A method for designing a compressive sensing matrix for machine learning, comprising:

receiving an image associated with a classification task;

generating a sensing matrix, the sensing matrix comprising an array of nonzero elements of the image;

providing a prism array comprising a plurality of prism elements, the prism array in communication with the sensing matrix;

mapping a row of values corresponding with an input angle of the prism array to a respective column corresponding with a detector;

detecting via the detector an output angle of a prism element of the prism array associated with a respective input angle;

fabricating a physical model of the detector;

generating a compressed representation of the image via the physical model;

applying a machine learning classification algorithm to the compressed representation of the image; and

generating an optimized non-invertible final determination of the image.

2. The method of claim 1 , further comprising: implementing the machine learning classification algorithm by applying at least one blurring kernel.

3. The method of claim 2 , wherein the at least one blurring kernel comprises a prism kernel and a Fresnel kernel.

4. The method of claim 1 , wherein the machine learning classification algorithm comprises a Bayesian neural network, the Bayesian neural network comprises a plurality of weights in which each weight of the plurality of weights is sampled from a categorical distribution and a probability for each weight is learned.

5. The method of claim 4 , further comprising:

optimizing the Bayesian neural network in a first phases using a Gaussian approximation for the categorical distribution; and

freezing a sensing layer and using the categorical distributions to tune a subsequent layer of the Bayesian neural network;

wherein the sensing matrix comprises a discrete sensing matrix.

6. The method of claim 5 , further comprising simulating a polychromatic blurring kernel programmatically using Fresnel diffraction.

7. The method of claim 4 , further comprising providing a plurality of prism elements for each non-zero element of the sensing matrix to vary the associated weights.

8. The method of claim 7 , further comprising assigning the smallest non-zero weight a weight value of one and sequentially assigning the weight value in corresponding multiples of the smallest non-zero weight value;

adding prism elements to the prism array based on the assigned weight value of the sensing matrix; and

using a penalty to sparsify when optimizing the sensing matrix and enabling variable weight values across a scene;

wherein the sensing matrix being binned into a plurality of discrete weights.

9. The method of claim 8 , wherein the penalty comprises an L1 penalty or an approximate L0 norm penalty.

10. A prism array architecture for a classification task for reducing a dimensionality of an optical measurement and generating an optical component, comprising:

a sensing matrix configured to map values in object space to measurements in image space; wherein the sensing matrix having one or more columns representing a plurality of separated nonzero values;

a prism array comprising a plurality of prism elements arranged to map a plurality of input angles to a single detector wherein each prism element maps an input angle to a corresponding output location;

wherein a transmission of the prism array corresponds to a weighting of the sensing matrix; and

a processor configured to execute a machine learning classification algorithm applied to a compressed representation of the optical component to generate an optimized non-invertible final determination of the optical component.

11. The prism array architecture of claim 10 , further comprising;

optimizing the respective angle of each prism element of the prism array by a sequential raytrace program to position the prism element relative to the detector to optimize the angle of the prism element.

12. The prism array architecture of claim 10 , wherein the respective prism elements having an index of refraction of approximately 1.5 for all relevant wavelengths.

13. The prism array architecture of claim 10 , further comprising a digital micromirror device (DMD); the prism array configured to divide a stop; wherein an object is imaged onto the DMD and the stop is imaged onto the detector; and wherein the stop and a field of view are separated at the DMD; the field of view overlapping at the detector, and a channel corresponding with each detector is separated; the channels formed by dividing an aperture using the prism array.

14. The prism array architecture of claim 10 , wherein the processor is configured to apply at least one blurring kernel.

15. The prism array architecture of claim 14 , wherein the at least one blurring kernel comprises a prism kernel, and a Fresnel kernel.

16. The prism array architecture of claim 15 , wherein the sensing matrix is binned into a plurality of discrete weights.

17. The prism array architecture of claim 15 , wherein the processor is further configured to assign a smallest non-zero weight a weight value of one and sequentially assigning a weight value in corresponding multiples of the smallest non-zero weight value;

add prism elements to the prism array based on the assigned weight value of the sensing matrix; and

sparsify when optimizing the sensing matrix and enabling variable weight values across a scene by applying an L1 penalty.

18. The prism array architecture of claim 10 , wherein the machine learning classification algorithm comprises a Bayesian neural network, the Bayesian neural network comprising a plurality of weights in which each weight of the plurality of weights is sampled from a categorical distribution and a probability for each weight is learned.

19. The prism array architecture of claim 10 , wherein the sensing matrix comprises a discrete sensing matrix wherein the Bayesian neural network is arranged in a first phases using a Gaussian approximation for the categorical distribution; and

the sensing layer uses the categorical distributions to tune a subsequent layer of the machine learning classification algorithm.

20. A non-transitory, computer-readable medium comprising instructions that, when executed by one or more processors, cause the one or more processors to perform operations comprising:

receiving an image associated with a classification task;

generating a sensing matrix, the sensing matrix comprising an array of nonzero elements of the image;

providing a prism array comprising a plurality of prism elements, the prism array in communication with the sensing matrix;

mapping a row of values corresponding with an input angle of the prism array to a respective column corresponding with a detector;

detecting via the detector an output angle of a prism element of the prism array associated with a respective input angle;

fabricating a physical model of the detector;

generating a compressed representation of the image via the physical model;

applying a machine learning classification algorithm to the compressed representation of the image; and

generating an optimized non-invertible final determination of the image.

21. The non-transitory, computer-readable medium of claim 20 , further comprising: implementing the machine learning classification algorithm by applying at least one blurring kernel.

22. The non-transitory, computer-readable medium of claim 21 , wherein the at least one blurring kernel comprises a prism kernel, and a Fresnel kernel.

23. The non-transitory, computer-readable medium of claim 22 , wherein the machine learning classification algorithm comprises a Bayesian neural network, the Bayesian neural network comprises a plurality of weights in which each weight of the plurality of weights is sampled from a categorical distribution and a probability for each weight is learned.

24. The non-transitory, computer-readable medium of claim 23 , further comprising instructions for:

optimizing the Bayesian neural network in a first phases using a Gaussian approximation for the categorical distribution; and

freezing a sensing layer and using the categorical distributions to tune a subsequent layer of the machine learning classification algorithm;

wherein the sensing matrix comprises a discrete sensing matrix.

25. The non-transitory, computer-readable medium of claim 24 , further comprising instructions for simulating a polychromatic blurring kernel programmatically using Fresnel diffraction.

26. The non-transitory, computer-readable medium of claim 24 , further comprising instructions for assigning the smallest non-zero weight a weight value of one and sequentially assigning a weight value in corresponding multiples of the smallest non-zero weight value;

adding prism elements to the prism array based on the assigned weight value of the sensing matrix; and

using an L1 penalty to sparsify when optimizing the sensing matrix and enabling variable weight values across a scene;

wherein the sensing matrix being binned into a plurality of discrete weights.