# Image Forensics Using Non-Reducing Convolutional Neural Network for Consecutive Dual Operators
## 1 Introduction  
Digital images are a victim of manipulation due to the ease of availability of high precision but uncomplicated image editing tools. Image forensics is needed to detect the source, processing history, and genuineness of the image. Numerous methods [1; 2; 3] are provided to find the source device of the image. The mismatch of source assists in image forgery detection as a fake image is created usually by using two or more images. Most of the fake images look realistic by applying multiple spatial operations. The detection of operations such as resampling [4; 5], sharpening [6; 7; 8], and median filtering [9; 10] can make uncovering the image forgery easy. Many universal methods [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21] also exist to detect the image forgery operations simultaneously. However, universal methods can only effectively detect a single operation on an image. In the real scenario, more than one operation is applied to the image in general. In this paper, a sequence of operations can be detected perfectly to unfold the processing history of the image. Few techniques [22; 23; 24; 25; 26] exist that can detect the operations and the order of operations. Although the performance is not consistent according to different operations, JPEG compression has a significant role in the forensic analysis as the most common format. The performance in most of the existing techniques degrades while considering JPEG compression. In the recent era of a deep learning network, a convolutional neural network has given propitious results in many applications. A convolutional neural network (CNN) is utilized in the detection of median filtering, resampling, universal image manipulation, multipleJPEG compression, contrast enhancement, image splicing, etc. [PERSON] et al. [11] discovered that some existing techniques, especially LBP [27] and SRM [28], can effectively detect different types of image operations such as Gaussian filtering, median filtering, image resizing, gamma correction, and compression history. The experiments are performed on large-size images, where the experimental analysis is limited as different compression qualities and filter sizes are combined in one data set. [PERSON] and Stamm [12] introduced the CNN for the detection of additive white Gaussian noise, Gaussian filtering, median filtering, and image resizing for the first time. In particular, a constrained design is applied in the first layer of the proposed CNN. Experimental results are given for 227 \(\times\) 227 image blocks. However, no experimental analysis was given for low resolution and JPEG compressed images. The proposed idea of constraint is further extended with an improved CNN model [13], and JPEG compression is used in the experimental analysis. In the improved CNN architecture, a constrained convolutional layer is followed by four blocks, and each block contains a convolutional layer, batch normalization layer, ReLU layer, and pooling layer. Further, three softmax classification layers are used, and the outputs are classified using an extremely randomized tree classifier. The constrained convolutional layer filters can predict the errors by subtracting the resultant value from the central value of the filter window. The constraint is enforced during the training of each iteration. However, the performance of the improved CNN model falls in the most cases when two operators are applied consecutively on the image even on a large size image. [PERSON] et al. [14] selected some sub-models from SRM by calculating the out-of-bag error. The selection process can reduce the feature dimension noticeably. The results are analyzed for eleven image operations of several categories like spatial filtering, image enhancement, and JPEG compression. The proposed technique also claims good results in the detection of four anti-forensic operations such as JPEG compression, contrast enhancement, resampling, and median filtering. However, the performance degrades for small-size images.