Signal recovery with differentiable scalograms spectrogram

It involves reconstructing or enhancing signals directly from their time-frequency representations

Signal recovery with differentiable scalograms and spectrograms involves using techniques that allow for the reconstruction or enhancement of signals from their corresponding scalogram or spectrogram representations while maintaining differentiability for optimization purposes.

1. Scalograms: Scalograms are representations of signals in the time-frequency domain using wavelet transforms or similar techniques. They offer a way to analyze signals in both time and frequency simultaneously, providing valuable information about the signal's characteristics. Differentiable scalograms refer to scalogram representations that can be computed with operations that allow for gradients to be calculated, making them suitable for optimization tasks such as signal recovery.
2. Spectrograms: Spectrograms are similar to scalograms but are typically obtained using the Fourier transform. They display the frequency content of a signal over time. Just like scalograms, differentiable spectrograms allow for gradients to be computed, making them useful for optimization-based signal processing tasks.

Signal recovery with differentiable scalograms and spectrograms involves using optimization techniques to reconstruct or enhance signals directly from their representations. This can be useful in various applications such as denoising, inpainting, source separation, and audio enhancement. By exploiting the differentiability of the transformations used to compute scalograms or spectrograms, it becomes possible to train models to perform these tasks efficiently using techniques such as gradient descent or variants like stochastic gradient descent.

Overall, the ability to work with differentiable representations like scalograms and spectrograms opens up opportunities for more effective and flexible signal processing methods, particularly when combined with deep