Gabor is Enough: Interpretable Deep Denoising with a Gabor Synthesis Dictionary Prior

TL;DR

The paper investigates whether explicitly Gabor-like representations can be made efficient for image denoising. It replaces the learned filters in CDLNet with a parameterized mixture of 2D Gabor functions, creating the Gabor Dictionary Learning Network (GDLNet) that preserves expressivity with fewer parameters. Across single-noise and blind denoising tasks, GDLNet achieves near state-of-the-art performance and retains generalization to unseen noise levels, with ablations highlighting the pivotal role of the scale parameter in a sparse-coding interpretation. The work suggests that simple, interpretable Gabor-based dictionaries can underpin effective low-level imaging networks and may generalize to other inverse problems.

Abstract

Image processing neural networks, natural and artificial, have a long history with orientation-selectivity, often described mathematically as Gabor filters. Gabor-like filters have been observed in the early layers of CNN classifiers and even throughout low-level image processing networks. In this work, we take this observation to the extreme and explicitly constrain the filters of a natural-image denoising CNN to be learned 2D real Gabor filters. Surprisingly, we find that the proposed network (GDLNet) can achieve near state-of-the-art denoising performance amongst popular fully convolutional neural networks, with only a fraction of the learned parameters. We further verify that this parameterization maintains the noise-level generalization (training vs. inference mismatch) characteristics of the base network, and investigate the contribution of individual Gabor filter parameters to the performance of the denoiser. We present positive findings for the interpretation of dictionary learning networks as performing accelerated sparse-coding via the importance of untied learned scale parameters between network layers. Our network's success suggests that representations used by low-level image processing CNNs can be as simple and interpretable as Gabor filterbanks.

Figures (4)

• Figure 1: Left: Block diagram of GDLNet, CDLNet with mixture of Gabor (MoG) filterbanks. Analysis and synthesis convolutions map from $1 \rightarrow M$ and $M \rightarrow 1$ channels, respectively. We emphasize that GDLNet/CDLNet do not process signals in a "learned feature domain" in contrast to the multi-channel filtering ($M \rightarrow M$ channels) in popular DNNs such as DnCNN DnCNN. Right: Mixture of Gabor filters are generated as a sum of parameterized Gabor filters.
• Figure 2: (a,b) Performance of different denoising networks trained on $\sigma^{\mathrm{train}}$ and tested on $\sigma^{\mathrm{test}}$. Average PSNR calculated over BSD68 bsd. (c,d) Visual comparison of different networks tested on noise-level $\sigma^{\mathrm{test}}=50$. GDLNet is MoG order 3. Details are better visible by zooming.
• Figure 3: Synthesis dictionary ($\bm{D}$) filters for (a) CDLNet janjuvsevic2021cdlnet, (b) GDLNet with MoG order 3, (c) GDLNet with MoG order 1, and (d) initial Gabor dictionary of (c). All models trained on $\sigma^{\mathrm{train}}=[20,30]$. Filters are ordered by relative usage over the BSD68 dataset bsd.
• Figure 4: Effect of untied parameters between layers $k=0,1,\dots, K-1$ on performance of GDLNet (MoG 1). PSNR averaged over BSD68 bsd, $\sigma^{\mathrm{train}} = \sigma^{\mathrm{test}} = 25$. Refer to \ref{['eq:gabor']} for description of Gabor filter parameters.