## 1 Introduction  
The majority of digital images are stored in compressed form. Generally, image classification using convolution neural network (CNN) is done in uncompressed form rather than compressed one. Training the CNN in the compressed domain eliminates the requirement for decompression process and results in improved efficiency, minimal storage, and lesser cost. Compressive sensing (CS) is one of the effective and efficient method for signal acquisition and recovery and CNN training on CS measurements makes the entire process compact. The most popular sensing phenomenon used in CS is based on image acquisition using single pixel camera (SPC) which has complex design implementation and usually a matrix simulation is used to represent the SPC process in numerical demonstration. The CS measurements using this phenomenon are visually different from the image and to add this in the training set of the compressed learning framework, there is a need for an inverse SPC process that is to be applied all through the training and testing dataset image samples. In this paper we proposed a simple sensing phenomenon which can be implemented using the image output of a standard digital camera by retaining few pixels and forcing the rest of the pixels to zero and this reduced set of pixels is assumed as CS measurements. This process is modeled by a binary mask application on the image and the resultant image still subjectively legible for human vision and can be used directly in the training dataset. This sensing mask has very few active pixels at arbitrary locations and there is a lot of scope to heuristically learn the sensing mask suitable for the dataset. Only very few attempts had been made to learn the sensing matrix and the sole effect of this learning process on the improvement of CNN model accuracy is not reported. We proposed to have an ablation approach to study how this sensing matrix learning improves the accuracy of the basic CNN architecture. We applied CS for two class image dataset by applying a Primitive Walsh Hadamard (PWH) binary mask function and performed the classification experiment using a basic CNN. By retaining arbitrary amount of pixel in the training and testing dataset we applied CNN on the compressed measurements to perform image classification and studied and reported the model performance in terms of training and validation accuracies by varying the amount of pixels retained. A novel Genetic Algorithm-based compressive learning (GACL) method is proposed to learn the PWH mask to optimize the model training accuracy by using two different crossover techniques. In the experiment conducted for the case of compression ratio (CR) 90% by retaining only 10% of the pixels in every images both in training and testing dataset that represent two classes, the training accuracy is improved from 67% to 85% by using diagonal crossover in offspring creation of GACL. The robustness of the method is examined by applying GACL for user defined multiclass dataset and achieved better CNN model accuracies. This work will bring out the strength of sensing matrix learning which can be integrated with advanced training models to minimize the amount of information that is to be sent to central servers and will be suitable for a typical IoT frame work. **Keywords:** binary sensing matrix; compressive domain; compressive sensing (CS); convolution neural network (CNN); genetic algorithm based compressive learning (GACL); primitive Walsh Hadamard (PWH); single pixel camera (SPC)  
## 1 Introduction  
The Shannon-Nyquist sampling theorem states that the sample rate must be at least twice of the maximum signal frequency and this provides the foundation for signal reconstruction from discrete measurements. In order to be precisely reconstructed in the discrete situation, the number of measurements must be at least equal to the signal length. However, this strategy may necessitate a huge storage space, a long detecting time, lot of power, and a greater number of sensors.