SMFrWF: Segmented Modified Fractional Wavelet Filter: Fast Low-Memory Discrete Wavelet Transform (DWT)

Abstract

This paper proposes a novel algorithm to compute the 2-D discrete wavelet transform (DWT) of high-resolution (HR) images on low-cost visual sensor and Internet of Things (IoT) nodes. The main advantages of the proposed segmented modified fractional wavelet filter (SMFrWF) are reduced computation (time) complexity and energy consumption compared to the state-of-the-art low-memory 2-D DWT computation methods. In particular, the conventional convolution-based DWT is very fast but requires large random access memory (RAM), as the entire image needs to be in the system memory. The fractional wavelet filter (FrWF) requires only a small RAM but has high complexity due to multiple readings of image lines. The proposed SMFrWF avoids the multiple readings of image lines, thus reducing the memory read access time and, thereby, the complexity. We evaluated the proposed SMFrWF through MATLAB simulations with 70 popular gray-scale test images of dimensions ranging from $256 \times 256$ up to $8192 \times 8192$ pixels. The results show that for images of size $2048\times 2048$ pixels, the proposed SMFrWF (with four segments per line) has 16.8% and 53.6% lower time complexities than the conventional DWT and FrWF, respectively. The proposed SMFrWF has also been modeled in a hardware description language (HDL) and implemented on an Artix-7 field-programmable gate array (FPGA) platform to evaluate the hardware performance. We observed that the proposed SMFrWF has 65% lower energy consumption than the FrWF (both implemented on the same board). Thus, the proposed SMFrWF appears suitable for computing the wavelet transform coefficients of HR images on low-cost visual sensors and IoT platforms.