FaSST: Fast Sparsifying Secondary Transform

TL;DR

FaSST introduces a low-complexity, data-driven secondary transform framework that enhances residual coding efficiency in video codecs by approximating sparse orthonormal transforms with Givens rotations.

Contribution

It proposes a novel, efficient method for designing data-dependent secondary transforms using Givens rotations, improving coding gains with significantly reduced computational complexity.

Findings

FaSST matches RD performance of LFNST.

Reduces computations by 83.67%.

Achieves up to 1.80% BD-rate savings.

Abstract

Data-dependent secondary transforms, which aim to decorrelate coefficients of a separable primary transform, can improve residual coding efficiency; however, their deployment is often constrained by computational complexity. Recent video codecs use variants of the low-frequency non-separable transform (LFNST), which discards some high-frequency secondary transform coefficients, limiting achievable coding gains. Moreover, existing data-dependent secondary transforms lack explicit rate-distortion (RD) optimal design criteria. In this work, we propose a framework for designing low-complexity data-dependent secondary transforms, termed Fast Sparsifying Secondary Transforms (FaSSTs). Our approach approximates data-driven sparse orthonormal transforms (SOTs) by factorizing them into a sequence of Givens rotations. The rotations are efficiently determined using an alternating minimization strategy combined with an approximate Givens factorization procedure. Our method adapts the number of rotations based on the prediction mode, further reducing computational complexity. We design mode-dependent secondary transforms for intra-prediction residuals in AV2 using FaSST. Experimental results show that mode-adaptive FaSST matches the RD performance of LFNST while reducing the number of computations by 83.67%. Moreover, by avoiding fixed-coefficient truncation, FaSST achieves up to 1.80% BD-rate savings relative to LFNST while operating at 66.24% lower complexity.