# Error Resilience for Block Compressed Sensing with Multiple-Channel Transmission
## 1 Introduction  
Data compression has long been an important topic in the field of signal processing. With the broad use of smartphone and tablet cameras, vast amounts of multimedia content, mostly images, have accumulated. Thus, how a mechanism for efficiently performing data compression on the multimedia contents is urgent. There have been successful and popular standards for image compression including the well-known JPEG, which employs discrete cosine transform (DCT), and JPEG2000, which applies discrete wavelet transform (DWT), to still images. With the evolution of new techniques, advancements in data compression can also be expected, and compressed sensing techniques present new and novel concepts.  
Compressed sensing (CS) is one recently developed technique of lossy data compression research and applications [1; 2; 3; 4]. In addition to international standards in multimedia compression, such as JPEG [5] or JPEG2000 [6], it would be constructive to explore new innovative compression techniques. The major research looking at JPEG, JPEG2000, and CS focuses on compression performance by balancing the amount of compressed data and the reconstructed quality. In CS, this requires a sampling rate that is far less than the Nyquist rate and has the ability to reconstruct the original signal of lossy compression. The primary goal in compressed sensing research is the compression capability. Therefore, a method for effectively decoding the extremely small amount of compressed signals and comparing this to counterparts in JPEG or JPEG2000 would be of great interest and is currently a major challenge [7; 8; 9]. In this paper, in addition to looking at compression performance, we consider practical scenarios of robust transmission of compressed sensing signals using block compressed sensing(BCS) [10; 11; 12]. We transmitted compressed signals over lossy channels to observe the effect of packet losses. To reduce quality degradation of robust transmission [13; 14; 15], we employed the transmission of BCS signals over multiple independent channels. Multiple description coding (MDC) [16; 17] was employed to protect and reconstruct the BCS signals. To better explore the performance of BCS, we used adaptive sampling [18; 19]. This way, the enhanced quality of the reconstructed image can be observed for error controlled transmission. Therefore, the novelty of this paper is the error resilient transmission of BCS with MDC. We observed enhanced performance using our algorithm.  
This paper is organized as follows. In Section 2 we briefly describe the fundamentals and mathematical representations of BCS. In Section 3 we present the proposed method for error resilient transmission of compressed sensing signals over multiple independent and lossy channels. The simulation results are demonstrated in Section 4. Here we point out the vulnerability of compressively sensed signals transmitted over a single channel and how our algorithm for multiple-channel transmission for grey-level and color images reduced image quality degradation. Finally, we address the conclusion of this paper in Section 5.