Arbitrary Nonnegative Matrix Research Articles

Entire frame image display employing monotonic convergent nonnegative matrix factorization

The average life spans of light-emitting diodes (LEDs) used in organic light-emitting diode displays are negatively influenced by high current operation in short duty cycles. Since the time average brightness of a pixel LED is a function only of the time integral of the delivered current, it is desirable to achieve brightness by adopting pixel addressing schemes that employ long duty cycles. Conventional addressing methods which cannot operate more than one row of pixels at a time inherently have very short duty cycles. We solve the problem by proposing entire frame addressing, made possible by a new image factorization called monotonic-nonnegative matrix factorization (M-NNMF). Using M-NNMF, we develop a converging image series representation of an arbitrary nonnegative matrix (image). Each element of the series has unit rank, which allows it to drive an entire frame simultaneously. Each application of the M-NNMF algorithm produces a dominant unit rank component for the series, and a residue image of higher rank, the input to the next iteration. We drive the display with these unit rank components, called sub-frames, each for a duration proportional to its energy. The sum of sub-frames approximates the original image and provides the same visual effect, due to inherent perceptual integration. M-NNMF, more efficient and less time complex compared to existing NNMF algorithms, is our primary contribution in this paper and is likely to find applications in many other situations. We also obtain an even faster converging series with a randomized version of M-NNMF. The proposed approach of entire frame image display is demonstrated on a wide variety of images.

Statistical limit point theorems

It is known that given a regular matrix A and a bounded sequence x there is a subsequence (respectively, rearrangement, stretching) y of x such that the set of limit points of Ay includes the set of limit points of x. Using the notion of a statistical limit point, we establish statistical convergence analogues to these results by proving that every complex number sequence x has a subsequence (respectively, rearrangement, stretching) y such that every limit point of x is a statistical limit point of y. We then extend our results to the more general A‐statistical convergence, in which A is an arbitrary nonnegative matrix.