A novel elementary spatial expanding scheme form on SISR method with modifying Geman & McClure function

Because of the feasible and impressive fallout, the classical Super-Resolution Reconstruction (SRR) is the contemporary algorithm for improving spatial information and reducing noise and SISR (Single-Image Super-Resolution) method, which is form on the classical SRR, is solely developed for improving spatial information. Disastrously, deficiency of the classical SISR method is conceptually computed from three specifications (b, h, k) and the simulating calculation of the optimized specifications for interpolating the better and higher spatial information images with highest PSNR is so burdersome. For figuring out this issue, the Geman&McClure function is proposed to replace with the ordinary SISR function because this function is conceptually computed from only one specification (T), contrary to three specifications similar to classical SISR method hence this analytic article focuses to offer a novel elementary spatial expanding scheme form on SISR method with modifying Geman&McClure function. Therefore, the fallout of a proposed spatial expanding scheme approximately matches to classical SISR method. From these reason, a novel elementary spatial expanding scheme is easily implemented for real works.

ISSN: 1693-6930 ◼ offer a novel elementary spatial expanding scheme form on SISR method and modifying Geman&McClure function.
The analytic article can be adjusted as ensuing.The first organized content is the complementary investigation of the SSR method and SISR method.Next, the second organized content is the classical spatial expanding scheme form on SISR method.Subsequently, the third organized content is the novel spatial expanding scheme form on proposed Geman&McClure SISR method.Later, the forth organized content is computer computation substantiation, which are comparatively assessed to three ordinary spatial expanding schemes: nearest, bilinear and bicubic, on bountiful images.Finally, the fifth organized content is the theatrical concision.

The Classical Spatial Expanding Scheme form on SISR Method
This organized content rapidly expounds the algorithmic apprehension of ordinary SISR method [18] using boundary constructing techniques, which is computed from boundary constructing procedure (as exhibit in Figure 1) and Geman&McClure regularization procedure.

Boundary Constructing Procedure
The vital target of this boundary constructing procedure [18] is for constructing the boundary, detail and edge of the better and higher spatial information images with highest PSNR.At second, operating a ordinary spatial expanding scheme, a class of more spatial information images are constructed from each low spatial information images (from first procedure) as  .At fifth, by operating the least square interporating scheme, the boundary, detail and edge image of the higher spatial information images

Ordinary Regularization Procedure
The vital target of this boundary constructing procedure is for forceing the upper limitation of the detail and edge image of the higher spatial information ( ( ) ) that is constructed by the boundary constructing procedure with the ordinary regularization procedure as ensuing: where b , k and h are fix specifications At final, the high spatial information image can be constructed by addng of the boundary, detail and edge image of the higher spatial information images, which are multiypled with the fallout of the regularization procedure ( ( ) ( ) ( ) ) and the higher spatial information image ( ( ) mn  , which is constructed by operating a ordinary spatial expanding scheme.

The Novel Elementary Spatial Expanding Scheme form on SISR Method with Modifying Geman&McClure Function
As expounds in the prevous orgianzied content, the ordinary regularization procedure [18], which is defined in (1), conceptually computed from three specifications (b, h, k) thereby the simulating calculation of the optimized specifications for interpolating the better and higher spatial information images with highest PSNR is so burdersome.For figuring out this issue, the Geman&McClure function [26] is conceptually computed from only one specification (T), contrary to three specifications similar to classical SISR method.
The Geman&McClure function and its gradient is defined as ensuing ( 2) and ( 3), respectively: , where GM T is Geman&McClure specification, which is computed by full search method.

Computer Computation Substatntiation
This organized content exhaustively expounds substantiation from computer computation, which are covered bountiful images such as Cameraman, Tree, House, Resolution chart, Stream and bridge, Sailboat, Peppers, Tiffany, Baboon, Lena, F-16, Mobile Frame10, Pentagon, Aerial [24,25] as expound in Table 1 and are computing by MATLAB software.At first, each ordinary image is scaled down and combined with noise for reconstruction the recorded image.Next, the novel elementary spatial expanding SISR scheme, the ordinary spatial expanding SISR scheme, spatial expanding nearest scheme, spatial expanding bilinear scheme and spatial expanding bicubic scheme are operated on each recorded image for comparatively assessing the feasible and impressive fallout of the proposed spatial expanding scheme.

