Abstract-This paper seeks to combine linear time-invariant (LTI) filtering and sparsity-based denoising in a principled way in order to effectively filter (denoise) a wider class of signals. LTI filtering is most suitable for signals restricted to a known frequency band, while sparsity-based denoising is suitable for signals admitting a sparse representation with respect to a known transform. However, some signals cannot be accurately categorized as either band-limited or sparse. This paper addresses the problem of filtering noisy data for the particular case where the underlying signal comprises a low-frequency component and a sparse or sparse-derivative component. A convex optimization approach is presented and two algorithms derived: one based on majorization-minimization (MM), and the other based on the alternating direction method of multipliers (ADMM). It is shown that a particular choice of discrete-time filter, namely zero-phase noncausal recursive filters for finite-length data formulated in terms of banded matrices, makes the algorithms effective and computationally efficient. The efficiency stems from the use of fast algorithms for solving banded systems of linear equations. The method is illustrated using data from a physiological-measurement technique (i.e., near infrared spectroscopic time series imaging) that in many cases yields data that is well-approximated as the sum of low-frequency, sparse or sparse-derivative, and noise components.
We conclude that MIG-10 mediates the guidance of AVM and PVM axons in response to the extracellular UNC-6 and SLT-1 guidance cues. The attractive and repulsive guidance cues orient MIG-10-dependant axon outgrowth to cause a directional response.
Axon migrations are guided by extracellular cues that induce asymmetric outgrowth activity in the growth cone. Several intracellular signaling proteins have been implicated in the guidance response. However, how these proteins interact to generate asymmetric outgrowth activity is unknown. Here, we present evidence that in C. elegans, the CED-10/Rac1 GTPase binds to and causes asymmetric localization of MIG-10/lamellipodin, a protein that regulates actin polymerization and has outgrowth-promoting activity in neurons. Genetic analysis indicates that mig-10 and ced-10 function together to orient axon outgrowth. The RAPH domain of MIG-10 binds to activated CED-10/Rac1, and ced-10 function is required for the asymmetric MIG-10 localization that occurs in response to the UNC-6/netrin guidance cue. We also show that asymmetric localization of MIG-10 in growth cones is associated with asymmetric concentrations of f-actin and microtubules. These results suggest that CED-10/Rac1 is asymmetrically activated in response to the UNC-6/netrin signal and thereby causes asymmetric recruitment of MIG-10/lamellipodin. We propose that the interaction between activated CED-10/Rac1 and MIG-10/lamellipodin triggers local cytoskeletal assembly and polarizes outgrowth activity in response to UNC-6/netrin.
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