REST API v3: Filtering assets from JSON input.

I am attempting to use the REST API v3 via Powershell to get a list of all assets in Service Desk. However, I would like to pre-filter this list, since we have well over 2,000 assets listed, most of which are not relevant to my needs. I would like to filter by a specific product name.

Here is how I am currently fetching:

[int]$index = "1"
while (!$check) {
$input = @"
{
"list_info": {
"row_count": 100,
"start_index": $index,
"sort_field": "name",
"sort_order": "desc",
"get_total_count": true,
}
}
}
"@
$header = @{TECHNICIAN_KEY=$ApiKey}
$params = @{input_data=$input;format='json'}
$Uri = $SdpUri + "/api/v3/assets"
$result = Invoke-RestMethod -Method GET -Uri $Uri -Headers $header -Body $params -ContentType "application/x-www-form-urlencoded"
if ($result) {
$result.assets | Select-Object name,@{n="Product";e={$_.product.name}},@{n="User";e={$_.user.name}} | Where-Object {$_.product -like "*7070*"}
$index = $index+100
}
Else {
$check = $true
Write-Host "Ending run"
break
}
}

This relies on post-processing the data to get what I want, which is extremely time consuming and resource intensive.

is there a way that I can add an option to to the JSON input pre-filter to get only the computer assets that I want based on model? The property name on the Powershell output is Product.Name.