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Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking spatial coordinates as inputs. However, unlike traditional pixel representations, little is known about the sample complexity of estimating images using INRs in the context of linear inverse problems. Towards this end, we study the sampling requirements for recovery of a continuous domain image from its low-pass Fourier coefficients by fitting a single hidden-layer INR with ReLU activation and a Fourier features layer using a generalized form of weight decay regularization. Our key insight is to relate minimizers of this non-convex parameter space optimization problem to minimizers of a convex penalty defined over a space of measures. We identify a sufficient number of samples for which an image realized by a width-1 INR is exactly recoverable by solving the INR training problem, and give a conjecture for the general width-W case. To validate our theory, we empirically assess the probability of achieving exact recovery of images realized by low-width single hidden-layer INRs, and illustrate the performance of INR on super-resolution recovery of more realistic continuous domain phantom images.
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SINCO: A Novel Structural Regularizer for Image Compression Using Implicit Neural Representations
Implicit neural representations (INR) have been recently proposed as deep learning (DL) based solutions for image compression. An image can be compressed by training an INR model with fewer weights than the number of image pixels to map the coordinates of the image to corresponding pixel values. While traditional training approaches for INRs are based on enforcing pixel-wise image consistency, we propose to further improve image quality by using a new structural regularizer. We present structural regularization for INR compression (SINCO) as a novel INR method for image compression. SINCO imposes structural consistency of the compressed images to the groundtruth by using a segmentation network to penalize the discrepancy of segmentation masks predicted from compressed images. We validate SINCO on brain MRI images by showing that it can achieve better performance than some recent INR methods.
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- Award ID(s):
- 2043134
- PAR ID:
- 10504929
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing
- ISSN:
- 1520-6149
- ISBN:
- 978-1-7281-6327-7
- Page Range / eLocation ID:
- 1 to 5
- Format(s):
- Medium: X
- Location:
- Rhodes Island, Greece
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICASSP49357.2023.10095531
