Graph-Cut-based Compression Algorithm for Compressed-Sensed Image Acquisition Julide Gulen Alaydin Seden Hazal Gulen Cankaya University Eskisehir Yolu 29.km Yenimahalle Ankara 06810, Turkiye {julidegulen, s.hazalgulen}@gmail.com Maria Trocan Institut Superieur d’Electronique de Paris 28 rue NdC, Paris 75006, France Email: maria.trocan@isep.fr Behcet Ugur Toreyin Cankaya University Eskisehir Yolu 29.km Yenimahalle Ankara 06810, Turkiye Email: toreyin@cankaya.edu.tr Abstract—The purpose of the paper is to find the best quantizer allocation for compressed-sensed acquired images, by using a graph-cut quantizer allocation method. The compressed sensed acquisition is realized in a block-based manner, using a random projection matrix, and on the obtained block measurements a graph-cut-based quantizer allocation method is applied, in order to further reduce the bitrate associated to the measurements. Finally, the quantized measurements are reconstructed using a Smooth Projected Landweber recovery method. The proposed compression method for compressed sensed acquisition shows better results when compared to JPEG2000. I. Introduction Images in today’s era of digital media have become the creative convergence of human expression, communication, social interaction, education and promotion of digital arts. The problem that we face today is with their transmission i.e., they generally occupy much more space in a hard disk, or bandwidth in a transmission system, than their proverbial counterpart, thus compression of an image becomes necessary to reduce storage and transmission resources and to avoid data redundancy. Nowadays many compression techniques are presented like JPEG, JPEG2000 etc.to compress images efficiently. In this paper, we will compare the proposed method with JPEG2000 which has some disadvantages. For instance, it produces ringing artifacts within the image, and it is not adapted for noisy signals, as the compressed-sensed acquired images can be seen. The proposed method which we will present below gives visually better results and better compres- sion ratio when it is compared with JPEG2000. In addition to this, it reduces cost and power consumption by using fewer sensors than what is used in traditional acquisition methods. As it is known, Nyquist-Shannon sampling theory has a big role in signal processing area. It says that the number of samples necessary to reconstruct a signal without error is determined by its bandwidth, and the number of samples should be half of the bandwidth to prevent data loss. However, an alternative theory Compressed Sensing (CS) is presented in recent years by f D. Donoho, E. Candes, T. Tao and J. Romberg [1][2][9][11] which shows that signals and images can be reconstructed from fewer data than it is considered necessary in Nyquist-Shannon sampling theory, by compressing and sampling data simultaneously. It says that the entire process of acquiring the full signal, computing all the transform coefficients, encoding the largest coefficients and discarding all the others and then applying compression is unnecessary, exerts much power and wastes time. Because of all these disadvantages, it is not economic. Therefore, sampling and compressing data simultaneously makes more sense. However, most of the studies in Compressed Sensing remain at the theoretical level and it is realized that compressed sensing is not suitable for real-time sensing of images because the measurement process requires access to the entire signal at once [2][3]. Thus, L. Gan developed an alternative method called Block Compressed Sensing [4] where the original image is divided into small blocks and each block is sampled independently using the same measurement operator. Since each block is processed independently, the initial solution can be easily obtained and the reconstruction process can be considerably accelerated. As it is mentioned above, reducing the storage is substantial in digital media. In order to do this each pixel is labeled before they are stored. If the pixels of images have near or same values, then they get the same label quantity. The task of assigning a minimum and appropriate number of labels to the pixels of an image, in order to compress efficiently, is a challenge in the image compression area. Thus, in order to find a better solution to the labeling problem, a Graph- Cut minimization algorithm is developed and proposed by Y. Boykov and O. Veksler [5]. The Graph-Cut algorithm can also be employed in another areas like image segmentation, motion estimation, etc., in a flexible manner, the challenging part being the definition of the energies (or costs) to be minimized within the graph. In this work we will use the algorithm in [5] for the minimization of the quantization noise. In our paper, we employ Compressed Sensing technique for image acquisition and the graph-cut based quantization cost minimization on the compressed-sensed measurements in order to further reduce the transmission cost, avoid redundant operations and get better compression results. At first, original image is divided into B × B blocks and sampled using a random projection matrix. Then, a graph-cut based quantizer 13