VP5-VP19C particles were purified from cells infected with recombinant baculoviruses expressing only VP5 and VP19C as described previously .
The ice-embedded VP5-VP19C particles were imaged with flood beam illumination. Microscope alignment, specimen assessment, and focusing were performed using a Gatan (Pleasanton, CA) 1 k × 1 k slow-scan charge-coupled device camera . All micrographs were recorded at a magnification of 30,000× on Kodak SO163 film in a JEOL4000 electron cryomicroscope operating at 400 kV using a LaB6 filament, under minimal dose conditions (~7 electrons/Å2).
Image digitization and selection
Forty selected micrographs were digitized on a Zeiss SCAI scanner (Carl Zeiss, Englewood, Colorado) at a step size of 4.67Å/pixel. 1300 particle images (240 × 240 pixels) were selected automatically . The image quality was assessed by evaluating the contrast transfer function rings visualized in the incoherently averaged Fourier transforms of particle images . 700 particles from these micrographs with the first zeros of their contrast transfer functions between 1/20 - 1/24 Å-1 were used for further analysis.
Most of the subsequent computational steps were performed using IMAGIC-5 software  on an SGI (Silicon Graphics, Inc) Onyx2 supercomputer with 24 parallel processors.
Wavelet Bases Choice
An investigation to choose the best wavelet bases for electron cryomicroscopic images was performed. During this study, simulated and real electron cryomicroscopy images were used. Testing of the majority of the wavelet basis [17, 21–24] existing in Matlab-5 software, has been made. The criterion used to determine the best wavelet base is one which optimizes the signal-to-noise ratio in a broad spectrum of spatial frequencies. The biorthogonal wavelets basis [25, 26] especially the 3.5 basis in Matlab has yielded the best average signal-to-noise ratio in the range of the spatial frequency (1/100 - 1/8 Å-1) relevant to our data analysis.
In diverse fields from planetary science to molecular spectroscopy, scientists are faced with the problem of recovering a true signal from incomplete or noisy data. Wavelets help to solve this problem through a technique called wavelet shrinkage and thresholding methods  and multi-resolution by contrast modification filtering method .
Wavelet decomposition has the power to separate the signal into low-resolution information (approximation) and high resolution information (details). The high-resolution information contains the details of the image and the noise. The characteristic of the noise is randomly distributed in the image and does not have any structured information like (edges, contours, segment in horizontal, vertical or diagonal directions), the wavelets filters strengthen the structured information, all other components are down weighted, mainly the noise which has a random distribution in the object. This means that the high amplitude of gray values in the histogram of each component are mainly "details" [27, 28] of the object, and the values close to zero are mainly due to the contribution of the noise. In other words, if the details are small they might be omitted without substantially affecting the main feature of the data set. The idea of thresholding then is to set to zero all coefficients less than a particular threshold. The histograms of the details components are used to set the threshold in each component in order to reduce that noise. Once those values are removed it means that those pixels will be dumped to zeros and will not contribute to the reconstructed image. In a multi-resolution processing  method the approximation component is used as the filtered image. The approximated image is smaller in size, which helps to accelerate the processing, but lower in resolution because all the details and noise have been removed from the image. The level of reduction of the original image, depends on the application, and on the resolution required. The following section describes the use of the multi-resolution processing for the 3D reconstruction of VP5-VP19C.
3D Reconstruction of VP5-VP19C
Wavelets filtering and classification
In order to determine the orientation of the particles accurately, two pre-processing steps are commonly used in order to enhance the signal-to-noise ratio of the particle. First is filtering of individual particle. The second step is the classification, which consists on grouping the particles having similar orientation in one class, and then averages them, to get a further noise reduction and restoration of some flexible part of the particle. This classification is obtained by MSA procedure in IMAGIC-5 software . This step generally gives much better improvement of the signal-to-noise ratio of the particle, which helps the orientation determination algorithms to be more accurate. The accuracy of the classification process is noise dependent. For close-to-focus data (highly noisy data) a better filtering is needed before classification of particles into different groups. A wavelet filtering is proposed as an alternative to the Fourier Gaussian filter, to be used before classification when the noise level is very high.
During this step, the average particles of the approximation components of wavelet decomposition (using biorthogonal filters) were used. Figure 2-b shows a wavelet approximation of figure 2-a. For comparison purpose, the Fourier-filtered version having the same sub-sampling (factor two in each direction) is shown in figure 2-c. The angular reconstitution method  was used to assign Euler angles to each class average. Then a 3D reconstruction was calculated using the exact-filter back-projection algorithm . The orientations of individual particles were initially assigned as those of the class averages to which they belonged. They were then iteratively refined using projections computed from the preliminary reconstruction. The resolution of the model obtained from the wavelet approximation images is very low (37 Å).
The low-resolution model of the VP5-VP19C particles did not make use of all the information inherent in our raw image data. Therefore, the final map was reconstructed from the original VP5-VP19C particle images without wavelet approximation and class averaging . First, the low-resolution model was scaled up to the same dimension as the original image (240 × 240). A wavelet filtering using the thresholding technique was applied to the original data, a threshold of one standard deviation was chosen as trade-off between detail retention, and noise suppression. Initial orientation for original size images were assigned from the approximation components. Projections were computed from the scaled model to refine the Euler angles for each of the particle images using the angular reconstitution technique. Consequently, an improved 3D reconstruction was computed and used for further angles and centre refinement. This reconstruction-refinement procedure was iterated for several rounds until no further significant improvement was obtained.