A green prospective for learned post-processing in sparse-view tomographic reconstruction

Deep Learning is developing interesting tools that are of great interest for inverse imaging applications. In this work, we consider a medical imaging reconstruction task from subsampled measurements, which is an active research field where Convolutional Neural Networks have already revealed their great potential. However, the commonly used architectures are very deep and, hence, prone to overfitting and unfeasible for clinical usages. Inspired by the ideas of the green AI literature, we propose a shallow neural network to perform efficient Learned Post-Processing on images roughly reconstructed by the filtered backprojection algorithm. The results show that the proposed inexpensive network computes images of comparable (or even higher) quality in about one-fourth of time and is more robust than the widely used and very deep ResUNet for tomographic reconstructions from sparse-view protocols

Medical Image Enhancement using Deep Learning and Tensor Factorization Techniques

La résolution spatiale des images acquises par tomographie volumique à faisceau conique (CBCT) est limitée par la géométrie des capteurs, leur sensibilité, les mouvements du patient, les techniques de reconstruction d'images et la limitation de la dose de rayonnement. Le modèle de dégradation d'image considéré dans cette thèse consiste en un opérateur de ou avec la fonction d'étalement du système d'imagerie (PSF), un opérateur de décimation, et du bruit, qui relient les volumes CBCT à une image 3D super-résolue à estimer. Les méthodes proposées dans cette thèse (SISR - single image super-résolution) ont comme objectif d'inverser ce modèle direct, c'est à dire d'estimer un volume haute résolution à partir d'une image CBCT. Les algorithmes ont été évalués dans le cadre d'une application dentaire, avec comme vérité terrain les images haute résolution acquises par micro CT (µCT), qui utilise des doses de rayonnement très importantes, incompatibles avec les applications cliniques. Nous avons proposé une approche de SISR par deep learning, appliquée individuellement à des coupes CBCT. Deux types de réseaux ont été évalués : U-net et subpixel. Les deux ont amélioré les volumes CBCT, avec un gain en PSNR de 21 à 22 dB et en coefficient de Dice pour la segmentation canalaire de 1 à 2.2 %. Le gain a été plus particulièrement important dans la partie apicale des dents, ce qui représente un résultat important étant donnée son importance pour les applications cliniques. Nous avons proposé des algorithmes de SISR basés sur la décomposition canonique polyadique des tenseurs. Le principal avantage de cette méthode, lié à l'utilisation de la théorie des tenseur, est d'utiliser la structure 3D des volumes CBCT. L'algorithme proposé regroupe plusieurs étapes: débruitage base sur la factorisation des tenseurs, déconvolution et super-résolution, avec un faible nombre d'hyperparamètres. Le temps d'exécution est très faible par rapport aux algorithmes existants (deux ordres de magnitude plus petit), pour des performances légèrement supérieures (gain de 1.2 à 1.5 dB en PSNR). La troisième contribution de la thèse est en lien avec la contribution 2 : l'algorithme de SISR basé sur la décomposition canonique polyadique des tenseurs est combiné avec une méthode d'estimation de la PSF, inconnues dans les applications pratiques. L'algorithme résultant effectue les deux tâche de manière alternée, et s'avère précis et rapide sur des données de simulation et expérimentales. La dernière contribution de la thèse a été d'évaluer l'intérêt d'un autre type de décomposition tensorielle, la décomposition de Tucker, dans le cadre d'un algorithme de SISR. Avant la déconvolution, le volume CBCT est débruité en tronquant sa décomposition de Tucker. Comparé à l'algorithme de la contribution 2, cette approche permet de diminuer encore plus le temps de calcul, d'un facteur 10, pour des performances similaires pour des SNR importants et légèrement supérieures pour de faibles SNR. Le lien entre cette méthode et les algorithmes 2D basés sur une SVD facilite le réglage des hyperparamètres comparé à la décomposition canonique polyadique.The resolution of dental cone beam computed tomography (CBCT) images is imited by detector geometry, sensitivity, patient movement, the reconstruction technique and the need to minimize radiation dose. The corresponding image degradation model assumes that the CBCT image is a blurred (with a point spread function, PSF), downsampled, noisy version of a high resolution image. The quality of the image is crucial for precise diagnosis and treatment planning. The methods proposed in this thesis aim to give a solution for the single image super-resolution (SISR) problem. The algorithms were evaluated on dental CBCT and corresponding highresolution (and high radiation-dose) µCT image pairs of extracted teeth. I have designed a deep learning framework for the SISR problem, applied to CBCT slices. I have tested the U-net and subpixel neural networks, which both improved the PSNR by 21-22 dB, and the Dice coe_cient of the canal segmentation by 1-2.2%, more significantly in the medically critical apical region. I have designed an algorithm for the 3D SISR problem, using the canonical polyadic decomposition of tensors. This implementation conserves the 3D structure of the volume, integrating the factorization-based denoising, deblurring with a known PSF, and upsampling of the image in a lightweight algorithm with a low number of parameters. It outperforms the state-of-the-art 3D reconstruction-based algorithms with two orders of magnitude faster run-time and provides similar PSNR (improvement of 1.2-1.5 dB) and segmentation metrics (Dice coe_cient increased on average to 0.89 and 0.90). Thesis II b: I have implemented a joint alternating recovery of the unknown PSF parameters and of the high-resolution 3D image using CPD-SISR. The algorithm was compared to a state-of-the-art 3D reconstruction-based algorithm, combined with the proposed alternating PSF-optimization. The two algorithms have shown similar improvement in PSNR, but CPD-SISR-blind converged roughly 40 times faster, under 6 minutes both in simulation and on experimental dental computed tomography data. I have proposed a solution for the 3D SISR problem using the Tucker decomposition (TD-SISR). The denoising step is realized _rst by TD in order to mitigate the ill-posedness of the subsequent deconvolution. Compared to CPDSISR the algorithm runs ten times faster. Depending on the amount of noise, higher PSNR (0.3 - 3.5 dB), SSI (0.58 - 2.43%) and segmentation values (Dice coefficient, 2% improvement) were measured. The parameters in TD-SISR are familiar from 2D SVD-based algorithms, so their tuning is easier compared to CPD-SISR

