DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES
Ph.D. Thesis Colloquium
Speaker: Mr. Arghya Sinha
S.R. Number: 06-18-01-10-12-21-1-19979
Title: “Stable Denoiser-Driven Regularization: From Kernel Methods to Constrained and Pretrained Deep Models”
Research Supervisor: Prof. Kunal N. Chaudhury and Prof. Debnath Pal
Date & Time : August 20, 2026 (Thursday), 10:15 AM
Venue : #102, CDS Seminar Hall
ABSTRACT
In classical model-based image reconstruction, the forward measurement model is combined with an explicit regularizer that captures prior knowledge about the unknown image. Keeping these components separate allows the same regularizer to be paired with different forward models and used across imaging modalities. Regularizers promote meaningful spatial structure by suppressing noise, artifacts, and unwanted variations. Since denoisers perform a closely related task, they can naturally serve as regularizers. This connection underlies frameworks such as Plug-and-Play (PnP) and Regularization by Denoising (RED), which incorporate an image denoiser into classical gradient and proximal reconstruction algorithms. These methods have proved highly effective in computational imaging problems such as deblurring, superresolution, tomography, and magnetic resonance imaging.
Despite this success, understanding when and why these methods converge remains an important open problem. Their analysis involves a fixed-point operator formed by the denoiser and the forward model. Classical convergence results require properties such as nonexpansiveness or averagedness. Modern deep denoisers are generally trained without such constraints, since these can limit their expressive power and reconstruction performance. This creates a tradeoff between performance and theoretical guarantees. When an unconstrained denoiser is applied repeatedly within PnP or RED, the iterates may fail to converge, and reconstruction quality may initially improve but later deteriorate. This characteristic peak-and-collapse behavior motivates methods that retain the performance of modern deep models while making iterative reconstruction stable and reliable.
In this thesis, we study this problem across a progression of increasingly expressive denoiser models. We begin with classical kernel denoisers, which recover an image by averaging pixels or patches according to a prescribed similarity function. Once the similarity weights are fixed, the denoiser can be represented as a linear operator. This structure allows us to use tools from operator and spectral theory to establish convergence, uniqueness, and linear-rate guarantees for several PnP and RED algorithms. We then carry these ideas into a trained setting. Instead of prescribing the similarity function, we train it from data and use the resulting weights to construct a denoising operator that remains linear for each input instance. By controlling its spectral properties, we obtain trained denoisers that perform well empirically while remaining globally nonexpansive. Under suitable conditions on the forward model, this makes the overall reconstruction operator contractive, guaranteeing a unique fixed point and linear convergence of the iterates.
In a different direction, we ask whether powerful pretrained networks can be stabilized without retraining or modifying them. Treating these networks as black-box operators with no useful structural guarantees, we introduce a data-driven framework based on contractive anchoring. The method measures the local expansiveness of the reconstruction operator through a stability index and adaptively blends its output with a lightweight contractive anchor. Anchoring is used only when required, allowing the original operator to remain dominant while keeping the iterates bounded. The resulting method acts as a drop-in wrapper, requires no additional parameter tuning, and consistently suppresses peak-and-collapse behavior across computational imaging problems, proximal algorithms, and deep denoiser architectures.
Together, the thesis shows how ideas from operator theory and spectral theory can be used to understand structured kernel denoisers, guide the training of stable denoisers, and ultimately stabilize powerful pretrained networks. This allows us to move from mathematically tractable models to modern trained denoisers while retaining meaningful stability guarantees for the resulting reconstruction algorithms.
ALL ARE WELCOME
