Jianing Shi

A Nonlinear Inverse Scale Space Method for a Convex Multiplicative Noise Model

We are motivated by a recently developed nonlinear inverse scale space method for image denoising [M. Burger, G. Gilboa, S. Osher, and J. Xu, Commun. Math. Sci., 4 (2006), pp. 179-212; M. Burger, S. Osher, J. Xu, and G. Gilboa, in Variational, Geometric, and Level Set Methods in Computer Vision, Lecture Notes in Comput. Sci. 3752, Springer, Berlin, 2005, pp. 25-36], whereby noise can be removed with minimal degradation. The additive noise model has been studied extensively, using the Rudin-Osher-Fatemi model [L. I. Rudin, S. Osher, and E. Fatemi, Phys. D, 60 (1992), pp. 259-268], an iterative regularization method [S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, Multiscale Model. Simul., 4 (2005), pp. 460-489], and the inverse scale space flow [M. Burger, G. Gilboa, S. Osher, and J. Xu, Commun. Math. Sci., 4 (2006), pp. 179-212; M. Burger, S. Osher, J. Xu, and G. Gilboa, in Variational, Geometric, and Level Set Methods in Computer Vision, Lecture Notes in Comput. Sci. 3752, Springer, Berlin, 2005, pp. 25-36]. However, the multiplicative noise model has not yet been studied thoroughly. Earlier total variation models for the multiplicative noise cannot easily be extended to the inverse scale space, due to the lack of global convexity. In this paper, we review existing multiplicative models and present a new total variation framework for the multiplicative noise model, which is globally strictly convex. We extend this convex model to the nonlinear inverse scale space flow and its corresponding relaxed inverse scale space flow. We demonstrate the convergence of the flow for the multiplicative noise model, as well as its regularization effect and its relation to the Bregman distance. We investigate the properties of the flow and study the dependence on flow parameters. The numerical results show an excellent denoising effect and significant improvement over earlier multiplicative models.

Perceptual decision making investigated via sparse decoding of a spiking neuron model of V1

Recent empirical evidence supports the hypothesis that invariant visual object recognition might result from non-linear encoding of the visual input followed by linear decoding [1]. This hypothesis has received theoretical support through the development of neural network architectures which are based on a non-linear encoding of the input via recurrent network dynamics followed by a linear decoder [2], [3]. In this paper we consider such an architecture in which the visual input is non-linearly encoded by a biologically realistic spiking model of V1, and mapped to a perceptual decision via a sparse linear decoder. Novel is that we 1) utilize a large-scale conductance based spiking neuron model of V1 which has been well-characterized in terms of classical and extra-classical response properties, and 2) use the model to investigate decoding over a large population of neurons. We compare decoding performance of the model system to human performance by comparing neurometric and psychometric curves.

Perceptual Decision Making “Through the Eyes” of a Large-scale Neural Model of V1

Sparse coding has been posited as an efficient information processing strategy employed by sensory systems, particularly visual cortex. Substantial theoretical and experimental work has focused on the issue of sparse encoding, namely how the early visual system maps the scene into a sparse representation. In this paper we investigate the complementary issue of sparse decoding, for example given activity generated by a realistic mapping of the visual scene to neuronal spike trains, how do downstream neurons best utilize this representation to generate a “decision.” Specifically we consider both sparse (L1-regularized) and non-sparse (L2 regularized) linear decoding for mapping the neural dynamics of a large-scale spiking neuron model of primary visual cortex (V1) to a two alternative forced choice (2-AFC) perceptual decision. We show that while both sparse and non-sparse linear decoding yield discrimination results quantitatively consistent with human psychophysics, sparse linear decoding is more efficient in terms of the number of selected informative dimension.

Decoding simulated neurodynamics predicts the perceptual consequences of age-related macular degeneration.

Age-related macular degeneration (AMD) is the major cause of blindness in the developed world. Though substantial work has been done to characterize the disease, it is difficult to predict how the state of an individuals retina will ultimately affect their high-level perceptual function. In this paper, we describe an approach that couples retinal imaging with computational neural modeling of early visual processing to generate quantitative predictions of an individuals visual perception. Using a patient population with mild to moderate AMD, we show that we are able to accurately predict subject-specific psychometric performance by decoding simulated neurodynamics that are a function of scotomas derived from an individuals fundus image. On the population level, we find that our approach maps the disease on the retina to a representation that is a substantially better predictor of high-level perceptual performance than traditional clinical metrics such as drusen density and coverage. In summary, our work identifies possible new metrics for evaluating the efficacy of treatments for AMD at the level of the expected changes in high-level visual perception and, in general, typifies how computational neural models can be used as a framework to characterize the perceptual consequences of early visual pathologies.