The DLBL method is operated and tested using a set of images, until the effectiveness is verified. The experimental results of the proposed algorithms are variously compared with those of the D-AMP [8] algorithm, ReconNet algorithm [21], TVAL3 algorithm [10], DR2-Net algorithm [11], and RNDWT algorithm [12].

Before presenting and discussing the results, a brief description of the database is presented in “Data set description” section. Also, the main criteria to evaluate the performance of the proposed method are presented in “Measurement parameters” section.

### Data set description

The data set here is represented as a set of images. These images were collected from various sources: first one—COCO2014 data set, Barbara and fingerprint, as shown in Fig. 7a, b, respectively. The secondary images, video images, were collected from underground projects, coal cutter and tunnel boring machine shown in Fig. 7c and d, respectively [22].

### Measurement parameters

To evaluate quality of recovered images using two image quality matrices: peak-signal-to-noise ratio PSNR and structural similarity index measure (SSIM) [23]. The PSNR is used as a quantitative evaluation, defined by Eq. 8 [24].

$${\text{PSNR}}\left( {x,\hat{x}} \right) = 10 \log \frac{{d^{2} }}{{{\text{MSE}}\left( {x,\hat{x}} \right)}}$$

(8)

where *d* is the highest scale value of the 8-bits greyscale. The PSNR results from the calculation of the mean square error (MSE) of an image, as defined by Eq. 9 [24].

$${\text{MSE}}\left( {x,\hat{x}} \right) = \frac{1}{MN}\mathop \sum \limits_{i = 1}^{M} \mathop \sum \limits_{j = 1}^{N} \left( {x - \hat{x}} \right)^{2}$$

(9)

The MSE approaches zero, and accordingly, PSNR value approaches infinity. Hence, low PSNR means low imagequality which implies high mathematical differences between images, which means reconstructed image have low quality value. On the contrary, a high value of PSNR indicates the presence of low mathematical discrepancies between the images, this indicates the high quality. PSNR is uncomplicated to compute, has clear materialistic meaning, and is mathematical advantageous regarding enhancement. Yet, it experiences an absence of articulation in the visual quality [23, 25].

Whereas SSIM is a good representation for visual quality evaluation, to quantify the closeness between images, SSIM as defined by Eq. 10 depends on three parameters for calculations mainly: loss of correlation, luminance distortion, and contrast distortion as shown in Eqs. 11–13 [26].

$${\text{SSIM}}\left( {x,\hat{x}} \right) = I\left( {x,\hat{x}} \right) \cdot C\left( {x,\hat{x}} \right) \cdot S\left( {x,\hat{x}} \right)$$

(10)

$$I\left( {x,\hat{x}} \right) = \left( {\frac{{2\mu_{x} \mu_{{\hat{x}}} + C_{1} }}{{\mu_{x}^{2} + \mu_{{\hat{x}}}^{2} + C_{1} }}} \right)$$

(11)

$$C\left( {x,\hat{x}} \right) = \left( {\frac{{2\sigma_{x} \sigma_{{\hat{x}}} + C_{2} }}{{\sigma_{x}^{2} + \sigma_{{\hat{x}}}^{2} + C_{2} }}} \right)$$

(12)

$$S\left( {x,\hat{x}} \right) = \left( {\frac{{\sigma_{{x\hat{x}}} + C_{3} }}{{\sigma_{x} \sigma_{{\hat{x}}} + C_{3} }}} \right)$$

(13)

I in Eq. 11 is the comparison function, which estimates the level of similarity between the mean luminance \(\left( {\mu_{x} \;{\text{and}}\;\mu_{{\hat{x}}} } \right)\) for two different images. The maximum value of I equals to one at \(\mu_{x} = \mu_{{\hat{x}}}\). Here C is defined by Eq. 12 which is the contrast comparison function. This term measures the closeness of the contrast between the two images by using the standard luminance deviation \(\sigma_{x} \;{\text{and}}\;\sigma_{{\hat{x}}}\). The maximum value of C equals to one if \(\sigma_{x} = \sigma_{{\hat{x}}}\). Last term S in Eq. 13 is indicating the structure comparison function responsible for computing the covariance between the two images x and x^, where \(\sigma_{{x\hat{x}}}\) is the covariance between x and x^. The value of SSIM is between 0 and 1. If SSIM value equals one that means the two images are identical where zero value means no correlation between images. The positive constants C1, C2, and C3 are utilized to prevent an invalid denominator.