Computational Tutorial of Steepest Descent Method and Its Implementation in Digital Image Processing

Vorapoj Patanavijit
Assumption University


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 [1] 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

Signal Processing.

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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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