Abstract
Remotely sensed hyperspectral images provide data of the earth’s surface components. The data provided is collected through airborne devices such as satellites with the capability to collect large amounts of data to be sent to ground stations for processing. The main disadvantage of this scenario is the limited bandwidth connection between the airborne devices and the ground station on Earth which affects the information sending and real time processing. A possible solution is to include an on-board data processor. Field-Programmable Gate Arrays (FPGAs) are excellent target platform that allows the design reconfigurability, powerful computing and high performance levels. One of the most commonly used techniques in hyperspectral data analysis is linear spectral unmixing. In the last decade, L1/2 sparsity constrained Nonnegative Matrix Factorization (NMF), a linear spectral unmixing algorithm, and its extensions have been heavily studied to unmix the hyperspectral images and recover their material spectra. L1/2 regularizer is proven to have much better results in terms of sparsity and accuracy than other regularizers yet, to the best of our knowledge, has not been implemented. In this paper, we present an FPGA design for the L1/2 sparsity constrained NMF (L1/2-NMF) algorithm. The proposed design is tested on both synthetic and real data sets and implemented on Altera Family FPGAs. Implementation results show that the proposed design successfully unmixes the data with maximum frequency of 52.6 MHz and a speedup factor of 3.9 for the synthetic data set and a frequency of 104.32 MHz and a speedup factor of 1.14 for the real data set. The implementation results are compared to the simulation results and ground truth signatures using Spectral Angular Distance (SAD) measure. Calculations show that the implementation results have comparable SAD values to the simulation results.
Highlights
The launch of earth observation satellites has enhanced the field of remote sensing considerably in the past few years
SIMULATION AND IMPLEMENTATION TOOLS The hardware implementation of the L1/2-Nonnegative Matrix Factorization (NMF) algorithm described in section III is designed using Mentor Graphics FPGAdv 8.1
Our tests show that the simulation run time for the algorithm on MATLAB is 52.11 seconds while the implementation run time on Field-Programmable Gate Arrays (FPGAs) is 13.33 seconds which results in a speedup factor of 3.9
Summary
The launch of earth observation satellites has enhanced the field of remote sensing considerably in the past few years. Despite providing good results in extracting end-members from the hyperspectral image, the geometrical based approaches depend on the assumption of having a pure pixel in the data. In [32], the authors introduce a linear hyperspectral unmixing method based on L1-L2 sparsity and Total Variation (TV) regularization (L1-L2SUnSALTV) This algorithm forces strong sparsity through calculating the difference between the first and second norms. The proposed hardware architecture of the L1/2-NMF Algorithm contains an off-chip memory to save the augmented hyperspectral image, memory controller to select the data from the required addresses and the system main modules namely Cost Function Calculation Module, Update A Module and Update S Module implementing equations 3, 6 and 7 respectively
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