Deep Learning Based Medical Image Analysis with Limited Data

Deep Learning Methods have shown its great effort in the area of Computer Vision. However, when solving the problems of medical imaging, deep learning’s power is confined by limited data available. We present a series of novel methodologies for solving medical imaging analysis problems with limited Computed tomography (CT) scans available. Our method, based on deep learning, with different strategies, including using Generative Adversar- ial Networks, two-stage training, infusing the expert knowledge, voting based or converting to other space, solves the data set limitation issue for the cur- rent medical imaging problems, specifically cancer detection and diagnosis, and shows very good performance and outperforms the state-of-art results in the literature. With the self-learned features, deep learning based techniques start to be applied to the biomedical imaging problems and various structures have been designed. In spite of its simplity and anticipated good performance, the deep learning based techniques can not perform to its best extent due to the limited size of data sets for the medical imaging problems. On the other side, the traditional hand-engineered features based methods have been studied in the past decades and a lot of useful features have been found by these research for the task of detecting and diagnosing the pulmonary nod- ules on CT scans, but these methods are usually performed through a series of complicated procedures with manually empirical parameter adjustments. Our method significantly reduces the complications of the traditional proce- dures for pulmonary nodules detection, while retaining and even outperforming the state-of-art accuracy. Besides, we make contribution on how to convert low-dose CT image to full-dose CT so as to adapting current models on the newly-emerged low-dose CT data

Methods for Photoacoustic Image Reconstruction Exploiting Properties of Curvelet Frame

Curvelet frame is of special significance for photoacoustic tomography (PAT) due to its sparsifying and microlocalisation properties. In this PhD project, we explore the methods for image reconstruction in PAT with flat sensor geometry using Curvelet properties. This thesis makes five distinct contributions: (i) We investigate formulation of the forward, adjoint and inverse operators for PAT in Fourier domain. We derive a one-to-one map between wavefront directions in image and data spaces in PAT. Combining the Fourier operators with the wavefront map allows us to create the appropriate PAT operators for solving limited-view problems due to limited angular sensor sensitivity. (ii) We devise a concept of wedge restricted Curvelet transform, a modification of standard Curvelet transform, which allows us to formulate a tight frame of wedge restricted Curvelets on the range of the PAT forward operator for PAT data representation. We consider details specific to PAT data such as symmetries, time oversampling and their consequences. We further adapt the wedge restricted Curvelet to decompose the wavefronts into visible and invisible parts in the data domain as well as in the image domain. (iii) We formulate a two step approach based on the recovery of the complete volume of the photoacoustic data from the sub-sampled data followed by the acoustic inversion, and a one step approach where the photoacoustic image is directly recovered from the subsampled data. The wedge restricted Curvelet is used as the sparse representation of the photoacoustic data in the two step approach. (iv) We discuss a joint variational approach that incorporates Curvelet sparsity in photoacoustic image domain and spatio-temporal regularization via optical flow constraint to achieve improved results for dynamic PAT reconstruction. (v) We consider the limited-view problem due to limited angular sensitivity of the sensor (see (i) for the formulation of the corresponding fast operators in Fourier domain). We propose complementary information learning approach based on splitting the problem into visible and invisible singularities. We perform a sparse reconstruction of the visible Curvelet coefficients using compressed sensing techniques and propose a tailored deep neural network architecture to recover the invisible coefficients

Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github

Neural Radiance Fields: Past, Present, and Future

The various aspects like modeling and interpreting 3D environments and surroundings have enticed humans to progress their research in 3D Computer Vision, Computer Graphics, and Machine Learning. An attempt made by Mildenhall et al in their paper about NeRFs (Neural Radiance Fields) led to a boom in Computer Graphics, Robotics, Computer Vision, and the possible scope of High-Resolution Low Storage Augmented Reality and Virtual Reality-based 3D models have gained traction from res with more than 1000 preprints related to NeRFs published. This paper serves as a bridge for people starting to study these fields by building on the basics of Mathematics, Geometry, Computer Vision, and Computer Graphics to the difficulties encountered in Implicit Representations at the intersection of all these disciplines. This survey provides the history of rendering, Implicit Learning, and NeRFs, the progression of research on NeRFs, and the potential applications and implications of NeRFs in today's world. In doing so, this survey categorizes all the NeRF-related research in terms of the datasets used, objective functions, applications solved, and evaluation criteria for these applications.Comment: 413 pages, 9 figures, 277 citation