No Outlier
At first, the organized sub-content expounds the optimization of Geman&McClure specification ( GM T ) that is modified during 0 to 2000 for interpolating the better and higher spatial information images with highest PSNR.The computer computation substantiation of no outlier is expounded in the Figure 2. From this substantiation in this figure, it can be firmed that the Geman&McClure specification is fix to be optimized at 900-1050 for normal images and the Geman&McClure specification is fix to be optimized at 1250-1450 for image with bountiful boundary, detail and edge information.The global computation substantiation in PSNR is expounded in Table 2 for no outlier.The feasible and impressive fallout of the novel elementary spatial expanding scheme approximately matches to classical SISR method nevertheless the simulating calculation of the optimized specification is so readily and rapidly compared with classical SISR method (with three specification).

Gaussian Outlier
At first, for Gaussian outlier at 35 dB, the vital target of this computation substantiation is the calculation of the optimized specifications which is modified during 0 to 2000 for interpolating the better and higher spatial information images with highest PSNR as expounded in the Figure 3. From this substantiation in this figure, it can be firmed that the Geman&McClure specification is fix to be optimized at 1050-1250 for normal images and the Geman&McClure specification is fix to be optimized at 1400-1600 for image with bountiful boundary, detail and edge information.The global computation substantiation in PSNR is expounded in Table 3 for 35dB Gaussian outlier.The feasible and impressive fallout of the novel elementary spatial expanding scheme approximately matches to classical SISR method nevertheless the simulating calculation of the optimized specification is so readily and rapidly compared with classical SISR method (with three specification).At second, for Gaussian outlier at 30 dB, the vital target of this computation substantiation is the calculation of the optimized specifications which is modified during 0 to 2000 for interpolating the better and higher spatial information images with highest PSNR as expounded in the Figure 4. From this substantiation in this figure, it can be firmed that the Geman&McClure specification is fix to be optimized at 1600-1650 for normal images and  4 for 30 dB Gaussian outlier.The feasible and impressive fallout of the novel elementary spatial expanding scheme approximately matches to classical SISR method nevertheless the simulating calculation of the optimized specification is so readily and rapidly compared with classical SISR method (with three specification).

Conclusion
In this analytic assessing, this analytic article focuses to offer a novel elementary spatial expanding scheme form on SISR method with modifying Geman&McClure function that is conceptually computed from only one specification (T), contrary to three specifications (b, h, k) similar to classical SISR method.By examining on bountiful images, which are debased by copious outlier patterns, in analytical observation section, the impressive fallout of a novel elementary spatial expanding scheme approximately matches to classical SISR method nevertheless the simulating calculation of the optimized specification (which is based on 2x10 3 search points) is so readily and rapidly compared with classical SISR method (which is based on 8x10 9 search points).From these reason, a novel elementary spatial expanding scheme is easily implemented for real works.

1 ,
At first, the recorded low spatial information image ( ( ) 0 , G x y at mn  ) spatially scales down to constructing a class of low spatial information images as ( )

TELKOMNIKAFigure 1 .Figure 2 .
Figure 1.A novel elementary spatial expanding scheme form on SISR method with boundary

Figure 3 .
Figure 3.The computer computation substantiation of the Geman&McClure specification and the feasible fallout of a novel elementary spatial expanding scheme at 35dB Gaussian outlier

TELKOMNIKA
ISSN: 1693-6930 ◼ A novel elementary spatial expanding scheme form on SISR method... (Darun Kesrarat) 2559 the Geman&McClure specification is fix to be optimized at 1900-2000 for image with bountiful boundary, detail and edge information.The global computation substantiation in PSNR is expounded in Table

Figure 4 .
Figure 4.The computer computation substantiation of the Geman&McClure specification and the feasible fallout of a novel elementary spatial expanding scheme at 30dB Gaussian outlier

Table 1 .
The Computer Computation Substantiation

Table 3 .
The Global Computation Substantiation in PSNR of 35dB Gaussian Outlier

Table 4 .
The Global Computation Substantiation in PSNR of 30dB Gaussian Outlier