Single Spatial Filter Research Articles

Correlated Initialization for Correlated Data

Spatial data exhibits the property that nearby points are correlated. This also holds for learnt representations across layers, but not for commonly used weight initialization methods. Our theoretical analysis quantifies the learning behavior of weights of a single spatial filter. It is thus in contrast to a large body of work that discusses statistical properties of weights. It shows that uncorrelated initialization (1) might lead to poor convergence behavior and (2) training of (some) parameters is likely subject to slow convergence. Empirical analysis shows that these findings for a single spatial filter extend to networks with many spatial filters. The impact of (correlated) initialization depends strongly on learning rates and l2-regularization.

Soft information assisted space-time multiuser detection for highly loaded CDMA

This letter presents an effective space-time multiuser detector (MUD) with the assistance of soft information in multipath code division multiple access (CDMA) channels. The space-time MUD considered is a simple, separable spatial-temporal filter which consists of a single spatial filter and a single temporal filter. Based on the soft-decision outputs determined in the previous iteration, the soft information is then exchanged in the alternating updates of either the spatial filters or the temporal filters. Furnished simulations show that the proposed scheme can offer substantial performance improvement compared with previous works, especially in highly loaded scenarios.

A Multiscale Filtering Explanation of Gradient Induction and Remote Brightness Induction Effects: A Reply to Logvinenko (2003)

Grating induction is a brightness effect in which a counterphase spatial brightness variation (a grating) is induced in a homogeneous test strip that is surrounded by an inducing luminance grating (McCourt, 1982 Vision Research 22 119-134). Moulden and Kingdom (1991 Vision Research 31 1999-2008) introduced an interesting variant of grating induction (sometimes referred to as gradient induction) in which multiple strips of either a linear luminance ramp or a sine-wave grating were interlaced with strips of homogeneous luminance. We (Blakeslee and McCourt, 1999 Vision Research 39 4361-4377) demonstrated that a simple multiscale filtering explanation could account for grating induction. Recently, however, Logvinenko (2003 Perception 32 621-626) presented several arguments impugning the adequacy of spatial filtering approaches to understanding brightness induction in gradient induction stimuli. We propose that Logvinenko's arguments apply only to a limited class of filtering models, specifically those which employ only a single spatial filter. To test this hypothesis we modeled gradient induction stimuli as a function of inducing contrast, as well as Logvinenko's (2003) remote induction stimulus, using our multiscale oriented difference-of-Gaussians (ODOG) model (Blakeslee and McCourt 1999). The ODOG model successfully predicts the appearance of the inducing strips and the homogeneous test strips in the gradient induction stimuli and the appearance of the test patches in the remote induction stimuli. These results refute Logvinenko's (2003) claims, and we interpret them as providing strong evidence for a multiscale filtering approach to understanding both gradient induction and remote brightness induction effects.

Combined multiuser detection and beamforming for CDMA systems: filter structures

Code-division multiple-access (CDMA) systems are interference limited, and therefore efficient interference management is necessary to enhance the capacity of a CDMA system. In this paper, we consider combining two effective receiver-based interference management strategies: multiuser detection (temporal filtering) and receiver beamforming (spatial filtering). We formulate and examine the performance of several two-dimensional linear filter structures, which are all based on minimum mean squared error (MMSE) criterion but differ in how the MMSE problems are defined in the temporal and spatial domains, i.e., jointly or in cascade. It is shown that while the joint optimum MMSE filter achieves the maximum signal-to-interference ratio (SIR) among all possible matrix filters, the constrained optimum MMSE filter which results in a single temporal and single spatial filter, outperforms all combined single-user/multiple-user approaches and cascaded optimization approaches either uniformly or asymptotically. The constrained optimum MMSE filter is near-far resistant in all but very highly loaded systems and enjoys low complexity.

Detection of low spatial frequencies: a single filter or multiple filters?

Ever since it was first reported that the contrast sensitivity for low spatial frequency sinusoidal gratings falls off with a slope approximating unity it has been suggested that this may represent gradient detection by a single spatial filter tuned to higher spatial frequencies. We have further investigated this possibility using aperiodic as well as periodic stimuli. Experiments are presented that involve manipulations of luminance, field size and spatial adaptation, and the results are consistent with a multiple filter model accounting for the detection of low spatial frequency (0.2-2 c/deg) periodic and aperiodic stimuli.