The Role Of The Receptive Field Structure In Neuronal Compressive Sensing Signal Processing

The receptive field structure ubiquitous in the visual system is believed to play a crucial role in encoding stimulus characteristics, such as contrast and spectral composition. However, receptive field architecture may also result in unforeseen difficulties in processing particular classes of images. We explore the potential functional benefits and shortcomings of localization and center-surround paradigms in the context of an integrate-and-fire neuronal network model. Utilizing the sparsity of natural scenes, we derive a compressive-sensing based theoretical framework for network input reconstructions based on neuronal firing rate dynamics [1, 2]. This formalism underlines a potential mechanism for efficiently transmitting sparse stimulus information, and further suggests sensory pathways may have evolved to take advantage of the sparsity of visual stimuli [3, 4]. Using this methodology, we investigate how the accuracy of image encoding depends on the network architecture. We demonstrate that the receptive field structure does indeed facilitate marked improvements in natural stimulus encoding at the price of yielding erroneous information about specific classes of stimuli. Relative to uniformly random sampling, we show that localized random sampling yields robust improvements in image reconstructions, which are most pronounced for natural stimuli containing a relatively large spread of dominant low frequency components. This suggests a novel direction for compressive sensing theory and sampling methodology in engineered devices. However, for images with specific gray-scale patterning, such as the Hermann grid depicted in Fig. 1, we show that localization in sampling produces systematic errors in image encoding that may underlie several optical illusions. We expect that these connections between input characteristics, network topology, and neuronal dynamics will give new insights into the structure-function relationship of the visual system

Efficient Image Processing Via Compressive Sensing Of Integrate-And-Fire Neuronal Network Dynamics

Integrate-and-fire (I&F) neuronal networks are ubiquitous in diverse image processing applications, including image segmentation and visual perception. While conventional I&F network image processing requires the number of nodes composing the network to be equal to the number of image pixels driving the network, we determine whether I&F dynamics can accurately transmit image information when there are significantly fewer nodes than network input-signal components. Although compressive sensing (CS) theory facilitates the recovery of images using very few samples through linear signal processing, it does not address whether similar signal recovery techniques facilitate reconstructions through measurement of the nonlinear dynamics of an I&F network. In this paper, we present a new framework for recovering sparse inputs of nonlinear neuronal networks via compressive sensing. By recovering both one-dimensional inputs and two-dimensional images, resembling natural stimuli, we demonstrate that input information can be well-preserved through nonlinear I&F network dynamics even when the number of network-output measurements is significantly smaller than the number of input-signal components. This work suggests an important extension of CS theory potentially useful in improving the processing of medical or natural images through I&F network dynamics and understanding the transmission of stimulus information across the visual system

ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing

With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional optimization-based methods and the speed of recent network-based ones. Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general $\ell_1$ norm CS reconstruction model. To cast ISTA into deep network form, we develop an effective strategy to solve the proximal mapping associated with the sparsity-inducing regularizer using nonlinear transforms. All the parameters in ISTA-Net (\eg nonlinear transforms, shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than being hand-crafted. Moreover, considering that the residuals of natural images are more compressible, an enhanced version of ISTA-Net in the residual domain, dubbed {ISTA-Net}$^+$, is derived to further improve CS reconstruction. Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and network-based CS methods by large margins, while maintaining fast computational speed. Our source codes are available: \textsl{http://jianzhang.tech/projects/ISTA-Net}.Comment: 10 pages, 6 figures, 4 Tables. To appear in CVPR 201

A Computational Study Of The Role Of Spatial Receptive Field Structure In Processing Natural And Non-Natural Scenes

The center-surround receptive field structure, ubiquitous in the visual system, is hypothesized to be evolutionarily advantageous in image processing tasks. We address the potential functional benefits and shortcomings of spatial localization and center-surround antagonism in the context of an integrate-and-fire neuronal network model with image-based forcing. Utilizing the sparsity of natural scenes, we derive a compressive-sensing framework for input image reconstruction utilizing evoked neuronal firing rates. We investigate how the accuracy of input encoding depends on the receptive field architecture, and demonstrate that spatial localization in visual stimulus sampling facilitates marked improvements in natural scene processing beyond uniformly-random excitatory connectivity. However, for specific classes of images, we show that spatial localization inherent in physiological receptive fields combined with information loss through nonlinear neuronal network dynamics may underlie common optical illusions, giving a novel explanation for their manifestation. In the context of signal processing, we expect this work may suggest new sampling protocols useful for extending conventional compressive sensing theory