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

Xavier Gibert,Rama Chellappa,Demetrio Labate,Vishal M Patel

doi:10.1186/1687-6180-2014-64

Abstract

Shearlets have emerged in recent years as one 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 the computational complexity of current software implementations. For example, denoising a single 512 × 512 image using a current implementation of the shearlet-based shrinkage algorithm can take between 10 s and 2 min, depending on the number of CPU cores, and much longer processing times are required for video denoising. On the other hand, due to the parallel nature of the shearlet transform, it is possible to use graphics processing units (GPU) to accelerate its implementation. In this paper, we present an open source stand-alone implementation of the 2D discrete shearlet transform 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 in textured images. In this application, computation times can be reduced by a factor of 50 or more, compared to multicore CPU implementations.

Highlights

During the last decade, a new generation of multiscale systems has emerged which combines the power of the classical multiresolution analysis with the ability to process directional information with very high efficiency
In particular, offer a unique combination of very remarkable features: they have a simple and wellunderstood mathematical structure derived from the theory of affine systems [3,6]; they provide optimally sparse representations, in a precise sense, for a large class of images and other multidimensional data where wavelets are suboptimal [7,8]; and the directionality is controlled by shear matrices rather than rotations
The objective of this paper is to introduce and demonstrate a new implementation of the 2D and 3D discrete shearlet transform which takes advantage of the computational capabilities of the graphics processing unit (GPU)

Summary

Introduction

A new generation of multiscale systems has emerged which combines the power of the classical multiresolution analysis with the ability to process directional information with very high efficiency. The elements of such systems form a pyramid of well-localized waveforms ranging across various scales and locations, and across various orientations and with highly anisotropic shapes Due to their richer structure, these more sophisticated multiscale systems are able to overcome the poor directional sensitivity of traditional multiscale systems and Shearlets, in particular, offer a unique combination of very remarkable features: they have a simple and wellunderstood mathematical structure derived from the theory of affine systems [3,6]; they provide optimally sparse representations, in a precise sense, for a large class of images and other multidimensional data where wavelets are suboptimal [7,8]; and the directionality is controlled by shear matrices rather than rotations. Running times for alternative shearlet implementations from Shearlab [10] as well as for the current implementation of the curvelet transform [22] are comparable

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Conclusion