What does the retina know about natural scenes?
Neural Computation
Digital Image Processing
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Toeplitz and circulant matrices: a review
Communications and Information Theory
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
MIMO transceiver design via majorization theory
Foundations and Trends in Communications and Information Theory
Towards a theory of early visual processing
Neural Computation
IEEE Transactions on Information Theory
Source encoding in the presence of random disturbance (Corresp.)
IEEE Transactions on Information Theory
Transmission of noisy information to a noisy receiver with minimum distortion
IEEE Transactions on Information Theory
Robust Coding Over Noisy Overcomplete Channels
IEEE Transactions on Image Processing
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Robust coding has been proposed as a solution to the problem of minimizing decoding error in the presence of neural noise. Many real-world problems, however, have degradation in the input signal, not just in neural representations. This generalized problem is more relevant to biological sensory coding where internal noise arises from limited neural precision and external noise from distortion of sensory signal such as blurring and phototransduction noise. In this note, we show that the optimal linear encoder for this problem can be decomposed exactly into two serial processes that can be optimized separately. One is Wiener filtering, which optimally compensates for input degradation. The other is robust coding, which best uses the available representational capacity for signal transmission with a noisy population of linear neurons. We also present spectral analysis of the decomposition that characterizes how the reconstruction error is minimized under different input signal spectra, types and amounts of degradation, degrees of neural precision, and neural population sizes.