A hybrid alternating proximal method for blind video restoration

International audienceOld analog television sequences suffer from a number of degradations. Some of them can be modeled through convolution with a kernel and an additive noise term. In this work, we propose a new blind deconvolution algorithm for the restoration of such sequences based on a variational formulation of the problem. Our method accounts for motion between frames, while enforcing some level of temporal continuity through the use of a novel penalty function involving optical flow operators, in addition to an edge-preserving regularization. The optimization process is performed by a proximal alternating minimization scheme benefiting from theoretical convergence guarantees. Simulation results on synthetic and real video sequences confirm the effectiveness of our method

Low-rank and sparse reconstruction in dynamic magnetic resonance imaging via proximal splitting methods

Dynamic magnetic resonance imaging (MRI) consists of collecting multiple MR images in time, resulting in a spatio-temporal signal. However, MRI intrinsically suffers from long acquisition times due to various constraints. This limits the full potential of dynamic MR imaging, such as obtaining high spatial and temporal resolutions which are crucial to observe dynamic phenomena. This dissertation addresses the problem of the reconstruction of dynamic MR images from a limited amount of samples arising from a nuclear magnetic resonance experiment. The term limited can be explained by the approach taken in this thesis to speed up scan time, which is based on violating the Nyquist criterion by skipping measurements that would be normally acquired in a standard MRI procedure. The resulting problem can be classified in the general framework of linear ill-posed inverse problems. This thesis shows how low-dimensional signal models, specifically lowrank and sparsity, can help in the reconstruction of dynamic images from partial measurements. The use of these models are justified by significant developments in signal recovery techniques from partial data that have emerged in recent years in signal processing. The major contributions of this thesis are the development and characterisation of fast and efficient computational tools using convex low-rank and sparse constraints via proximal gradient methods, the development and characterisation of a novel joint reconstruction–separation method via the low-rank plus sparse matrix decomposition technique, and the development and characterisation of low-rank based recovery methods in the context of dynamic parallel MRI. Finally, an additional contribution of this thesis is to formulate the various MR image reconstruction problems in the context of convex optimisation to develop algorithms based on proximal splitting methods

Spatial Multizone Soundfield Reproduction Design

It is desirable for people sharing a physical space to access different multimedia information streams simultaneously. For a good user experience, the interference of the different streams should be held to a minimum. This is straightforward for the video component but currently difficult for the audio sound component. Spatial multizone soundfield reproduction, which aims to provide an individual sound environment to each of a set of listeners without the use of physical isolation or headphones, has drawn significant attention of researchers in recent years. The realization of multizone soundfield reproduction is a conceptually challenging problem as currently most of the soundfield reproduction techniques concentrate on a single zone. This thesis considers the theory and design of a multizone soundfield reproduction system using arrays of loudspeakers in given complex environments. We first introduce a novel method for spatial multizone soundfield reproduction based on describing the desired multizone soundfield as an orthogonal expansion of formulated basis functions over the desired reproduction region. This provides the theoretical basis of both 2-D (height invariant) and 3-D soundfield reproduction for this work. We then extend the reproduction of the multizone soundfield over the desired region to reverberant environments, which is based on the identification of the acoustic transfer function (ATF) from the loudspeaker over the desired reproduction region using sparse methods. The simulation results confirm that the method leads to a significantly reduced number of required microphones for an accurate multizone sound reproduction compared with the state of the art, while it also facilitates the reproduction over a wide frequency range. In addition, we focus on the improvements of the proposed multizone reproduction system with regard to practical implementation. The so-called 2.5D multizone oundfield reproduction is considered to accurately reproduce the desired multizone soundfield over a selected 2-D plane at the height approximately level with the listener’s ears using a single array of loudspeakers with 3-D reverberant settings. Then, we propose an adaptive reverberation cancelation method for the multizone soundfield reproduction within the desired region and simplify the prior soundfield measurement process. Simulation results suggest that the proposed method provides a faster convergence rate than the comparative approaches under the same hardware provision. Finally, we conduct the real-world implementation based on the proposed theoretical work. The experimental results show that we can achieve a very noticeable acoustic energy contrast between the signals recorded in the bright zone and the quiet zone, especially for the system implementation with reverberation equalization