FPGA design for real-time implementation of constrained energy minimization for hyperspectral target detection

The constrained energy minimization (CEM) has been widely used for hyperspectral detection and classification. The feasibility of implementing the CEM as a real-time processing algorithm in systolic arrays has also been demonstrated. The main challenge of realizing the CEM in hardware architecture is the computation of the inverse of the data correlation matrix performed in the CEM, which requires a complete set of data samples. In order to cope with this problem, the data correlation matrix must be calculated in a causal manner that only needs data samples up to the sample at the time it is processed. This chapter presents a Field Programmable Gate Arrays (FPGA) design of such a causal CEM. The main feature of the proposed FPGA design is to use the Coordinate Rotation Digital Computer (CORDIC) algorithm, which can convert a Givens rotation of a vector to a set of shift-add operations. As a result, the CORDIC algorithm can be easily implemented in hardware architectures, and therefore in FPGA. Since the computation of the inverse of the data correlation matrix involves a series of Givens rotations, the utility of the CORDIC algorithm allows the causal CEM to perform real-time processing in FPGA. In this chapter, an FPGA implementation of the causal CEM will be studied and its detailed architecture will be also described.