A reconstructed image is the decoder’s approximation of an input image after the encoder has compressed it into a lower-dimensional latent representation. Encoding is lossy, so subtle variations may disappear; training instead preserves as much essential visual information as the latent-size budget allows. section 9.1.4 section 14.5
Let x denote the input and x̃ the reconstructed image. Reconstruction loss measures their mismatch, and end-to-end training adjusts the encoder and decoder to reduce it. The ideal output matches the input as closely as the architecture and latent budget permit, but exact equality is generally impossible after information loss. section 14.5 section 14.7.2
Common reconstruction-loss choices include:
- Binary cross-entropy compares normalized pixel intensities across image positions, treating the input image as the target rather than as a one-hot class vector. section 9.1.4
- In a variational autoencoder, reconstruction loss is minimized alongside KL divergence, which regularizes the encoder-generated latent distribution. section 14.7.2
Convolutional autoencoder
For a 32×32 image, convolution, ReLU, and max-pooling layers reduce spatial dimensions before a linear layer produces a latent vector. Transposed convolutions then expand that vector into a reconstructed image, ending with a sigmoid output.
