Quantum Boolean image denoising

Abstract

A quantum Boolean image processing methodology is presented in this work, with special emphasis in image denoising. A new approach for internal image representation is outlined together with two new interfaces: classical to quantum and quantum to classical. The new quantum Boolean image denoising called quantum Boolean mean filter works with computational basis states (CBS), exclusively. To achieve this, we first decompose the image into its three color components, i.e., red, green and blue. Then, we get the bitplanes for each color, e.g., 8 bits per pixel, i.e., 8 bitplanes per color. From now on, we will work with the bitplane corresponding to the most significant bit (MSB) of each color, exclusive manner. After a classical-toquantum interface (which includes a classical inverter), we have a quantum Boolean version of the image within the quantum machine. This methodology allows us to avoid the problem of quantum measurement, which alters the results of the measured except in the case of CBS. Said so far is extended to quantum algorithms outside image processing too. After filtering of the inverted version of MSB (inside quantum machine), the result passes through a quantum-classical interface (which involves another classical inverter) and then proceeds to reassemble each color component and finally the ending filtered image. Finally, we discuss the more appropriate metrics for image denoising in a set of experimental results.

Teleporting Digital Images

“…First, we need to decompose all digital images in their 3 color components (red, green, blue) [31]. Thus, we will obtain 24 bitplanes (8 bitplanes for every color) thanks to a procedure known as bit slicing [31]. We get 8 bitplanes per color, where the 7th bitplane (the closest to the observer) is It is evident, from here on, that an element in black in every bitplane is a classical bit equal to 1 and will be represented with a qubit equal to 1 , while, an element in white in every bitplane is a classical bit equal to 0 and will be represented with a qubit equal to 0 in a future Cl2Qu interface.…”

“…In fact, the definitive Cl2Qu interface is absolutely compact and henceforth it will be considered as a unified block. Finally, we will apply the Hadamard's gate to the last set of equations according to Figures 6 and 7 [24,25], thus, for b2 = 0 and b1 = 0, we will have, 00 00 0 1 0 0 0 00 01 00 0 0 0 1 0 (31) for b2 = 0 and b1 = 1, 00 00 0 1 0 0 0 00 01 00 0 0 0 0 0 0 1 1 0 10…”

Quantum image processing?

“…: this technology is presented as a viable alternative to the problem of practical implementation of algorithms for quantum image processing (QuIP) [50]. The algorithms grouped under this technology does not suffer the ravages of the quantum measurement.…”

“…Definitely, the problem lies in the hostile relationship between the internal representation of the image (inside quantum machine), the outcome measurement, and the recovery of the image outside of quantum machine. Therefore, the only technique of QuIP that survives is QuBoIP [50]. This is because it works with CBS, exclusively, and the quantum measurement does not affect the value of states.…”

Optimal Estimate of Quantum States

“…On the other hand, a new technology allows us to avoid the problem of quantum measurement [2] [3]. However, this technology lets us work exclusively with Computational Basis States (CBS), i.e., pure and orthogonal quantum base states.…”