Sensitivity of color LMMSE restoration of images to the spectral estimate

Multichannel restoration with limited a priori information [electron microscopy of biological macromolecules]

“…By consistency we mean that if the output portion (the nonnoise related portion of the output) were fed back into the input of the system, then we would obtain the same idealized noise-free values [cf. (1)] that were obtained when the input was . At this point the only constraint that we have placed upon our system is that it must be a projection operator.…”

“…Mathematically, the recording process for an -channel system can be represented by (1) where is the recorded data for channel are idealized noise-free recorded values, is signal independent additive noise, is the continuous input, and is the impulse response in the th channel. Note that in practice the only information available is and .…”

“…Due to the significant amount of noise in electron micrographs, it is necessary in practice to use regularization in estimating (e.g. windowing or parametric methods [1]). Methods discussed in [16] may be of particular significance for this problem.…”

“…M ULTICHANNEL restoration problems occur in many image processing applications including color imaging, electron microscopy, and remote sensing [1]- [4]. Classically, the restoration problem is framed in the discrete domain which constrains the signals to be bandlimited.…”

“…Statistical multichannel deconvolution approaches such as Wiener filtering [2], [9], or Bayesian methods [10], [11] require prior information about the input signal, which may be difficult to obtain in practice, especially in a case such as electron microscopy in which a prototype image is not available. Without the correct signal statistics, the use of statistical methods can result in a distorted signal estimate [1], [11], [12]. In addition, the exact amount of noise reduction achieved in the postprocessing must be known for the statistical methods if significant smoothing is to be avoided.…”