Advanced Restoration Techniques for Images and Disparity Maps

With increasing popularity of digital cameras, the field of Computa- tional Photography emerges as one of the most demanding areas of research. In this thesis we study and develop novel priors and op- timization techniques to solve inverse problems, including disparity estimation and image restoration. The disparity map estimation method proposed in this thesis incor- porates multiple frames of a stereo video sequence to ensure temporal coherency. To enforce smoothness, we use spatio-temporal connec- tions between the pixels of the disparity map to constrain our solution. Apart from smoothness, we enforce a consistency constraint for the disparity assignments by using connections between the left and right views. These constraints are then formulated in a graphical model, which we solve using mean-field approximation. We use a filter-based mean-field optimization that perform efficiently by updating the dis- parity variables in parallel. The parallel updates scheme, however, is not guaranteed to converge to a stationary point. To compare and demonstrate the effectiveness of our approach, we developed a new optimization technique that uses sequential updates, which runs ef- ficiently and guarantees convergence. Our empirical results indicate that with proper initialization, we can employ the parallel update scheme and efficiently optimize our disparity maps without loss of quality. Our method ranks amongst the state of the art in common benchmarks, and significantly reduces the temporal flickering artifacts in the disparity maps. In the second part of this thesis, we address several image restora- tion problems such as image deblurring, demosaicing and super- resolution. We propose to use denoising autoencoders to learn an approximation of the true natural image distribution. We parametrize our denoisers using deep neural networks and show that they learn the gradient of the smoothed density of natural images. Based on this analysis, we propose a restoration technique that moves the so- lution towards the local extrema of this distribution by minimizing the difference between the input and output of our denoiser. Weii demonstrate the effectiveness of our approach using a single trained neural network in several restoration tasks such as deblurring and super-resolution. In a more general framework, we define a new Bayes formulation for the restoration problem, which leads to a more efficient and robust estimator. The proposed framework achieves state of the art performance in various restoration tasks such as deblurring and demosaicing, and also for more challenging tasks such as noise- and kernel-blind image deblurring. Keywords. disparity map estimation, stereo matching, mean-field optimization, graphical models, image processing, linear inverse prob- lems, image restoration, image deblurring, image denoising, single image super-resolution, image demosaicing, deep neural networks, denoising autoencoder

Multiplicative versus additive noise in multi-state neural networks

The effects of a variable amount of random dilution of the synaptic couplings in Q-Ising multi-state neural networks with Hebbian learning are examined. A fraction of the couplings is explicitly allowed to be anti-Hebbian. Random dilution represents the dying or pruning of synapses and, hence, a static disruption of the learning process which can be considered as a form of multiplicative noise in the learning rule. Both parallel and sequential updating of the neurons can be treated. Symmetric dilution in the statics of the network is studied using the mean-field theory approach of statistical mechanics. General dilution, including asymmetric pruning of the couplings, is examined using the generating functional (path integral) approach of disordered systems. It is shown that random dilution acts as additive gaussian noise in the Hebbian learning rule with a mean zero and a variance depending on the connectivity of the network and on the symmetry. Furthermore, a scaling factor appears that essentially measures the average amount of anti-Hebbian couplings.Comment: 15 pages, 5 figures, to appear in the proceedings of the Conference on Noise in Complex Systems and Stochastic Dynamics II (SPIE International

GPU-based Iterative Cone Beam CT Reconstruction Using Tight Frame Regularization

X-ray imaging dose from serial cone-beam CT (CBCT) scans raises a clinical concern in most image guided radiation therapy procedures. It is the goal of this paper to develop a fast GPU-based algorithm to reconstruct high quality CBCT images from undersampled and noisy projection data so as to lower the imaging dose. For this purpose, we have developed an iterative tight frame (TF) based CBCT reconstruction algorithm. A condition that a real CBCT image has a sparse representation under a TF basis is imposed in the iteration process as regularization to the solution. To speed up the computation, a multi-grid method is employed. Our GPU implementation has achieved high computational efficiency and a CBCT image of resolution 512\times512\times70 can be reconstructed in ~5 min. We have tested our algorithm on a digital NCAT phantom and a physical Catphan phantom. It is found that our TF-based algorithm is able to reconstrct CBCT in the context of undersampling and low mAs levels. We have also quantitatively analyzed the reconstructed CBCT image quality in terms of modulation-transfer-function and contrast-to-noise ratio under various scanning conditions. The results confirm the high CBCT image quality obtained from our TF algorithm. Moreover, our algorithm has also been validated in a real clinical context using a head-and-neck patient case. Comparisons of the developed TF algorithm and the current state-of-the-art TV algorithm have also been made in various cases studied in terms of reconstructed image quality and computation efficiency.Comment: 24 pages, 8 figures, accepted by Phys. Med. Bio

Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements

Background subtraction has been a fundamental and widely studied task in video analysis, with a wide range of applications in video surveillance, teleconferencing and 3D modeling. Recently, motivated by compressive imaging, background subtraction from compressive measurements (BSCM) is becoming an active research task in video surveillance. In this paper, we propose a novel tensor-based robust PCA (TenRPCA) approach for BSCM by decomposing video frames into backgrounds with spatial-temporal correlations and foregrounds with spatio-temporal continuity in a tensor framework. In this approach, we use 3D total variation (TV) to enhance the spatio-temporal continuity of foregrounds, and Tucker decomposition to model the spatio-temporal correlations of video background. Based on this idea, we design a basic tensor RPCA model over the video frames, dubbed as the holistic TenRPCA model (H-TenRPCA). To characterize the correlations among the groups of similar 3D patches of video background, we further design a patch-group-based tensor RPCA model (PG-TenRPCA) by joint tensor Tucker decompositions of 3D patch groups for modeling the video background. Efficient algorithms using alternating direction method of multipliers (ADMM) are developed to solve the proposed models. Extensive experiments on simulated and real-world videos demonstrate the superiority of the proposed approaches over the existing state-of-the-art approaches.Comment: To appear in IEEE TI