Abstract
As distributed compute platforms and high-resolution imaging pipelines scale, uncompressed raw visual data presents a severe transmission bandwidth and memory storage wall. A 24-bit 1024 × 1024 uncompressed frame consumes 3.0 MB of storage, requiring over 7 minutes to transmit across legacy 64 Kbit/s ISDN channels, whereas a 10 : 1 compression reduces this footprint to 300 KB and sub-6-second latencies. This research paper presents a comprehensive mathematical, algorithmic, and microarchitectural evaluation of foundational transform coding paradigms—spanning Discrete Cosine Transform (DCT), Karhunen-Lo`eve Transform (KLT), Fractal Iterated Function Systems (IFS), Spline Regularization, and Multiresolution Discrete Wavelet Transforms (DWT). We formulate the mathematical underpinnings of orthonormal multiresolution spaces (Vj ⊂ Vj+1), Quadrature Mirror Filter (QMF) sub-band decomposition, and Linde-Buzo-Gray (LBG) Voronoi vector quantization. Furthermore, we establish the computer architecture principles required to map continuous wavelet transforms into O(N) hardware lifting schemes, line-buffer streaming architectures, and memory-tiled VLSI accelerators. Finally, we provide an extensive quantitative evaluation comparing JPEG and JPEG2000 standards across Signalto-Noise Ratio (SNR), rate-distortion curves, spatial locality, and VLSI silicon energy efficiency.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Tummala, Gopi K., "Architectural and Mathematical Foundations of Transform Coding in Image Compression: From Multiresolution Wavelet Pyramids to Hardware-Accelerated Discrete Wavelet Transform Silicon Engines", Technical Disclosure Commons, (August 26, 2026)
https://www.tdcommons.org/dpubs_series/11494