Discrete shearlet transform on GPU with applications in anomaly detection and denoising

Correspondence: [email protected] UMIACS, University of Maryland, College Park, MD 20742-3275, USA Full list of author information is available at the end of the article †Equal contributor Abstract Shearlets have emerged in recent years as one of of the most successful methods for the multiscale analysis of multidimensional signals. Unlike wavelets, shearlets form a pyramid of well-localized functions defined not only over a range of scales and locations, but also over a range of orientations and with highly anisotropic supports. As a result, shearlets are much more effective than traditional wavelets in handling the geometry of multidimensional data and this was exploited in a wide range of applications from image and signal processing. However, despite their desirable properties, the wider applicability of shearlets is limited by its computational complexity. For example, denoising a single 512× 512 image using a current implementation of the shearlet-based shrinkage algorithm can take between 10 seconds and 2 minutes, depending on the number of CPU cores, and much longer processing times are required for video denoising. However, due to the parallel nature of the shearlet transform, it is possible to use Graphical Processing Units (GPU) to accelerate it. We provide an open source standalone implementation of the 2D shearlet using CUDA C++ as well as GPU-accelerated MATLAB implementations of the 2D and 3D shearlet transforms. We have instrumented the code so that we can analyze the running time of each kernel under different GPU hardware. In addition to denoising, we describe a novel application of shearlets for detecting anomalies on textured images. In this application, computation times can be reduced by a factor of 50 or more, compared to multi-core CPU implementations.