When problems are scaled to "big data," researchers must often come up with new solutions, leveraging ideas from multiple research areas--as we frequently witness in today's big data techniques and tools for machine learning, bioinformatics, and data visualization. Beyond these heavily studied topics, there exist other classes of general problems that must be rethought at scale. One such problem is that of large-scale signal reconstruction:4 taking a set of observations of relatively low dimensionality, and using them to reconstruct a high-dimensional, unknown signal. This class of problems arises when we can only observe a subset of a complex environment that we are seeking to model--for instance, placing a few sensors and using their readings to reconstruct an environment's temperature, or monitoring multiple points in a network and using the readings to estimate end-to-end network traffic, or using 2D slices to reconstruct a 3D image. The following paper is notable because it scalably addresses an underserved problem with practical impact, and does so in a clean, insightful, and systematic way. This signal reconstruction problem (SRP) is typically approached as an optimization task, in which we search for the high-dimensional signal that minimizes a loss function comparing it to the known properties of the signal.

In this paper, we address the problem of reconstructing a time-domain signal (or a phase spectrogram) solely from a magnitude spectrogram. Since magnitude spectrograms do not contain phase information, we must restore or infer phase information to reconstruct a time-domain signal. One widely used approach for dealing with the signal reconstruction problem was proposed by Griffin and Lim. This method usually requires many iterations for the signal reconstruction process and depending on the inputs, it does not always produce high-quality audio signals. To overcome these shortcomings, we apply a learning-based approach to the signal reconstruction problem by modeling the signal reconstruction process using a deep neural network and training it using the idea of a generative adversarial network. Experimental evaluations revealed that our method was able to reconstruct signals faster with higher quality than the Griffin-Lim method.