We succeeded in obtaining high-resolution images by a CCD sensor with a pixel size of 3.14 μm, even while bound by the need to satisfy the sampling theorem and by the CCD pixel size.
This theory proved that sparse signals can be accurately restored by data far less than the sampling theorem, which greatly facilitates the research and application of TV constraints in CT reconstruction, especially sparse projection data CT reconstruction [15 18].
When referring to maximally decimated signals, it is considered that the rate of the signals at the filter output is reduced to the minimum as it is defined by the Nyquist sampling theorem.
The 200 highest-intensity puncta that were between 4 and 70 pixels [the width of one pixel corresponds to 106 nm, imposed by the calculated Rayleigh's transverse resolution of 233 nm (at 535 nm emission) and by the Nyquist Shannon sampling theorem] in area were selected for trafficking analysis.
The ingenuity of the approach is in trying to choose the function F so that f ∈ B σ 2 (unknown part) and can be approximated by the WKS sampling theorem if its values at some equally spaced points are known; see [9 12].
First, by using the Shannon sampling theorem we rely on bases of infinite support, while we generally reconstruct signal samples in the finite domain [44].
In this view, given the almost periodic nature of nucleosome locations, the length of each tag can be actually shortened based on the intuition offered by the Nyquist-Shannon sampling theorem [ 19] from signal processing.
