For piecewise smooth data, edges can be recognized by jump discontinuities in the data. Successful edge detection is essential in digital signal processing as the most relevant information is often observed near the edges in each segmented region. In this paper, using the concentration property of existing local edge detectors and the clustering property of sigmoidal transformations, we provide...

Abstract. This paper addresses the recovery of piecewise smooth functions from their discrete data. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurat...

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...

Using the critical point theory of Szulkin (1986), we study elliptic problems with unilateral boundary conditions and discontinuous nonlinearities. We do not use the method of upper and lower solutions. We prove two existence theorems: one when the right-hand side is nondecreasing and the other when it is nonincreasing. 1. Introduction. In this paper, using the critical-point theory of Szulkin ...

This paper proposes a new method for performing multiresolution analysis (MRA) of non-uniform data with jump discontinuities and impulsive noise using robust M-estimatorbased local polynomial regression (LPR). The basic idea is to interpolate the smoothed estimate, after performing the robust LPR, on a uniform grid in order to perform the MRA using the ordinary wavelet transform. Simulation res...

Identifying the instances of jumps in a discrete-time-series sample jump diffusion model is challenging task. We have developed novel statistical technique for detection and volatility estimation return time series data using threshold method. The consistency estimator has been obtained. Since we derived simultaneously by solving an implicit equation, obtained unprecedented accuracy across wide...