Image modulation represents image by meaningful characters such as image instantaneous amplitude and instantaneous frequency. A perfect reconstruction image modulation method is proposed. In detail, the bidimensional empirical mode decomposition (BEMD) is first improved to adaptively decompose image into monocomponents. Then by the quaternionic analytic method, suitable analytic signals is acquired. A new polar form is further proposed to modulate images, then seven characters are derived including instantaneous amplitude and instantaneous frequencies. We demonstrate the techniques on both synthetic and natural images, depict the needle program of the estimated frequencies and obtain the reconstructions that are the same with the original images. The applications in image segmentation and separation establish the validity of characterizing images of this type as sums of locally narrow band modulated components.
We present a new criterion based on instantaneous frequency (IF) to distinguish mono-components (MCs). We first notice that the "offset of local extremum" caused by low-frequency envelope is often significant on envelope extraction, which determines the calculation of IF for MCs. We estimate the upper and lower bounds of the offset for a general family of signals. Conducted by the offset estimation, we propose a direct and effective algorithm to calculate IF. Our algorithm, which is based on an empirical pursuit of knots and natural splines, provides an accurate estimation of the envelope and derives a well-behaved IF. A theoretical explanation for the good approximation of proposed envelope is also stated. Experiment results show the fast convergence of our algorithm, which leads to a reliable IF and local mean to provide a flexible criterion for MC classification. We emphasize that it is important to pursue a certain balance among different requirements to define MC depending on specific applications.
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