Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play

Conscious and nonconscious processes: An ERP index of an anticipatory response in a conditioning paradigm using visually masked stimuli

This study investigates the nonconscious elicitation of a previously conditioned response by using a differential conditioning paradigm with visually masked affectively valent facial schematics. Electrodermal (skin conductance response [SCR]) and brain (event-related potential [ERP]) activity were main dependent measures. Following a preconditioning phase in which subjects viewed energy masked pleasant and unpleasant facial schematics, conditioning with an aversive shock was established to unmasked presentations of an unpleasant face in a partial factorial design. A postconditioning phase of masked presentations, when compared with the preconditioning phase, revealed how the conditional effect within awareness might affect the same stimuli when presented outside awareness. An adaptive staircase technique was used to establish individual threshold levels, which represented a methodological advance over procedures typically used in visual masking research. The results revealed that responses to the CS+ (unpleasant face) changed significantly in predicted directions from preconditioning to postconditioning phase when compared with responses to the CS− (pleasant face). The SCR results systematically replicated recent Ohman, Dimberg, and Esteves (1988) findings, with the pattern of responses resembling a resistance to extinction effect. A new finding emerged for the brain responses. For the CS+, distinct slow wave activity occurred just before the point at which the shock had been delivered in the conditioning phase; no such activity was found for the CS−. This slow wave activity is similar to what has been described by others as an expectancy wave. The results indicate that an anticipatory process, as indexed by different physiological systems, can be elicited entirely outside awareness. Implications are discussed in regard to the nature of conscious and nonconscious processes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74457/1/j.1469-8986.1994.tb01028.x.pd