Computational Tutorial of Steepest Descent Method and Its Implementation in Digital Image Processing
In the last decade, optimization techniques have extensively come up as one of
principal signal processing techniques, which are used for solving many previous
intractable problems in both digital signal processing (DSP) problems and digital
image processing (DIP) problem. Due to its low computational complexity and
uncomplicated implementation, the Gradient Descent (GD) method  is one of the
most popular optimization methods for problems, which can be formulated as a
differentiable multivariable functions. The GD method is ubiquitously used from
basic to advanced researches. First, this paper presents the concept of GD method and
its implementations for general mathematical problems. Next, the computation of GD
processes is shown step by step with the aim to understand the effect of important
parameters (such as its initial value and step size) to the performance of GD. Later,
the computational concept of GD method for DIP problems [2-5] is formulated and
the computation of GD is demonstrated step by step. The effect of the initial value and
the step size to the performance of GD method in DIP is also presented.
Keywords: Gradient Descent (GD) method, Digital Image Processing and Digital
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Vorapoj Patanavijit received the B.Eng., M.Eng. and Ph.D. degrees from the Department of Electrical Engineering at the Chulalongkorn University, Bangkok, Thailand, in 1994, 1997 and 2007 respectively.
He has served as a full-time lecturer at Department of Computer and Network Engineering, Faculty of Engineering, Assumption University since 1998 where he is currently an Assistance Professor in 2009.
He has authored and co-authored over 75 research publications in digital signal processing and digital image processing.
He works in the field of signal processing and multidimensional signal processing, specializing, in particular, on Image/Video Reconstruction, SRR (Super-Resolution Reconstruction), Compressive Sensing, Enhancement, Fusion, Denoising, Inverse Problems, Motion Estimation and Registration
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