This paper introduces a platform to support serverless computing for scalable event-driven data processing that features a multi-level elasticity approach combined with virtualization of GPUs. The platform supports the execution of applications based on Docker containers in response to file uploads to a data storage in order to perform the data processing in parallel. This is managed by an elastic Kubernetes cluster whose size automatically grows and shrinks depending on the number of files to be processed. To accelerate the processing time of each file, several approaches involving virtualized access to GPUs, either locally or remote, have been evaluated. A use case that involves the inference based on deep learning techniques on transthoracic echocardiography imaging has been carried out to assess the benefits and limitations of the platform. The results indicate that the combination of serverless computing and GPU virtualization introduce an efficient and cost-effective event-driven accelerated computing approach that can be applied for a wide variety of scientific applications.