The past few years have seen a significant rise in research and public interest in the use of generative machine learning and artificial intelligence (ML/AI) models for image-to-image translation tasks. Perhaps one of the more recognizable models is pix2pix [3], a deep generative model (DGM) and particularly a deep convolutional generative adversarial network (DCGAN) [2, 7] that is capable of translating between pairs of high-resolution images within a learned image data domain. The novelty of pix2pix laid in its model architecture which combined a deep U-Net generator that learns to generate mock data samples with a convolutional PatchGAN discriminator that learns to label regions, "patches," of inputs as "real" (sampled data) or "fake" (generated data). Much of the research interest in pix2pix has centred on image translation tasks but the inherent structure of the U-Net model does not limit it to images alone. In fact original developments of U-Net were for semantic segmentation [5]. Research into GANs as they stand within the wider DGM and even wider generative ML/AI ecosystem have not been limited to images either. Parallel work on one-dimensional (1D) GANs where time series training data is periodic [1] has observed that derived models that decompose demonstrated two-dimensional models into 1D counterparts with a wider learning aperture, which we set ourselves with the size of convolution kernels, are capable of generating convincing high-accuracy 1D time series (including audio) from a learned signal data domain. Wider convolutional apertures are necessary for models to see and learn the time series periodicity. Others before have taken the conceptual essence of signal-to-signal translation and adapted its generator U-Net models for other signal domains; spectrum translation [6] (spectral/frequency series-to-series), sensor translation [4] (time series-to-series, 2D), and sound translation [9] (time series-to-series, 1D) to name a few.

In this work, we develop a neural network-based method to convert a noisy motion signal generated from segmenting rebinned list-mode cardiac SPECT images, to that of a high-quality surrogate signal, such as those seen from external motion tracking systems (EMTs). This synthetic surrogate will be used as input to our pre-existing motion correction technique developed for EMT surrogate signals. In our method, we test two families of neural networks to translate noisy internal motion to external surrogate: 1) fully connected networks and 2) convolutional neural networks. Our dataset consists of cardiac perfusion SPECT acquisitions for which cardiac motion was estimated (input: center-of-count-mass - COM signals) in conjunction with a respiratory surrogate motion signal acquired using a commercial Vicon Motion Tracking System (GT: EMT signals). We obtained an average R-score of 0.76 between the predicted surrogate and the EMT signal. Our goal is to lay a foundation to guide the optimization of neural networks for respiratory motion correction from SPECT without the need for an EMT.