ICML 2025

DEALing with Image Reconstruction: Deep Attentive Least Squares
Mehrsa Pourya 1 Erich Kobler 2 Michael Unser 1 Sebastian Neumayer 3
Abstract
State-of-the-art image reconstruction often relies
on complex, abundantly parameterized deep ar-
chitectures. We propose an alternative: a data-
driven reconstruction method inspired by the clas-
sic Tikhonov regularization. Our approach itera-
tively refines intermediate reconstructions by solv-
ing a sequence of quadratic problems. These up-
dates have two key components: (i) learned filters
to extract salient image features; and (ii) an atten-
tion mechanism that locally adjusts the penalty of
the filter responses. Our method matches leading
plug-and-play and learned regularizer approaches
in performance while offering interpretability, ro-
bustness, and convergent behavior. In effect, we
bridge traditional regularization and deep learning
with a principled reconstruction approach.
Code: https://github.com/mehrsapo/DEAL.
1. Introduction
Image reconstruction plays a fundamental role in compu-
tational imaging and computer vision (McCann & Unser,
2019; Zeng, 2001). The task is to recover an unknown im-
age of interest x ∈Rd from noisy measurements y ∈RM.
Their relation is modeled as y = Hx, where the forward op-
erator H ∈RM×d encodes the acquisition process. When
H is ill-conditioned, one can resort to the regularized recon-
struction
ˆx ∈arg min
x∈Rd

∥Hx −y∥2
2 + λR(x)

.
(1)
The data fidelity ∥Hx −y∥2
2 controls the consistency of
the reconstruction with the measurements. The regularizer
R: Rd →R≥0 encodes prior information about the solu-
tion and is also intended to make the problem well-posed.
1Biomedical Imaging group, EPFL Lausanne, Switzerland
2Institute for Machine Learning, JKU Linz, Austria 3Faculty
of Mathematics, TU Chemnitz, Germany. Correspondence to:
Mehrsa Pourya <mehrsa.pourya@epfl.ch>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025...