An Inexact Newton Method For Unconstrained Total Variation-Based Image Denoising by Approximate Addition

The Inexact Newton method using the conjugate gradient has been widely used to solve large-scale unconstrained optimization problems, such as the total variation-based image denoising. To improve energy and latency, this paper initially proposes an additional step length parameter (
$\alpha $
), such that the required number of iterations (and therefore its energy dissipation) decreases. Then, a floating-point adder (32-bits) made of approximate or truncated cells is utilized to reduce the energy dissipation in each iteration. These two techniques are finally combined to reduce the total processing time and energy dissipation for image denoising. The results show that
$\ \alpha $
significantly reduces the number of iterations; the proposed technique is tested on a set of images taken from a public domain library and is found that when 1.39<
$\alpha $
<1.45, the number of iterations is the lowest. Moreover, the energy dissipation of the denoising algorithm decreases by applying an approximate adder at a very small loss of accuracy and quality of the output image; the number of iterations remains constant when the number of approximate or truncated cells in the least significant positions (given by so-called NAB) is below 10. Irrespective of the noise level and approximate cell type, the quality of the output images does not incur in a significant degradation when NAB<18.