The JPEG image compression standard is very sensitive to errors. Even though it contains error resilience features, it cannot easily cope with induced errors from computer soft faults prevalent in remote-sensing applications. Hence, new fault tolerance detection methods are developed to sense the soft errors in major parts of the system while also protecting data across the boundaries where data flow from one subsystem to the other. The design goal is to guarantee no compressed or decompressed data contain computer-induced errors without detection. Detection methods are expressed at the algorithm level so that a wide range of hardware and software implementation techniques can be covered by the fault tolerance procedures while still maintaining the JPEG output format. The major subsystems to be addressed are the discrete cosine transform, quantizer, entropy coding, and packet assembly. Each error detection method is determined by the data representations within the subsystem or across the boundaries. They vary from real number parities in the DCT to bit-level residue codes in the quantizer, cyclic redundancy check parities for entropy coding, and packet assembly. The simulation results verify detection performances even across boundaries while also examining roundoff noise effects in detecting computer-induced errors in processing steps.

The JPEG 2000 image compression standard is designed for a broad range of data compression applications. The new standard is based on wavelet technology and layered coding in order to provide a rich feature compressed image stream. The implementations of the JPEG 2000 codec are susceptible to computer-induced soft errors. One situation requiring fault tolerance is remote-sensing satellites, where high energy particles and radiation produce single event upsets corrupting the highly susceptible data compression operations. This paper develops fault tolerance error-detecting capabilities for the major subsystems that constitute a JPEG 2000 standard. The nature of the subsystem dictates the realistic fault model where some parts have numerical error impacts whereas others are properly modeled using bit-level variables. The critical operations of subunits such as discrete wavelet transform (DWT) and quantization are protected against numerical errors. Concurrent error detection techniques are applied to accommodate the data type and numerical operations in each processing unit. On the other hand, the embedded block coding with optimal truncation (EBCOT) system and the bitstream formation unit are protected against soft-error effects using binary decision variables and cyclic redundancy check (CRC) parity values, respectively. The techniques achieve excellent error-detecting capability at only a slight increase in complexity. The design strategies have been tested using Matlab programs and simulation results are presented.

Wavelet transforms are the central to many applications in image processing and data compression. They have banks of multirate filters that are difficult to protect from computer-induced numerical errors. An efficient algorithm-based fault tolerance approach is proposed for detecting arithmetic errors in the output data. Concurrent weighted parity values are designed to detect the effects of a single numerical error within the transform structure. The parity calculations use weighted sums of data, where the input parity weighting is related to the weighting used on the output data. Each parity computation is properly viewed as an inner product between weighting values and the data motivating the use of dual space functionals related to the error gain matrices that describe error propagations to the output. The parity weighting values are defined by a combination of dual space functionals. An iterative procedure for evaluating the design of the parity weights has been incorporated in Matlab code.

Wavelet transforms, central to multiresolution signal analysis and important in the JPEG2000 image compression standard, are quite susceptible to computer-induced errors because of their pipelined structure and multirate processing requirements. Such errors emanate from computer hardware, software bugs, or radiation effects from the surrounding environment. Implementations use lifting schemes, which employ update and prediction estimation stages, and can spread a single numerical error caused by failures to many output transform coefficients without any features to warn data users. We propose an efficient method to detect the arithmetic errors using weighted sums of the wavelet coefficients at the output compared with an equivalent parity value derived from the input data. Two parity values may straddle a complete multistage transform or several values may be used, each pair covering a single stage. There is greater error-detecting capability at only a slight increase in complexity when parity pairs are interspersed between stages. With the parity weighting design scheme, a single error introduced at a lifting section can be detected. The parity computation operation is properly viewed as an inner product between weighting values and the data, motivating the use of dual space functionals related to the error gain matrices. The parity weighting values are generated by a combination of dual space functionals. An iterative procedure for evaluating the design of the parity weights has been incorporated in Matlab code and simulation results are presented.