Iterative Linear Interpolation Based on Fuzzy Gradient Model for Low-Cost VLSI Implementation

In this paper, we propose an iterative linear interpolation (ILI) algorithm, which produces quadratic ILI polynomials to perform the most cost-effective interpolation among state-of-the-art quadratic and cubic methods. Unlike traditional point and area pixel models, the ILI adopts the fuzzy gradient model to estimate gradients of the target point according to its neighbor sample points in different directions. By weighing the gradients using fuzzy membership grades, the ILI estimates the difference between the target point and its neighbor sample points and finally obtains the target point. In 1-D signal reconstructions, using only three multipliers, the ILI obviously outperforms both conventional quadratic Lagrange interpolation and cubic interpolation. To approximate 2-D signals, we use five 1-D ILIs, which costs only eight multipliers to obtain similar peak signal-to-noise ratio (PSNR) performance but better robustness compared with bi-cubic interpolation. Reusing the ILI polynomials of the previous target point, we further reduce the cost of ILI to three multipliers and eight adders. The VLSI implementation using TSMC 0.18-μm technology shows that only 7256 gates are required for running a 200-MHz, 8-bit input/output, 15-bit fix-point data path, and 10-stage pipelined 2-D ILI, which is the quadratic interpolation of lowest cost but with PSNR performance closest to state-of-the-art bi-cubic methods.