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.

Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.

A priori prediction of aggregation efficiency and rate constant for fluidized bed melt granulation

This paper presents a predictive aggregation rate model for spray fluidized bed melt granulation. The aggregation rate constant was derived from probability analysis of particle–droplet contact combined with time scale analysis of droplet solidification and granule–granule collision rates. The latter was obtained using the principles of kinetic theory of granular flow (KTGF). The predicted aggregation rate constants were validated by comparison with reported experimental data for a range of binder spray rate, binder droplet size and operating granulator temperature. The developed model is particularly useful for predicting particle size distributions and growth using population balance equations (PBEs).

Build-up of auditory stream segregation induced by tone sequences of constant or alternating frequency and the resetting effects of single deviants

A sequence of constant-frequency tones can promote streaming in a subsequent sequence of alternating-frequency tones, but why this effect occurs is not fully understood and its time course has not been investigated. Experiment 1 used a 2.0-s-long constant-frequency inducer (10 repetitions of a low-frequency pure tone) to promote segregation in a subsequent, 1.2-s test sequence of alternating low- and high-frequency tones. Replacing the final inducer tone with silence substantially reduced reported test-sequence segregation. This reduction did not occur when either the 4th or 7th inducer was replaced with silence. This suggests that a change at the induction/test-sequence boundary actively resets build-up, rather than less segregation occurring simply because fewer inducer tones were presented. Furthermore, Experiment 2 found that a constant-frequency inducer produced its maximum segregation-promoting effect after only three tones—this contrasts with the more gradual build-up typically observed for alternating-frequency sequences. Experiment 3 required listeners to judge continuously the grouping of 20-s test sequences. Constant-frequency inducers were considerably more effective at promoting segregation than alternating ones; this difference persisted for ~10 s. In addition, resetting arising from a single deviant (longer tone) was associated only with constant-frequency inducers. Overall, the results suggest that constant-frequency inducers promote segregation by capturing one subset of test-sequence tones into an ongoing, preestablished stream, and that a deviant tone may reduce segregation by disrupting this capture. These findings offer new insight into the dynamics of stream segregation, and have implications for the neural basis of streaming and the role of attention in stream formation. (PsycINFO Database Record (c) 2013 APA, all rights reserved)

Effect of target distance on accommodative amplitude measured using the minus lens technique

Background: The aim was to investigate the effect on the measured amplitude of accommodation and repeatability of using the minus lens technique with the target at distance or near. Methods: Forty-three students (average age: 21.17 ± 1.50 years, 35 female) had their amplitude of accommodation measured with minus lenses on top of their distance correction in a trial frame with the target at far (6.0m) or near (0.4m). The minus lens power was gradually added with steps of 0.25D. Measurements were taken on two occasions at each distance, which were separated by a time interval of at least 24 hours. Results: The measured amplitude at six metres was significantly lower than that with the target at 40cm, by 1.56 ± 1.17D (p < 0.001) and this varied between individuals (r = 0.716, intraclass correlation coefficient = 0.439). With either target distance, repeated measurement was highly correlated (r > 0.9) but the agreement was better at 6.0m (±0.74D) than at 40cm (± 0.92D). Conclusion: The measurements of the amplitude of accommodation with the minus lens technique using targets at far or near are not comparable and the difference between the target distances may provide clinically relevant information. © 2013 Optometrists Association Australia.

Simple eye-closure penalty estimate for amplitude noise-degraded signals

We present a simplified model for a simple estimation of the eye-closure penalty for amplitude noise-degraded signals. Using a typical 40-Gbit/s return-to-zero amplitude-shift-keying transmission, we demonstrate agreement between the model predictions and the results obtained from the conventional numerical estimation method over several thousand kilometers.