An Efficient VLSI Architecture for FastICA by Using the Algebraic Jacobi Method for EVD

Abstract

Blind source separation (BSS) is a problem that appears in many research fields. Fast Independent components analysis (FastICA) is one of the techniques to solve the problem. The researchers have verified the effectiveness of the technique through the offline analysis of the public datasets. The development of a real-time portable system involving such a computationally complex analysis requires an efficient hardware implementation of FastICA. A Field programmable gate array (FPGA) and an applicationspecific integrated circuit (ASIC) are two promising hardware platforms to implement FastICA. This work proposes a new method, called ALgebraic Jacobi Method (ALJM), for performing eigenvalue decomposition (EVD) required for the implementation of FastICA. We use a simplification, a polynomial approximation, and the Newton-Raphson method for calculating the Jacobi rotation. In this way, we ensure hardware reusability between the EVD stage and the weight vector estimation (WVE) stage of FastICA which reduces the computational complexity and the power consumption, without compromising its computation speed. We evaluate the ALJM-based FastICA by performing BSS on the linear mixtures of the deterministic and the random signals and comparing the performance results with the existing methods. After verifying its functionality and numerical stability, we propose a scalable systolic processing array (SPA) for the ALJMbased FastICA and implement it on Spartan-6 FPGA. By comparing the existing implementations of FastICA, in terms of speed, area, and power, we conclude that the ALJM-based FastICA is one of the most efficient methods for prototyping and commercializing a real-time portable system comprising FastICA.

An Intelligent Sorting Method of Film in Cotton Combining Hyperspectral Imaging and the AlexNet-PCA Algorithm

“…(2) Finding the matrix W . We let k be the number of iterations, and the iterative computation of can be expressed as [ 27 ] where denotes a hyperbolic tangent function, is the first derivative of , indicates mean function.…”

Configurable Independent Component Analysis Preprocessing Accelerator

“…5 and 6 in [14] respectively. The latency for [15] is analyzed based on the calculations mentioned in Section IV-B in [15] and the throughput of [20] is computed based on Table 3 of [20]. b The latency and throughput are scaled based on the EVD of a complex-valued 8 × 8 matrix.…”

“…The EVD unit proposed in [15] is based on a structure containing four PEs, so the latency was calculated according to Section IV-B in that work. Moreover, the latency for processing a real-valued 8 × 8 matrix in the design of [20] is reported in Table 3 in [20]. The complexity was estimated based on Tables 2 and 5 in that work.…”

“…Since the architecture of [14] was designed for a complex-valued matrix, the scaled latency is the same as the original latency. The scaled latency was doubled and the scaled SA throughput was halved for the designs in [15] and [20] because of the complex-valued EVD. However, the scaled ICA throughput for [11], [15], [20] was limited by the input of the matrix from the centering and covariance units.…”

“…Compared to [15], the throughput of the proposed EVD unit is lower while the complexity is also much reduced. The design in [20] leads to a heavily degraded throughput due to the low operating frequency. The efficiency FOM is also used to compare the proposed EVD in ICA preprocessing by the different designs.…”