FPGA Implementation of Real-Time Compressive Sensing with Partial Fourier Dictionary

This paper presents a novel real-time compressive sensing (CS) reconstruction which employs high density field-programmable gate array (FPGA) for hardware acceleration. Traditionally, CS can be implemented using a high-level computer language in a personal computer (PC) or multicore platforms, such as graphics processing units (GPUs) and Digital Signal Processors (DSPs). However, reconstruction algorithms are computing demanding and software implementation of these algorithms is extremely slow and power consuming. In this paper, the orthogonal matching pursuit (OMP) algorithm is refined to solve the sparse decomposition optimization for partial Fourier dictionary, which is always adopted in radar imaging and detection application. OMP reconstruction can be divided into two main stages: optimization which finds the closely correlated vectors and least square problem. For large scale dictionary, the implementation of correlation is time consuming since it often requires a large number of matrix multiplications. Also solving the least square problem always needs a scalable matrix decomposition operation. To solve these problems efficiently, the correlation optimization is implemented by fast Fourier transform (FFT) and the large scale least square problem is implemented by Conjugate Gradient (CG) technique, respectively. The proposed method is verified by FPGA (Xilinx Virtex-7 XC7VX690T) realization, revealing its effectiveness in real-time applications

FPGA-Based On-Board Geometric Calibration for Linear CCD Array Sensors

With increasing demands in real-time or near real-time remotely sensed imagery applications in such as military deployments, quick response to terrorist attacks and disaster rescue, the on-board geometric calibration problem has attracted the attention of many scientists in recent years. This paper presents an on-board geometric calibration method for linear CCD sensor arrays using FPGA chips. The proposed method mainly consists of four modules—Input Data, Coefficient Calculation, Adjustment Computation and Comparison—in which the parallel computations for building the observation equations and least squares adjustment, are implemented using FPGA chips, for which a decomposed matrix inversion method is presented. A Xilinx Virtex-7 FPGA VC707 chip is selected and the MOMS-2P data used for inflight geometric calibration from DLR (Köln, Germany), are employed for validation and analysis. The experimental results demonstrated that: (1) When the widths of floating-point data from 44-bit to 64-bit are adopted, the FPGA resources, including the utilizations of FF, LUT, memory LUT, I/O and DSP48, are consumed at a fast increasing rate; thus, a 50-bit data width is recommended for FPGA-based geometric calibration. (2) Increasing number of ground control points (GCPs) does not significantly consume the FPGA resources, six GCPs is therefore recommended for geometric calibration. (3) The FPGA-based geometric calibration can reach approximately 24 times faster speed than the PC-based one does. (4) The accuracy from the proposed FPGA-based method is almost similar to the one from the inflight calibration if the calibration model and GCPs number are the same