Many times, the field measurements of ECG signals is embedded in high noise, to a point that traditional signal processing methods fail to uncover any discernible signal. In this paper, we present the use of differentiable scalograms and spectrograms to recover a time-domain ECG signal embedded in high noise. The use of differentiable time-frequency transforms allows us to obtain an approximation of the original signal without the need for phase information or the need to explicitly invert the time-frequency transform. Most often, the phase information in a time-frequency representation is discarded in favor of the magnitudes. There are a number of reasons for this. One reason is simply that the complex-valued time-frequency representations containing phase information are difficult to plot and interpret. This may lead people to retain only the magnitudes. In these applications, it still may be useful or even necessary to recover an approximation of the original signal. The techniques for doing this are referred to as phase retrieval. Phase retrieval is, in general, ill-posed, and prior iterative methods suffer from the non-convexity of the formulation, and therefore convergence to an optimal solution is impossible to guarantee. With the introduction of automatic differentiation and differentiable signal processing, we can now use gradient descent with the usual convex loss functions to perform high-fidelity phase retrieval. This methodology helps recover the ECG signal embedded in high noise. Additionally in this paper, the gradient-descent-based technique using differentiable spectrograms is compared against the Griffin-Lim algorithm, and it is shown that the proposed method has a better L2-norm error than the Griffin-Lim algorithm.