# Discrete Wavelet Transform

Provenance watermarks for diffusion-generated images were previously suppressed by removal attacks with little visible quality loss. WaveMark embeds the message in the initial noise's wavelet domain, using a key to spread replicas of each message bit across spatial positions, wavelet orientations, and scales, then encodes each bit in a carrier's projection magnitude. On SD2.1 it reaches 100.0% bit accuracy without attacks and retains 88.66% and 88.06% under MarkNull and MarkNull-A, above the compared baselines.

Provenance watermarks for diffusion-generated images were previously suppressed by removal attacks with little visible quality loss. WaveMark embeds the message in the initial noise's wavelet domain, using a key to spread replicas of each message bit across spatial positions, wavelet orientations, and scales, then encodes each bit in a carrier's projection magnitude. On SD2.1 it reaches 100.0% bit accuracy without attacks and retains 88.66% and 88.06% under MarkNull and MarkNull-A, above the compared baselines.

On hourly PM2.5 data from two roadside stations in Guildford, UK, a quantum neural network clearly beat classical MLP and LSTM baselines on raw, undecomposed series, with the depth-4 model lifting Pearson correlation from roughly 0.29–0.31 to 0.599. Adding five-level discrete wavelet decomposition, a 172-qubit depth-4 model reached the study's highest average correlation of 0.729 and lowest NMSE of 0.488 over the full six-hour horizon, though the classical MLP came close at that point. The results come from the Dynex neuromorphic quantum annealing emulation platform and have not been validated on physical quantum hardware.

On hourly PM2.5 data from two roadside stations in Guildford, UK, a quantum neural network clearly beat classical MLP and LSTM baselines on raw, undecomposed series, with the depth-4 model lifting Pearson correlation from roughly 0.29–0.31 to 0.599. Adding five-level discrete wavelet decomposition, a 172-qubit depth-4 model reached the study's highest average correlation of 0.729 and lowest NMSE of 0.488 over the full six-hour horizon, though the classical MLP came close at that point. The results come from the Dynex neuromorphic quantum annealing emulation platform and have not been validated on physical quantum hardware.

The authors propose Detail Consistent Distillation (DCD), which applies a 3D discrete wavelet transform to teacher and student encoder features at every stage during training and aligns only the directional detail subband D (excluding the low-frequency approximation A and the most noise-prone extreme high-frequency band S) after inverse-wavelet reconstruction in the spatial domain, raising the mDice of a 4x channel-reduced student from 63.60% to 68.51% on BraTS 2024 and from 70.21% to 73.95% on ISLES 2022 with no inference-time overhead.

The authors propose Detail Consistent Distillation (DCD), which applies a 3D discrete wavelet transform to teacher and student encoder features at every stage during training and aligns only the directional detail subband D (excluding the low-frequency approximation A and the most noise-prone extreme high-frequency band S) after inverse-wavelet reconstruction in the spatial domain, raising the mDice of a 4x channel-reduced student from 63.60% to 68.51% on BraTS 2024 and from 70.21% to 73.95% on ISLES 2022 with no inference-time overhead.