Nania Francesco
7th October 2025, 19:58
My Unexpected Journey
From Spatial Polynomials to a Stable Hybrid Transform (DCHT)
My initial research focused on pushing the limits of lossy compression through spatial domain techniques, specifically exploring adaptive-block polynomial curve-fitting. I painstakingly tested nearly every polynomial formula, aiming for a significant gain in quality, compression ratio, and final visual fidelity—enough to compete with the highly optimized Discrete Cosine Transform (DCT).
However, the results were consistently underwhelming. Despite elaborate adaptive schemes, no polynomial approach could deliver the necessary energy compaction or provide the stability and superior visual performance needed to challenge DCT's dominance. This frustrating plateau made it clear that the future didn't lie in spatial approximations alone.
The Hybrid Breakthrough: Introducing the DCHT
Driven by this roadblock, I pursued a bold new idea: to create a transform that retained the structural efficiency and block-based architecture of the DCT, but relied on a fundamentally different mathematical basis with a crucial spatial-domain linkage to overcome the inherent instability of the DCT when scaled up.
I named this solution the DCHT (Discrete Hermite Transform with a DCT structural call). Its core is a stable hybrid transform, drawing its superior energy compaction and spatial coherence properties from the Hermite-Gauss basis functions. The inclusion of 'DC' in the naming convention (DCHT) is purely a structural nod to the DCT's established two-dimensional compression framework.
The initial results of the DCHT were, frankly, discouraging. The first versions struggled, and the PSNR was initially only half of what DCT achieved, due to poor energy distribution across the AC coefficients.
Through meticulous iteration, focused on rebalancing the weighting of the hybrid components, I found a pivotal point of equilibrium. This balance resulted in a dramatic shift: the DCHT began to concentrate energy far more effectively than DCT.
By using a minimal, fixed number of low-frequency coefficients (196 out of 4096 for a 64×64 block), the new stable transform began to significantly outperform DCT at the same sparsity level.
A Transform in its Own Right
What started as an attempt to fix a problem evolved into a standalone, stable, and reasonably fast transform ready to challenge the DCT era. The DCHT's stability on large blocks, coupled with its superior energy compaction, has established it as a viable candidate for next-generation compression.
Based on these results, I have taken decisive steps to secure its future: the DCHT has been submitted for patent application, its source code has been filed with Zenodo for archival and verification, and most critically, the core mathematical paper has been submitted to the IEEE Journal of Selected Topics in Signal Processing (J-STSP) for peer review."
From Spatial Polynomials to a Stable Hybrid Transform (DCHT)
My initial research focused on pushing the limits of lossy compression through spatial domain techniques, specifically exploring adaptive-block polynomial curve-fitting. I painstakingly tested nearly every polynomial formula, aiming for a significant gain in quality, compression ratio, and final visual fidelity—enough to compete with the highly optimized Discrete Cosine Transform (DCT).
However, the results were consistently underwhelming. Despite elaborate adaptive schemes, no polynomial approach could deliver the necessary energy compaction or provide the stability and superior visual performance needed to challenge DCT's dominance. This frustrating plateau made it clear that the future didn't lie in spatial approximations alone.
The Hybrid Breakthrough: Introducing the DCHT
Driven by this roadblock, I pursued a bold new idea: to create a transform that retained the structural efficiency and block-based architecture of the DCT, but relied on a fundamentally different mathematical basis with a crucial spatial-domain linkage to overcome the inherent instability of the DCT when scaled up.
I named this solution the DCHT (Discrete Hermite Transform with a DCT structural call). Its core is a stable hybrid transform, drawing its superior energy compaction and spatial coherence properties from the Hermite-Gauss basis functions. The inclusion of 'DC' in the naming convention (DCHT) is purely a structural nod to the DCT's established two-dimensional compression framework.
The initial results of the DCHT were, frankly, discouraging. The first versions struggled, and the PSNR was initially only half of what DCT achieved, due to poor energy distribution across the AC coefficients.
Through meticulous iteration, focused on rebalancing the weighting of the hybrid components, I found a pivotal point of equilibrium. This balance resulted in a dramatic shift: the DCHT began to concentrate energy far more effectively than DCT.
By using a minimal, fixed number of low-frequency coefficients (196 out of 4096 for a 64×64 block), the new stable transform began to significantly outperform DCT at the same sparsity level.
A Transform in its Own Right
What started as an attempt to fix a problem evolved into a standalone, stable, and reasonably fast transform ready to challenge the DCT era. The DCHT's stability on large blocks, coupled with its superior energy compaction, has established it as a viable candidate for next-generation compression.
Based on these results, I have taken decisive steps to secure its future: the DCHT has been submitted for patent application, its source code has been filed with Zenodo for archival and verification, and most critically, the core mathematical paper has been submitted to the IEEE Journal of Selected Topics in Signal Processing (J-STSP) for peer review."