Non-blind deblurring — recovering a sharp image given a known blur kernel — is a classical problem in image processing. Traditional approaches rely on generative models with hand-crafted image priors (e.g., total variation, hyper-Laplacian). While effective, these methods require careful parameter tuning and iterative optimization, and their priors may not capture the true statistics of natural images. We propose a discriminative approach to non-blind deblurring that learns the regularization directly from training data using a cascade of shrinkage fields (CSF). Our model achieves state-of-the-art restoration quality with orders of magnitude faster runtime compared to iterative methods.

Image deblurring is typically decomposed into two stages: blind deblurring (estimating the blur kernel) and non-blind deblurring (recovering the sharp image given the kernel). While much recent attention has focused on the blind stage, the non-blind stage remains crucial — even a perfectly estimated kernel yields poor results if the subsequent restoration is suboptimal. Current state-of-the-art non-blind methods, such as those based on variational Bayes or ADMM, require many iterations of expensive convolution operations.

We challenge the dominant generative modeling paradigm for non-blind deblurring and instead adopt a discriminative learning framework. The key idea is to unroll a fixed number of optimization steps and learn all parameters end-to-end from training pairs of blurry and sharp images. This converts the iterative inference problem into a feed-forward prediction problem, enabling real-time processing at test time. Our approach bridges classical energy minimization and modern machine learning.

Classical non-blind deblurring methods frame the problem as MAP estimation with an image prior. Popular priors include total variation (TV), which promotes piecewise-smooth solutions, and hyper-Laplacian priors on image gradients. Zoran and Weiss proposed Expected Patch Log Likelihood (EPLL), modeling patches with a Gaussian mixture model. These generative approaches achieve high quality but are slow due to iterative optimization — typically requiring 50-200 iterations of conjugate gradient or similar solvers.

An alternative line of work explores learning-based approaches. Schuler et al. train a multi-layer perceptron for deblurring, while Burger et al. show that a large MLP can match BM3D for denoising. However, these "black-box" neural networks lack interpretability and do not incorporate domain knowledge about the blur formation process. Our work occupies a middle ground: we use a model architecture inspired by classical optimization but with parameters learned discriminatively.

Our model, the Cascade of Shrinkage Fields (CSF), consists of a fixed number of stages, each performing one half-quadratic splitting step. At each stage, the model applies learned convolution filters to extract features, followed by pointwise shrinkage functions that act as learned proximal operators. The output of each stage is fed into the next, mimicking the unrolled iterations of a classical optimization algorithm. Crucially, the filters and shrinkage functions are different at each stage, allowing the model to adapt its regularization strategy as the estimate improves.

All parameters — including filter weights, shrinkage function parameters, and data fidelity weights — are trained jointly by minimizing the mean squared error between the model's output and the ground-truth sharp image. The training set consists of pairs of synthetically blurred and clean images with diverse blur kernels. We use gradient-based optimization (L-BFGS) to learn the parameters, with gradients computed via backpropagation through the entire unrolled cascade. This end-to-end discriminative training ensures that all components are optimized for the final reconstruction quality, rather than each being tuned independently.

A key advantage of our formulation is that the learned shrinkage functions are non-parametric — they are represented as lookup tables (radial basis function interpolation) rather than fixed functional forms. This allows the model to discover regularization strategies that may have no closed-form expression but are empirically optimal for natural image statistics. In practice, the learned shrinkage functions qualitatively resemble soft-thresholding at early stages but become more nuanced at later stages.

We evaluate on standard benchmarks including the dataset of Levin et al. (4 images, 8 kernels, 32 test cases) and Sun et al.'s dataset with larger, more realistic kernels. Our 5-stage CSF achieves PSNR comparable to or exceeding EPLL and other state-of-the-art methods across all kernel sizes. In terms of speed, the CSF processes a 255x255 image in approximately 0.6 seconds, compared to 30-120 seconds for iterative methods. This represents a 50-200x speedup with no loss in quality.

We also conduct ablation studies to validate design choices. Increasing the number of stages from 1 to 5 steadily improves PSNR, with diminishing returns beyond 5 stages. Using stage-specific (non-shared) parameters outperforms shared parameters by 0.5-1.0 dB. The learned non-parametric shrinkage functions outperform fixed soft-thresholding by 0.8 dB on average. These results confirm that each component of our design contributes meaningfully to the final performance.

We have introduced a discriminative approach to non-blind image deblurring based on cascades of shrinkage fields. By unrolling a classical optimization algorithm and learning all parameters from data, our method combines the interpretability of model-based approaches with the efficiency and adaptability of discriminative learning. The resulting model achieves state-of-the-art quality with dramatically reduced computation time. We believe this paradigm of "learning to optimize" is broadly applicable to other inverse problems in imaging.