Compressive Imaging via Approximate Message Passing with Image Denoising

We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and runtime. To pursue our objective, we propose compressive imaging algorithms that employ the approximate message passing (AMP) framework. AMP is an iterative signal reconstruction algorithm that performs scalar denoising at each iteration; in order for AMP to reconstruct the original input signal well, a good denoiser must be used. We apply two wavelet based image denoisers within AMP. The first denoiser is the "amplitude-scaleinvariant Bayes estimator" (ABE), and the second is an adaptive Wiener filter; we call our AMP based algorithms for compressive imaging AMP-ABE and AMP-Wiener. Numerical results show that both AMP-ABE and AMP-Wiener significantly improve over the state of the art in terms of runtime. In terms of reconstruction quality, AMP-Wiener offers lower mean square error (MSE) than existing compressive imaging algorithms. In contrast, AMP-ABE has higher MSE, because ABE does not denoise as well as the adaptive Wiener filter.Comment: 15 pages; 2 tables; 7 figures; to appear in IEEE Trans. Signal Proces

Hacia el modelado 3d de tumores cerebrales mediante endoneurosonografía y redes neuronales

Las cirugías mínimamente invasivas se han vuelto populares debido a que implican menos riesgos con respecto a las intervenciones tradicionales. En neurocirugía, las tendencias recientes sugieren el uso conjunto de la endoscopia y el ultrasonido, técnica llamada endoneurosonografía (ENS), para la virtualización 3D de las estructuras del cerebro en tiempo real. La información ENS se puede utilizar para generar modelos 3D de los tumores del cerebro durante la cirugía. En este trabajo, presentamos una metodología para el modelado 3D de tumores cerebrales con ENS y redes neuronales. Específicamente, se estudió el uso de mapas auto-organizados (SOM) y de redes neuronales tipo gas (NGN). En comparación con otras técnicas, el modelado 3D usando redes neuronales ofrece ventajas debido a que la morfología del tumor se codifica directamente sobre los pesos sinápticos de la red, no requiere ningún conocimiento a priori y la representación puede ser desarrollada en dos etapas: entrenamiento fuera de línea y adaptación en línea. Se realizan pruebas experimentales con maniquíes médicos de tumores cerebrales. Al final del documento, se presentan los resultados del modelado 3D a partir de una base de datos ENS.Minimally invasive surgeries have become popular because they reduce the typical risks of traditional interventions. In neurosurgery, recent trends suggest the combined use of endoscopy and ultrasound (endoneurosonography or ENS) for 3D virtualization of brain structures in real time. The ENS information can be used to generate 3D models of brain tumors during a surgery. This paper introduces a methodology for 3D modeling of brain tumors using ENS and unsupervised neural networks. The use of self-organizing maps (SOM) and neural gas networks (NGN) is particularly studied. Compared to other techniques, 3D modeling using neural networks offers advantages, since tumor morphology is directly encoded in synaptic weights of the network, no a priori knowledge is required, and the representation can be developed in two stages: off-line training and on-line adaptation. Experimental tests were performed using virtualized phantom brain tumors. At the end of the paper, the results of 3D modeling from an ENS database are presented

Unsupervised Understanding of Location and Illumination Changes in Egocentric Videos

Wearable cameras stand out as one of the most promising devices for the upcoming years, and as a consequence, the demand of computer algorithms to automatically understand the videos recorded with them is increasing quickly. An automatic understanding of these videos is not an easy task, and its mobile nature implies important challenges to be faced, such as the changing light conditions and the unrestricted locations recorded. This paper proposes an unsupervised strategy based on global features and manifold learning to endow wearable cameras with contextual information regarding the light conditions and the location captured. Results show that non-linear manifold methods can capture contextual patterns from global features without compromising large computational resources. The proposed strategy is used, as an application case, as a switching mechanism to improve the hand-detection problem in egocentric videos.Comment: Submitted for publicatio

A Max-Product EM Algorithm for Reconstructing Markov-tree Sparse Signals from Compressive Samples

We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing Markov-tree sparse signals via belief propagation. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown approximately sparse signal and a zero-mean white Gaussian noise with an unknown variance. The signal is composed of large- and small-magnitude components identified by binary state variables whose probabilistic dependence structure is described by a Markov tree. Gaussian priors are assigned to the signal coefficients given their state variables and the Jeffreys' noninformative prior is assigned to the noise variance. Our signal reconstruction scheme is based on an EM iteration that aims at maximizing the posterior distribution of the signal and its state variables given the noise variance. We construct the missing data for the EM iteration so that the complete-data posterior distribution corresponds to a hidden Markov tree (HMT) probabilistic graphical model that contains no loops and implement its maximization (M) step via a max-product algorithm. This EM algorithm estimates the vector of state variables as well as solves iteratively a linear system of equations to obtain the corresponding signal estimate. We select the noise variance so that the corresponding estimated signal and state variables obtained upon convergence of the EM iteration have the largest marginal posterior distribution. We compare the proposed and existing state-of-the-art reconstruction methods via signal and image reconstruction experiments.Comment: To appear in IEEE Transactions on Signal Processin