Equivariant generative prior for inverse problems with unknown rotation
A processor-implemented method for estimating a channel by a deep generative model includes receiving, at a device, an observation of the channel and mapping, at the device, the observation to a mean value associated with the channel and a covariance matrix associated with the channel. The processor-implemented method also includes reconstructing, at the device, the channel based on the mean value and the covariance matrix.
1. A processor-implemented method for estimating a channel by a deep generative model, comprising:
receiving, at a device, an observation of the channel;
mapping, at the device, the observation to a mean value and a covariance matrix that together define a probability distribution representing an estimate of the channel associated with the observation; and
reconstructing, at the device, the channel based on the mean value and the covariance matrix.
2. The processor-implemented method of claim 1 , in which the deep generative model comprises an equivariant variational autoencoder (VAE).
3. The processor-implemented method of claim 2 , in which the observation is mapped to the mean value and the covariance matrix at an equivariant encoder of the equivariant VAE.
4. The processor-implemented method of claim 2 , in which the channel is reconstructed at an equivariant decoder of the equivariant VAE.
5. The processor-implemented method of claim 1 , further comprising generating a latent space representation based on the mean value and the covariance matrix.
6. The processor-implemented method of claim 5 , in which the channel is reconstructed based on the latent space representation.
7. The processor-implemented method of claim 1 , in which the channel is a wireless communication channel.
8. The processor-implemented method of claim 1 , further comprising training the deep generative model by mapping the observation to a latent code associated with the channel based on gradient descent over a latent space.
9. An apparatus for estimating a channel, comprising:
means for receiving, at a device, an observation of the channel;
means for mapping, at the device, the observation to a mean value and a covariance matrix that together define a probability distribution representing an estimate of the channel associated with the observation; and
means for reconstructing, at the device, the channel based on the mean value and the covariance matrix.
10. The apparatus of claim 9 , in which the apparatus comprises means for equivariant variational autoencoding.
11. The apparatus of claim 10 , in which the means for equivariant variational autoencoding comprises means for equivariant encoding.
12. The apparatus of claim 10 , in which the means for equivariant variational autoencoding comprises means for equivariant decoding.
13. The apparatus of claim 9 , further comprising means for generating a latent space representation based on the mean value and the covariance matrix.
14. The apparatus of claim 13 , in which the means for reconstructing the channel comprises means for reconstructing the channel based on the latent space representation.
15. The apparatus of claim 9 , in which the channel is a wireless communication channel.
16. The apparatus of claim 9 , further comprising means for training a deep generative network associated with the apparatus, the means for training comprising means for mapping the observation to a latent code associated with the channel based on gradient descent over a latent space.
17. An apparatus for estimating a channel via a deep generative model, comprising:
at least one processor; and
at least one memory coupled with the at least one processor and storing instructions operable, when executed by the at least one processor, to cause the apparatus to:
receive an observation of the channel;
map the observation to a mean value and a covariance matrix that together define a probability distribution representing an estimate of the channel associated with the observation; and
reconstruct the channel based on the mean value and the covariance matrix.
18. The apparatus of claim 17 , in which the deep generative model comprises an equivariant variational autoencoder (VAE).
19. The apparatus of claim 18 , in which the observation is mapped to the mean value and the covariance matrix at an equivariant encoder of the equivariant VAE.
20. The apparatus of claim 18 , in which the channel is reconstructed at an equivariant decoder of the equivariant VAE.
21. The apparatus of claim 17 , in which execution of the instructions further cause the apparatus to generate a latent space representation based on the mean value and the covariance matrix.
22. The apparatus of claim 21 , in which execution of the instructions further cause the apparatus to reconstruct the channel based on the latent space representation.
23. The apparatus of claim 17 , in which the channel is a wireless communication channel.
24. The apparatus of claim 17 , in which execution of the instructions further cause the apparatus to train the deep generative model by mapping the observation to a latent code associated with the channel based on gradient descent over a latent space.
25. A non-transitory computer-readable medium having program code recorded thereon for estimating a channel via a deep generative model, the program code executed by a processor and comprising:
program code to receive an observation of the channel;
program code to map the observation to a mean value and a covariance matrix that together define a probability distribution representing an estimate of the channel associated with the observation; and
program code to reconstruct the channel based on the mean value and the covariance matrix.
26. The non-transitory computer-readable medium of claim 25 , in which the deep generative model comprises an equivariant variational autoencoder (VAE).
27. The non-transitory computer-readable medium of claim 26 , in which the observation is mapped to the mean value and the covariance matrix at an equivariant encoder of the equivariant VAE.
28. The non-transitory computer-readable medium of claim 26 , in which the channel is reconstructed at an equivariant decoder of the equivariant VAE.
29. The non-transitory computer-readable medium of claim 25 , in which the program code further comprises program code to generate a latent space representation based on the mean value and the covariance matrix.
30. The non-transitory computer-readable medium of claim 29 , in which the program code further comprises program code to reconstruct the channel based on the latent space representation.