Novel Prospects of Image Restoration Inspired by Concepts of Quantum Mechanics (Sayantan DUTTA / Thesis / LPT). – 9/01/2023, 9H30

Sayantan DUTTA, Equipe MINDS IRIT et Equipe Cohérence quantique LPT

Lieu : Auditorium J. Herbrand – IRIT 

et Lien zoom :
https://univ-tlse3-fr.zoom.us/j/88599330360?pwd=RUJ5TUc2V2tMWWtnNSt6cUIxN0JWUT09
ID de réunion : 885 9933 0360
Code secret : 114975

Abstract : Decomposition of digital images into other basis or dictionaries than time or space domains is a very common and effective approach in image processing and analysis. Such a decomposition is commonly obtained using fixed transformations (e.g., Fourier or wavelet) or dictionaries learned from example databases or from the signal or image itself. In recent years, with the growth of computing power, data-driven strategies exploiting the redundancy within patches extracted from one or several images to increase sparsity have become more prominent. They have demonstrated very promising image restoration results. The question to pursue in this thesis is how to design such an adaptive transformation based on principles of quantum mechanics.

In this thesis, we explore new possibilities of constructing such image-dependent bases inspired by quantum mechanics. First, we construct an image-dependent basis using the wave solutions of the Schrödinger equation, in particular, by considering the image as a potential in the discretized Schrödinger equation. The efficiency of the proposed decomposition is illustrated through denoising results in the case of Gaussian, Poisson, and speckle noises and compared to the state-of-the-art algorithms. We further generalize our proposed adaptive basis by exploiting the data-driven strategy inspired by quantum many-body theory. Based on patch analysis, the similarity measures in a local image neighborhood are formalized through a term akin to interaction in quantum mechanics that can efficiently preserve the local structures of real images. The versatile nature of this adaptive basis extends the scope of its application to image-independent or image-dependent noise scenarios without any adjustment. We carry out a rigorous comparison with contemporary methods to demonstrate the denoising capability of the proposed algorithm regardless of the image characteristics, noise statistics and intensity. We show the ability of our approaches to deal with real-medical data such as clinical dental computed tomography image denoising and medical ultrasound image despeckling applications. We further extend our work to image deconvolution and super-resolution tasks exploiting our proposed quantum adaptive denoisers. In particular, following recent developments, we impose these external denoisers as a prior functions within the Plug-and-Play and Regularization by Denoising approaches.

Lastly, we present a deep neural network architecture unfolding our proposed baseline adaptive denoising algorithm, relying on the theory of quantum many-body physics. The key ingredients of the proposed method are on one hand, its ability to handle non-local image structures through the patch-interaction term and the quantum-based Hamiltonian operator, and, on the other hand, its flexibility to adapt the hyperparameters patch wisely, due to the training process. Furthermore, it is shown that with very slight modifications, this network can be enhanced to solve more challenging image restoration tasks such as image deblurring, super-resolution and inpainting. Despite a compact and interpretable (from a physical perspective) architecture, the proposed deep learning network outperforms several recent benchmark algorithms from the literature, designed specifically for each task. Finally, we address the problem of clinical cardiac ultrasound image enhancement to demonstrate the potential of our proposed deep unfolded network in real-world medical applications.